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# Прямая и обратная задачи геофлюидодинамики в приложении к прогнозированию зон АВПД в осадочных бассейнах 1. Теоретический аспект

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```ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ ɜ
ɩɪɢɥɨɠɟɧɢɢ ɤ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɸ ɡɨɧ ȺȼɉȾ ɜ ɨɫɚɞɨɱɧɵɯ
ɛɚɫɫɟɣɧɚɯ
1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɚɫɩɟɤɬ
Ⱥ.Ƚ. Ɇɚɞɚɬɨɜ1, Ⱥ.-ȼ.ɂ. ɋɟɪɟɞɚ2
1
ɇɂɂ Ɇɨɪɝɟɨɮɢɡɢɤɚ
ɋɭɞɨɜɨɞɢɬɟɥɶɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɆȽɌɍ, ɤɚɮɟɞɪɚ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɢ
ɢ ɩɪɨɝɪɚɦɦɧɨɝɨ ɨɛɟɫɩɟɱɟɧɢɹ ɗȼɆ
2
Ⱥɧɧɨɬɚɰɢɹ. Ɋɚɡɪɚɛɚɬɵɜɚɸɬɫɹ ɩɨɫɬɚɧɨɜɤɚ ɢ ɦɟɬɨɞɵ ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ ɢ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ
ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ ɜ ɦɚɫɲɬɚɛɟ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ ɜ ɩɪɢɥɨɠɟɧɢɢ ɤ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɸ ɚɧɨɦɚɥɶɧɨ
ɜɵɫɨɤɢɯ ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ (ȺȼɉȾ). ȼɜɨɞɢɬɫɹ ɛɚɡɢɫ ɱɭɜɫɬɜɢɬɟɥɶɧɵɯ ɤ ɪɚɡɜɢɬɢɸ ȺȼɉȾ ɩɚɪɚɦɟɬɪɨɜ
ɝɟɨɥɨɝɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɪɟɞɵ. ɉɪɹɦɚɹ ɡɚɞɚɱɚ ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ ɫɬɚɜɢɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɷɜɨɥɸɰɢɢ
ɭɩɥɨɬɧɟɧɢɣ, ɍȼ-ɧɚɫɵɳɟɧɢɣ ɢ ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ ɩɪɢ ɩɨɝɪɭɠɟɧɢɢ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɨɛɴɟɦɚ ɩɨɪɢɫɬɨɣ
ɩɨɪɨɞɵ ɜ ɩɪɨɰɟɫɫɟ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ. ȼ ɤɚɱɟɫɬɜɟ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɨɛɪɚɬɧɨɣ
ɡɚɞɚɱɢ (ɢɧɜɟɪɫɢɢ) ɢɫɩɨɥɶɡɭɸɬɫɹ ɢɡɦɟɪɟɧɢɹ ɞɚɜɥɟɧɢɣ, ɩɨɪɢɫɬɨɫɬɟɣ ɢ ɍȼ-ɧɚɫɵɳɟɧɢɣ ɜ ɫɤɜɚɠɢɧɚɯ. ɋ
ɰɟɥɶɸ ɩɨɜɵɲɟɧɢɹ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢ ɨɛɟɫɩɟɱɟɧɢɹ ɟɞɢɧɫɬɜɟɧɧɨɫɬɢ ɢ ɭɫɬɨɣɱɢɜɨɫɬɢ
ɪɟɲɟɧɢɹ ɩɪɨɛɥɟɦɵ ɢɧɜɟɪɫɢɢ ɪɚɡɦɟɪɧɨɫɬɶ ɡɚɞɚɱɢ ɫɜɨɞɢɬɫɹ ɤ ɷɮɮɟɤɬɢɜɧɨɣ 1.5D. Ɉɛɫɭɠɞɚɸɬɫɹ ɱɚɫɬɧɵɟ
ɫɥɭɱɚɢ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɨɞɧɨɪɨɞɧɨɣ ɢ ɦɧɨɝɨɫɥɨɣɧɨɣ ɫɪɟɞɟ. ɉɪɢɜɨɞɹɬɫɹ ɩɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ ɢ
ɨɛɪɚɬɧɨɣ ɡɚɞɚɱ ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ ɜ ɩɪɢɥɨɠɟɧɢɢ ɤ ɩɪɨɝɧɨɡɭ ȺȼɉȾ.
Abstract. In the paper the numerical solutions of the forward and inverse fluid dynamic problems for geological time
scale have been considered in connection to excess pore pressure (EPP) prediction. The set of the most sensitive to
the EPP evolution model parameters has been introduced. The forward problem of the fluid dynamics describes the
compaction, HC-saturation and overpressure evolution vs. time and depth. The corresponding real well data set is
used as an input for the inversion routine. The 1.5D reduction of the 3D inverse problem is developed. Such approach
allows to achieve a more unique and stable inverse problem solution in reasonable computing time. The particular
forward modelings for a homogeneous and layered medium are discussed. Applications of the approach to the EPP
prediction are demonstrated on the practical examples.
1. ȼɜɟɞɟɧɢɟ
ɉɨɧɢɦɚɧɢɟ ɬɚɤɢɯ ɹɜɥɟɧɢɣ ɝɟɨɥɨɝɢɢ ɨɫɚɞɨɱɧɵɯ ɩɨɪɨɞ, ɤɚɤ ɭɩɥɨɬɧɟɧɢɟ, ɝɟɧɟɪɚɰɢɹ ɡɨɧ
ɚɧɨɦɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ ɮɥɸɢɞɨɜ ɢ ɦɢɝɪɚɰɢɹ ɭɝɥɟɜɨɞɨɪɨɞɨɜ (ɍȼ) ɢɡ ɝɟɧɟɪɢɪɭɸɳɢɯ ɬɨɥɳ ɩɨ ɪɚɡɪɟɡɭ
ɩɨɫɬɨɹɧɧɨ ɨɩɟɪɟɠɚɟɬ ɩɨ ɮɭɧɞɚɦɟɧɬɚɥɶɧɨɫɬɢ ɨɩɢɫɚɧɢɹ ɩɨɞɯɨɞɵ ɤ ɢɯ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɸ. Ɂɚ ɩɨɫɥɟɞɧɟɟ
ɞɟɫɹɬɢɥɟɬɢɟ ɝɟɨɥɨɝɢ-ɧɟɮɬɹɧɢɤɢ ɩɨɥɭɱɢɥɢ ɜ ɫɜɨɢ ɪɭɤɢ ɦɨɳɧɵɟ ɢɧɫɬɪɭɦɟɧɬɵ ɛɚɫɫɟɣɧɨɜɨɝɨ
ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɨɫɧɨɜɚɧɧɵɟ ɧɚ ɱɢɫɥɟɧɧɵɯ ɪɟɲɟɧɢɹɯ ɦɧɨɝɨɮɚɡɧɵɯ 3D ɡɚɞɚɱ ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ
(Ɏɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɮɚɤɬɨɪ..., 1989; Ungerer, 1993; Verweij, 1993), ɚ "ɜɨɡ" ɩɪɨɝɧɨɡɨɜ ɢ ɧɵɧɟ ɫɬɨɢɬ ɜ
ɨɛɥɚɫɬɢ ɢɧɠɟɧɟɪɢɢ ɢ ɷɦɩɢɪɢɤɢ.
Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ɩɟɬɪɨɮɢɡɢɤɢ ɞɚɜɧɨ ɭɠɟ ɞɨɤɚɡɚɥɢ (Ⱥɜɱɚɧ ɢ ɞɪ., 1979; Mann, Mackenzie, 1990), ɱɬɨ
ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɢ ɪɚɡɜɢɬɢɟ ɡɨɧ ɚɧɨɦɚɥɶɧɨ ɜɵɫɨɤɢɯ ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ (ȺȼɉȾ) ɜ ɨɫɚɞɨɱɧɵɯ ɩɨɪɨɞɚɯ,
ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɝɥɭɛɢɧɚɯ ɫɜɵɲɟ 2.5-3 ɤɦ, ɭɠɟ ɧɢɤɚɤ ɧɟ ɦɨɠɟɬ ɨɛɴɹɫɧɹɬɶɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɹɜɥɟɧɢɟɦ
ɧɟɞɨɭɩɥɨɬɧɟɧɢɹ. ɇɚɱɢɧɚɹ ɫ ɬɟɦɩɟɪɚɬɭɪ 85-90° (ɝɥɭɛɢɧɵ 2.5-3 ɤɦ), ɫɚɦɨ ɩɨɧɹɬɢɟ "ɭɩɥɨɬɧɟɧɢɟ" ɞɥɹ ɩɨɪɨɞ,
ɩɨɞɜɟɪɝɚɸɳɢɯɫɹ ɚɤɬɢɜɧɨɣ ɰɟɦɟɧɬɚɰɢɢ ɢ ɞɢɚɝɟɧɟɡɭ, ɬɟɪɹɟɬ ɱɢɫɬɨ "ɦɟɯɚɧɢɫɬɢɱɟɫɤɢɣ" ɫɦɵɫɥ, ɬɨ ɟɫɬɶ ɨɧɨ
ɹɜɥɹɟɬɫɹ ɫɤɨɪɟɟ ɫɥɟɞɫɬɜɢɟɦ ɜɬɨɪɢɱɧɵɯ ɞɢɚɝɟɧɟɬɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ, ɱɟɦ ɫɨɛɫɬɜɟɧɧɨ ɩɪɨɰɟɫɫɨɜ
ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɭɩɥɨɬɧɟɧɢɹ ɩɨɪɨɞ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɬɪɟɫɫɚ. Ɍɟɦ ɧɟ ɦɟɧɟɟ, ɦɟɬɨɞɵ ɩɪɨɝɧɨɡɚ ɞɚɜɥɟɧɢɣ ɞɨ ɫɢɯ
ɩɨɪ ɨɫɧɨɜɚɧɵ ɜ ɨɫɧɨɜɧɨɦ ɧɚ ɚɧɚɥɢɡɟ ɨɬɤɥɨɧɟɧɢɣ ɱɭɜɫɬɜɢɬɟɥɶɧɵɯ ɤ ɩɨɪɢɫɬɨɫɬɢ ɩɚɪɚɦɟɬɪɨɜ (ɫɤɨɪɨɫɬɢ,
ɩɥɨɬɧɨɫɬɢ ɢ ɬ.ɩ.) ɨɬ ɥɢɧɢɢ "ɧɨɪɦɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ".
ȼ ɱɟɦ ɩɪɢɱɢɧɚ ɩɨɞɨɛɧɨɝɨ ɤɨɧɫɟɪɜɚɬɢɡɦɚ? ɉɪɢɱɢɧ, ɤɚɤ ɧɚɦ ɤɚɠɟɬɫɹ, ɧɟɫɤɨɥɶɤɨ.
ɉɟɪɜɚɹ – ɬɪɚɞɢɰɢɨɧɧɵɣ ɨɬɪɵɜ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɨɬ ɧɭɠɞ ɩɪɚɤɬɢɤɢ.
89
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ȼɬɨɪɚɹ – ɧɟɤɨɬɨɪɵɣ ɩɟɫɫɢɦɢɡɦ ɩɨ ɨɬɧɨɲɟɧɢɢ ɤ ɜɨɡɦɨɠɧɨɫɬɹɦ ɷɮɮɟɤɬɢɜɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ
ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɯ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ ɢ ɬɹɠɟɥɵɯ ɜ ɜɵɱɢɫɥɢɬɟɥɶɧɨɦ ɚɫɩɟɤɬɟ ɩɨɫɬɚɧɨɜɨɤ
ɩɪɹɦɵɯ ɡɚɞɚɱ ɞɥɹ ɪɟɚɥɶɧɵɯ ɧɭɠɞ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ȺȼɉȾ.
ɇɚɤɨɧɟɰ, ɬɪɟɬɶɹ – ɱɟɬɤɨɟ ɪɚɡɞɟɥɟɧɢɟ ɩɪɢɤɥɚɞɧɵɯ ɡɚɞɚɱ ɩɨ ɧɚɩɪɚɜɥɟɧɢɹɦ, ɝɨɪɚɡɞɨ ɛɨɥɟɟ
ɝɥɭɛɨɤɨɟ, ɱɟɦ ɬɪɟɛɭɟɬɫɹ ɜ ɦɧɨɝɨɞɢɫɰɢɩɥɢɧɚɪɧɨɦ ɩɨɞɯɨɞɟ ɤ ɛɚɫɫɟɣɧɨɜɨɦɭ ɦɨɞɟɥɢɪɨɜɚɧɢɸ (ɢɧɚɱɟ –
ɨɬɫɭɬɫɬɜɢɟ ɫɢɫɬɟɦɧɨɝɨ ɩɨɞɯɨɞɚ, ɧɟɨɛɯɨɞɢɦɨɝɨ ɞɥɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɪɟɲɟɧɢɹ ɩɨɞɨɛɧɵɯ ɡɚɞɚɱ). Ɍɚɤɢɦ
ɨɛɪɚɡɨɦ, ɩɪɚɤɬɢɱɟɫɤɢ ɚɧɚɥɢɡɨɦ ɞɚɧɧɵɯ ɨ ɩɟɪɜɢɱɧɨɣ ɦɢɝɪɚɰɢɢ ɍȼ ɡɚɧɢɦɚɸɬɫɹ ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ
ɝɟɨɯɢɦɢɤɢ-ɧɟɮɬɹɧɢɤɢ, ɚ ɩɪɨɝɧɨɡ ȺȼɉȾ – ɭɞɟɥ ɛɭɪɨɜɢɤɨɜ. Ɍɟɨɪɟɬɢɱɟɫɤɢɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɪɢ ɷɬɨɦ
ɩɨɫɜɹɳɟɧɵ ɜ ɨɫɧɨɜɧɨɦ ɩɪɨɛɥɟɦɚɦ ɛɚɫɫɟɣɧɨɜɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɢ ɩɪɚɤɬɢɱɟɫɤɢɟ ɚɫɩɟɤɬɵ
ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ȺȼɉȾ ɧɟ ɨɛɟɫɩɟɱɢɜɚɸɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɧɢɤɬɨ ɧɢɤɨɝɨ ɧɟ ɩɨɧɢɦɚɟɬ.
Ɇɟɠɞɭ ɬɟɦ ɨɛɳɚɹ ɬɨɱɤɚ ɩɪɢɥɨɠɟɧɢɹ ɢɧɬɟɪɟɫɨɜ ɬɟɨɪɟɬɢɤɨɜ ɢ ɩɪɚɤɬɢɤɨɜ ɜ ɧɟɮɬɹɧɨɣ ɝɟɨɥɨɝɢɢ
ɟɫɬɶ, ɢ ɥɟɠɢɬ ɨɧɚ ɜ ɩɨɫɬɚɧɨɜɤɟ ɢ ɪɟɲɟɧɢɢ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɛɚɫɫɟɣɧɨɜɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ.
ɇɚ ɫɚɦɨɦ ɞɟɥɟ ɛɨɥɶɲɢɧɫɬɜɨ ɩɨɥɭɷɦɩɢɪɢɱɟɫɤɢɯ ɫɩɨɫɨɛɨɜ ɩɪɨɝɧɨɡɚ ɭɩɥɨɬɧɟɧɢɹ, ɝɟɧɟɪɚɰɢɢ ɡɨɧ
ɚɧɨɦɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ ɮɥɸɢɞɨɜ ɢ ɧɟɮɬɟɝɚɡɨɜɨɝɨ ɧɚɫɵɳɟɧɢɹ ɤɨɥɥɟɤɬɨɪɨɜ ɟɫɬɶ ɧɟ ɱɬɨ ɢɧɨɟ, ɤɚɤ ɢɧɬɭɢɬɢɜɧɚɹ
ɢɧɜɟɪɫɢɹ ɜ ɪɚɦɤɚɯ ɱɚɫɬɧɵɯ ɦɨɞɟɥɟɣ. ɇɚɩɪɢɦɟɪ, ɤɥɚɫɫɢɱɟɫɤɢɟ ɫɩɨɫɨɛɵ ɩɪɨɝɧɨɡɚ ȺȼɉȾ, ɬɚɤɢɟ, ɤɚɤ ɦɟɬɨɞ
ɷɤɜɢɜɚɥɟɧɬɧɵɯ ɝɥɭɛɢɧ ɢɥɢ ɦɟɬɨɞ ɂɬɨɧɚ (Mouchet, Mitchell, 1989), ɨɛɪɚɳɚɸɬ ɞɚɧɧɵɟ, ɱɭɜɫɬɜɢɬɟɥɶɧɵɟ ɤ
ɩɨɪɢɫɬɨɫɬɢ, ɧɚ ɲɤɚɥɭ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ. Ȼɚɡɢɪɭɹɫɶ ɧɚ ɩɪɨɫɬɟɣɲɟɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɞɟɥɢ
ɭɩɥɨɬɧɟɧɢɹ ɨɫɚɞɤɨɜ (Magara, 1978), ɩɪɟɞɥɨɠɟɧɧɨɣ Ɍɟɪɰɚɝɢ ɟɳɟ ɜ 1924 ɝ., ɬɚɤɚɹ ɢɧɜɟɪɫɢɹ ɨɛɟɫɩɟɱɢɜɚɟɬ
ɟɞɢɧɫɬɜɟɧɧɨɫɬɶ ɢ ɭɫɬɨɣɱɢɜɨɫɬɶ ɪɟɲɟɧɢɹ. ɇɨ, ɤ ɫɨɠɚɥɟɧɢɸ, ɜ ɫɢɥɭ ɬɟɯ ɠɟ ɩɪɢɱɢɧ ɨɧɚ ɦɨɠɟɬ ɩɪɢɜɨɞɢɬɶ ɤ
ɫɨɜɟɪɲɟɧɧɨ ɨɲɢɛɨɱɧɵɦ ɪɟɡɭɥɶɬɚɬɚɦ, ɬɟɦ ɛɨɥɟɟ ɝɪɭɛɵɦ, ɱɟɦ ɫɥɨɠɧɟɟ ɢɫɬɨɪɢɹ ɪɚɡɜɢɬɢɹ ɢ ɪɚɡɧɨɨɛɪɚɡɢɟ
ɥɢɬɨɥɨɝɢɣ ɢɡɭɱɚɟɦɨɝɨ ɪɚɡɪɟɡɚ. ɍɬɨɱɧɢɬɶ ɠɟ ɪɟɲɟɧɢɟ ɡɚ ɫɱɟɬ ɩɪɢɜɥɟɱɟɧɢɹ ɞɪɭɝɢɯ ɞɚɧɧɵɯ ɧɟɜɨɡɦɨɠɧɨ,
ɩɨɫɤɨɥɶɤɭ ɩɪɨɫɬɚɹ ɦɨɞɟɥɶ ɭɩɥɨɬɧɟɧɢɹ ɧɟ ɜɤɥɸɱɚɟɬ ɛɨɥɟɟ ɫɥɨɠɧɵɟ, ɧɨ ɧɟ ɦɟɧɟɟ ɡɧɚɱɢɦɵɟ ɮɟɧɨɦɟɧɵ
ɦɢɝɪɚɰɢɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɜ ɩɪɨɰɟɫɫɟ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ.
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɜ ɪɚɛɨɬɚɯ (Lurch, 1991; Zhao, Lurch, 1993; Yu et al., 1995) ɭɠɟ ɫɮɨɪɦɭɥɢɪɨɜɚɧɵ
ɨɫɧɨɜɧɵɟ ɩɪɢɧɰɢɩɵ ɢ ɩɨɞɯɨɞɵ ɤ ɢɧɜɟɪɫɢɢ ɞɚɧɧɵɯ ɨ ɩɨɪɢɫɬɨɫɬɢ, ȺȼɉȾ ɢ ɡɪɟɥɨɫɬɢ ɍȼ-ɝɟɧɟɪɢɪɭɸɳɢɯ ɬɨɥɳ
ɜ ɨɛɥɚɫɬɶ ɩɚɪɚɦɟɬɪɨɜ, ɭɩɪɚɜɥɹɸɳɢɯ ɞɢɧɚɦɢɤɨɣ ɷɜɨɥɸɰɢɨɧɧɵɯ ɦɨɞɟɥɟɣ ɭɩɥɨɬɧɟɧɢɹ – ɍȼ-ɝɟɧɟɪɚɰɢɢ –
ɫɜɟɪɯɝɢɞɪɨɫɬɚɬɢɱɟɫɤɢɯ ɞɚɜɥɟɧɢɣ. Ɉɞɧɚɤɨ, ɛɭɞɭɱɢ ɩɢɨɧɟɪɫɤɢɦɢ, ɞɚɧɧɵɟ ɪɚɛɨɬɵ, ɧɚ ɧɚɲ ɜɡɝɥɹɞ, ɧɟ
ɩɪɨɪɚɛɨɬɚɧɵ ɞɨɫɬɚɬɨɱɧɨ ɝɥɭɛɨɤɨ ɜ ɬɟɨɪɟɬɢɱɟɫɤɨɦ ɩɥɚɧɟ ɢ ɫ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɞɥɹ ɪɟɚɥɶɧɨɣ
ɢɧɬɟɝɪɚɰɢɢ ɢɯ ɜ ɩɪɚɤɬɢɤɭ ɩɪɨɝɧɨɡɨɜ ȺȼɉȾ ɨɧɢ ɧɟ ɝɨɬɨɜɵ.
ɇɚɫɬɨɹɳɚɹ ɪɚɛɨɬɚ ɩɨɫɜɹɳɟɧɚ ɨɩɢɫɚɧɢɸ ɪɟɡɭɥɶɬɚɬɨɜ ɢɫɫɥɟɞɨɜɚɧɢɣ ɚɜɬɨɪɨɜ ɜ ɨɛɥɚɫɬɢ ɫɨɡɞɚɧɢɹ
ɩɪɚɤɬɢɱɟɫɤɢ ɩɪɢɦɟɧɢɦɨɣ ɦɟɬɨɞɢɤɢ ɩɪɨɝɧɨɡɚ ɫɜɟɪɯɝɢɞɪɨɫɬɚɬɢɱɟɫɤɢɯ ɞɚɜɥɟɧɢɣ ɢ ɫɜɹɡɚɧɧɵɯ ɫ ɷɬɢɦ
ɹɜɥɟɧɢɟɦ ɭɩɥɨɬɧɟɧɢɣ ɢ ɍȼ-ɝɟɧɟɪɢɪɭɸɳɟɝɨ ɩɨɬɟɧɰɢɚɥɚ ɪɚɡɪɟɡɚ, ɨɫɧɨɜɚɧɧɨɣ ɧɚ ɩɨɫɬɚɧɨɜɤɟ ɢ ɪɟɲɟɧɢɢ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɭɩɨɦɹɧɭɬɵɯ ɜɵɲɟ ɪɚɛɨɬ, ɞɚɧɧɚɹ ɪɚɛɨɬɚ ɞɨɜɟɞɟɧɚ ɞɨ
ɭɪɨɜɧɹ ɚɩɪɨɛɢɪɨɜɚɧɧɨɣ ɢ ɩɪɢɡɧɚɧɧɨɣ ɬɟɯɧɨɥɨɝɢɢ.
Ɉɫɧɨɜɧɨɣ ɚɤɰɟɧɬ ɜ ɢɡɥɨɠɟɧɢɢ ɫɞɟɥɚɧ ɧɚ ɞɨɫɬɚɬɨɱɧɨ ɫɬɪɨɝɨɦ ɢ ɞɟɬɚɥɶɧɨɦ ɪɚɫɫɦɨɬɪɟɧɢɢ
ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɨɫɧɨɜ ɩɪɟɞɥɚɝɚɟɦɨɝɨ ɩɨɞɯɨɞɚ ɢ ɨɛɫɭɠɞɟɧɢɢ ɟɝɨ ɨɫɧɨɜɧɵɯ ɩɪɢɧɰɢɩɨɜ.
2. Ʉɚɥɢɛɪɨɜɤɚ ɛɚɫɫɟɣɧɨɜɨɣ ɦɨɞɟɥɢ ɧɚ ɨɫɧɨɜɟ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɫɢɧɬɟɬɢɱɟɫɤɢɯ ɢ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ.
Ɉɛɳɚɹ ɫɯɟɦɚ
ɗɜɨɥɸɰɢɨɧɧɚɹ ɦɨɞɟɥɶ ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ ɮɥɸɢɞɨɜ ɞɚɠɟ ɜ ɨɞɧɨɦɟɪɧɨɦ ɫɥɭɱɚɟ ɨɩɢɫɵɜɚɟɬɫɹ
ɫɢɫɬɟɦɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɜ ɱɚɫɬɧɵɯ ɩɪɨɢɡɜɨɞɧɵɯ (ɫɦ. ɧɢɠɟ). Ⱥɧɚɥɢɬɢɱɟɫɤɢɟ ɪɟɲɟɧɢɹ
ɩɨɞɨɛɧɨɣ ɡɚɞɚɱɢ ɫɬɪɨɹɬɫɹ ɧɚ ɚɫɢɦɩɬɨɬɢɱɟɫɤɢɯ ɪɟɲɟɧɢɹɯ, ɫɩɪɚɜɟɞɥɢɜɵɯ ɜ ɜɟɫɶɦɚ ɭɡɤɢɯ ɨɤɪɟɫɬɧɨɫɬɹɯ
ɬɨɥɶɤɨ ɞɥɹ ɩɪɨɫɬɟɣɲɢɯ, ɞɚɥɟɤɢɯ ɨɬ ɪɟɚɥɶɧɨɫɬɢ ɦɨɞɟɥɟɣ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ. ȼɜɟɞɟɧɢɟ ɜ ɪɚɫɫɦɨɬɪɟɧɢɟ ɧɟ
ɨɞɧɨɣ, ɚ ɧɟɫɤɨɥɶɤɢɯ ɮɨɪɦɚɰɢɣ, ɨɬɥɢɱɚɸɳɢɯɫɹ ɡɚɤɨɧɚɦɢ ɭɩɥɨɬɧɟɧɢɹ, ɮɢɡɢɱɟɫɤɢɦɢ ɫɜɨɣɫɬɜɚɦɢ ɢ
ɜɪɟɦɟɧɟɦ ɧɚɤɚɩɥɢɜɚɧɢɹ, ɩɪɢɜɨɞɢɬ ɤ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɪɢɦɟɧɟɧɢɹ ɞɥɹ ɪɟɲɟɧɢɹ ɱɢɫɥɟɧɧɵɯ ɦɟɬɨɞɨɜ.
ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɟɦ ɢɥɢ ɢɧɵɦ ɦɨɞɟɥɹɦ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɨɩɟɪɚɬɨɪɵ, ɤɚɤ ɩɪɚɜɢɥɨ,
ɹɜɥɹɸɬɫɹ ɧɟɥɢɧɟɣɧɵɦɢ ɜ ɨɛɥɚɫɬɢ ɢɡɦɟɧɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ – ɩɚɪɚɦɟɬɪɨɜ ɮɨɪɦɚɰɢɣ, ɚ ɪɟɲɟɧɢɹ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɨɛɪɚɬɧɵɯ ɡɚɞɚɱ ɧɟɟɞɢɧɫɬɜɟɧɧɵ. ɋɭɬɶ ɨɫɧɨɜɧɵɯ ɩɨɞɯɨɞɨɜ ɫɜɨɞɢɬɫɹ ɤ ɦɢɧɢɦɢɡɚɰɢɢ
ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɪɟɚɥɶɧɵɯ ɢ ɦɨɞɟɥɶɧɵɯ ɞɚɧɧɵɯ. ɉɪɢ ɷɬɨɦ ɟɞɢɧɫɬɜɟɧɧɨɫɬɶ ɪɟɲɟɧɢɹ ɞɨɫɬɢɝɚɟɬɫɹ ɡɚ ɫɱɟɬ
ɜɜɟɞɟɧɢɹ ɩɟɬɪɨɮɢɡɢɱɟɫɤɢ ɨɛɨɫɧɨɜɚɧɧɵɯ ɨɝɪɚɧɢɱɟɧɢɣ, ɚ ɭɫɬɨɣɱɢɜɨɫɬɶ – ɡɚ ɫɱɟɬ ɪɟɝɭɥɹɪɢɡɚɰɢɢ ɦɨɞɟɥɢ ɧɚ
ɪɚɡɥɢɱɧɵɯ ɷɬɚɩɚɯ ɪɟɲɟɧɢɹ, ɫɬɚɛɢɥɢɡɢɪɭɸɳɟɣ ɱɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ.
ȼ ɞɚɧɧɨɦ ɪɚɡɞɟɥɟ ɦɵ ɫɮɨɪɦɭɥɢɪɭɟɦ ɡɚɞɚɱɭ ɤɚɥɢɛɪɨɜɤɢ ɧɟɥɢɧɟɣɧɵɯ ɦɨɞɟɥɟɣ ɭɩɥɨɬɧɟɧɢɹɦɢɝɪɚɰɢɢ ɧɚ ɨɩɟɪɚɬɨɪɧɨɦ ɭɪɨɜɧɟ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɜɵɞɜɢɧɭɬɶ ɨɫɧɨɜɧɵɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɩɪɚɤɬɢɱɟɫɤɨɣ
ɪɟɚɥɢɡɚɰɢɢ ɩɨɞɯɨɞɚ.
Ʉɚɤ ɭɠɟ ɛɵɥɨ ɫɤɚɡɚɧɨ, ɦɟɬɨɞɵ ɪɟɲɟɧɢɹ ɨɪɢɟɧɬɢɪɨɜɚɧɵ ɧɚ ɦɢɧɢɦɢɡɚɰɢɸ ɧɟɤɨɬɨɪɨɝɨ
ɮɭɧɤɰɢɨɧɚɥɚ J(F), ɨɰɟɧɢɜɚɸɳɟɝɨ ɫɬɟɩɟɧɶ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɫɢɧɬɟɬɢɱɟɫɤɨɝɨ ɢ ɪɟɚɥɶɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɧɟɤɨɬɨɪɨɝɨ ɰɟɥɟɜɨɝɨ ɮɚɤɬɨɪɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ, ɢɥɢ ɢɧɚɱɟ – ɤɨɦɩɨɧɟɧɬ
90
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɜɟɤɬɨɪɚ ɦɨɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ F. ɉɪɚɤɬɢɱɟɫɤɢ ɪɟɱɶ ɜɫɟɝɞɚ ɢɞɟɬ ɨ ɧɚɯɨɠɞɟɧɢɢ ɧɟ ɨɞɧɨɝɨ ɧɚɢɥɭɱɲɟɝɨ
ɜɟɤɬɨɪɚ ɦɨɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ, ɚ ɨɛ ɨɩɪɟɞɟɥɟɧɢɢ ɧɟɤɨɬɨɪɨɝɨ ɦɧɨɠɟɫɬɜɚ ɬɚɤɢɯ ɜɟɤɬɨɪɨɜ, ɩɨɡɜɨɥɹɸɳɟɝɨ
ɡɚɞɚɬɶ ɨɛɥɚɫɬɶ ɢɡɦɟɧɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ, ɜ ɩɪɟɞɟɥɚɯ ɤɨɬɨɪɨɣ ɫɢɧɬɟɬɢɱɟɫɤɢɟ ɞɚɧɧɵɟ
ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɫɨɝɥɚɫɭɸɬɫɹ ɫ ɪɟɚɥɶɧɵɦɢ. Ʉɪɢɬɟɪɢɣ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɨɛɵɱɧɨ ɫɜɹɡɵɜɚɟɬɫɹ ɫ
ɤɚɱɟɫɬɜɨɦ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ, ɬ.ɟ., ɜ ɱɚɫɬɧɨɫɬɢ, ɫ ɫɨɫɬɨɹɬɟɥɶɧɵɦɢ ɨɰɟɧɤɚɦɢ ɪɚɡɛɪɨɫɚ ɞɚɧɧɵɯ ɩɨɥɟɜɵɯ
ɷɤɫɩɟɪɢɦɟɧɬɨɜ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚɥɢɱɢɟ ɩɨɝɪɟɲɧɨɫɬɟɣ ɜ ɞɚɧɧɵɯ ɜɵɪɚɠɚɟɬɫɹ ɜ ɜɢɞɟ ɧɟɤɨɬɨɪɨɣ
"ɪɚɡɦɚɡɚɧɧɨɫɬɢ" ɨɬɨɛɪɚɠɟɧɢɹ ɜɟɤɬɨɪɚ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ ɧɚ ɦɧɨɠɟɫɬɜɟ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɟɝɨ ɫ ɫɢɧɬɟɬɢɱɟɫɤɢɦ
ɜɟɤɬɨɪɨɦ ɞɚɧɧɵɯ, ɢɥɢ, ɢɧɚɱɟ, – ɩɨɞɦɧɨɠɟɫɬɜɚ ɜɨɡɦɨɠɧɵɯ ɜɟɤɬɨɪɨɜ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ, ɚɫɫɨɰɢɢɪɨɜɚɧɧɨɝɨ
ɫ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨɣ ɪɟɚɥɢɡɚɰɢɟɣ ɷɬɨɝɨ ɜɟɤɬɨɪɚ.
ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɤɚɤ ɫɚɦɚ ɩɪɹɦɚɹ ɡɚɞɚɱɚ, ɬɚɤ ɢ ɫɩɨɫɨɛ ɟɟ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɩɪɟɞɩɨɥɚɝɚɸɬ
ɧɚɥɢɱɢɟ "ɫɢɫɬɟɦɚɬɢɱɟɫɤɨɣ" ɨɲɢɛɤɢ, ɜɯɨɞɹɳɟɣ ɜ ɫɢɧɬɟɬɢɱɟɫɤɢɟ ɪɟɡɭɥɶɬɚɬɵ. Ɉɧɢ ɫɜɹɡɚɧɵ ɫ ɧɟɞɨɭɱɟɬɨɦ
ɹɜɥɟɧɢɣ, ɨɬɧɟɫɟɧɧɵɯ ɤ "ɦɚɥɨɡɧɚɱɢɦɵɦ", ɢ ɫ ɤɨɧɟɱɧɨɫɬɶɸ ɲɚɝɚ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ – "ɲɭɦɨɦ" ɫɟɬɤɢ. Ɍɨɱɧɨ
ɬɚɤ ɠɟ, ɤɚɤ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɜɟɤɬɨɪɚ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ, ɜɦɟɫɬɨ ɬɨɱɤɢ ɜ ɦɧɨɝɨɦɟɪɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ
ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɫɨɜɦɟɫɬɧɨ ɫ ɜɟɤɬɨɪɨɦ ɫɢɧɬɟɬɢɱɟɫɤɢɯ ɞɚɧɧɵɯ ɞɨɥɠɧɨ ɨɩɪɟɞɟɥɹɬɶɫɹ ɩɨɞɦɧɨɠɟɫɬɜɨ
ɚɫɫɨɰɢɢɪɨɜɚɧɧɵɯ ɫ ɧɢɦ ɪɟɲɟɧɢɣ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚ ɨɛɥɚɫɬɢ ɫɨɩɨɫɬɚɜɥɟɧɢɹ, ɜɵɫɬɭɩɚɸɳɟɣ ɜ ɤɚɱɟɫɬɜɟ ɨɛɳɟɝɨ ɦɟɬɪɢɱɟɫɤɨɝɨ
ɛɚɡɢɫɚ, ɩɪɢ ɩɨɞɛɨɪɟ ɜɟɤɬɨɪɚ ɦɨɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ F ɭɱɢɬɵɜɚɸɬɫɹ ɧɟ ɬɨɱɤɢ, ɧɨ ɤɨɦɩɚɤɬɧɵɟ
ɩɨɞɦɧɨɠɟɫɬɜɚ, ɜɨ ɜɡɚɢɦɧɨɦ ɪɚɫɩɨɥɨɠɟɧɢɢ ɤɨɬɨɪɵɯ ɢ ɢɳɟɬɫɹ ɨɩɬɢɦɭɦ (Madatov, Sereda, 1997; Traub,
Woznjakovski, 1980).
ɋɮɨɪɦɭɥɢɪɭɟɦ ɬɟɩɟɪɶ ɡɚɞɚɱɭ ɤɚɥɢɛɪɨɜɤɢ ɛɨɥɟɟ ɮɨɪɦɚɥɶɧɨ, ɭɱɢɬɵɜɚɹ ɫɩɟɰɢɮɢɤɭ ɞɚɧɧɵɯ ɢ ɢɯ
ɦɨɞɟɥɶɧɨɝɨ ɨɩɢɫɚɧɢɹ.
ɉɭɫɬɶ ɦɨɞɟɥɶ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ, ɞɚɸɳɚɹ ɨɩɢɫɚɧɢɟ ɩɪɨɰɟɫɫɨɜ ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ ɫ
ɧɟɨɛɯɨɞɢɦɨɣ ɩɨɥɧɨɬɨɣ, ɧɚɫɱɢɬɵɜɚɟɬ M ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɵɯ ɷɥɟɦɟɧɬɨɜ. ɉɭɫɬɶ ɬɚɤɠɟ ɞɥɹ ɤɚɠɞɨɝɨ
ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ ɨɩɪɟɞɟɥɟɧ ɧɚɛɨɪ ɩɚɪɚɦɟɬɪɨɜ ɢɡ N ɤɨɦɩɨɧɟɧɬ ɞɥɹ ɢɧɜɚɪɢɚɧɬɧɨɝɨ ɩɨ
ɩɪɨɫɬɪɚɧɫɬɜɭ ɢ ɜɪɟɦɟɧɢ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɨɩɟɪɚɬɨɪɚ ɩɪɹɦɨɣ ɡɚɞɚɱɢ. ɉɚɪɚɦɟɬɪɵ ɩɪɟɞɩɨɥɚɝɚɸɬɫɹ
ɥɢɧɟɣɧɨ-ɧɟɡɚɜɢɫɢɦɵɦɢ ɢ ɦɨɝɭɬ ɛɵɬɶ ɨɬɧɨɪɦɢɪɨɜɚɧɵ ɩɨ ɫɪɟɞɧɢɦ ɡɧɚɱɟɧɢɹɦ. Ɍɨɝɞɚ ɜ ɦɧɨɝɨɦɟɪɧɨɦ
ɩɪɨɫɬɪɚɧɫɬɜɟ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɟɣ ɨɩɪɟɞɟɥɟɧ ɨɪɬɨɧɨɪɦɢɪɨɜɚɧɧɵɣ ɛɚɡɢɫ X, ɜ ɤɨɬɨɪɨɦ ɜɟɤɬɨɪ ɩɚɪɚɦɟɬɪɨɜ
ɩɨɞɛɢɪɚɟɦɨɣ ɦɨɞɟɥɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ F = {F11, F21, ..., FM1, F12, ..., FM2, F13, ..., FMN}Ɍ.
ɉɨ ɚɧɚɥɨɝɢɢ ɨɩɪɟɞɟɥɢɦ ɜɟɤɬɨɪɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ ɞɚɧɧɵɯ D ɫ ɷɥɟɦɟɧɬɨɦ d = {d11, d21, ..., dK1,
2
d1 , ..., dK2, d13, ..., dKL}Ɍ. Ɋɚɡɦɟɪɧɨɫɬɶ ɷɬɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɲɚɝɨɦ ɧɟɡɚɜɢɫɢɦɵɯ ɢɡɦɟɪɟɧɢɣ ɜ
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɨɛɥɚɫɬɢ ɤɚɥɢɛɪɨɜɚɧɢɹ K ɢ ɱɢɫɥɨɦ ɧɟɡɚɜɢɫɢɦɨ ɢɡɦɟɪɹɟɦɵɯ ɮɢɡɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ
L. Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɫɟɬɤɚ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ ɨɞɧɚ ɢ ɬɚ ɠɟ ɞɥɹ ɪɚɡɥɢɱɧɵɯ
ɢɡɦɟɪɟɧɢɣ ɢ, ɤɪɨɦɟ ɬɨɝɨ, ɫɨɝɥɚɫɨɜɚɧɚ ɫ ɫɟɬɤɨɣ ɪɚɫɱɟɬɚ ɫɢɧɬɟɬɢɱɟɫɤɢɯ ɞɚɧɧɵɯ.
Ɉɛɥɚɫɬɶ ɫɨɩɨɫɬɚɜɥɟɧɢɹ F ɨɩɪɟɞɟɥɢɦ ɤɚɤ ɨɛɥɚɫɬɶ ɜɟɤɬɨɪɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɜ ɤɨɬɨɪɨɦ
ɫɢɧɬɟɬɢɱɟɫɤɢɟ ɢ ɪɟɚɥɶɧɵɟ ɞɚɧɧɵɟ ɢɦɟɸɬ ɨɛɳɢɟ ɲɤɚɥɵ ɢ ɜɵɛɪɚɧɧɭɸ ɦɟɬɪɢɤɭ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ. ɂɧɵɦɢ
ɫɥɨɜɚɦɢ, ɩɪɨɢɡɜɨɥɶɧɵɣ ɜɟɤɬɨɪ f = {f1, f2, ..., fI}Ɍ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɞɟɫɶ ɥɢɛɨ ɩɭɬɟɦ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɩɨɥɟɜɵɯ
ɧɚɛɥɸɞɟɧɢɣ, ɡɚɞɚɧɧɵɯ ɧɚ ɧɟɤɨɬɨɪɨɣ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɫɟɬɤɟ, ɜ ɲɤɚɥɭ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɫ ɫɢɧɬɟɬɢɱɟɫɤɢɦɢ
ɞɚɧɧɵɦɢ, ɥɢɛɨ ɨɬɨɛɪɚɠɟɧɢɟɦ ɧɚ ɷɬɭ ɠɟ ɫɟɬɤɭ ɜɟɤɬɨɪɚ ɦɨɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ, ɩɭɬɟɦ ɩɪɢɦɟɧɟɧɢɹ ɤ ɧɟɦɭ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɨɩɟɪɚɬɨɪɚ ɩɪɹɦɨɣ ɡɚɞɚɱɢ.
91
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɢ ɨɛɟɫɩɟɱɟɧɢɹ ɜɨɡɦɨɠɧɨɫɬɢ ɚɧɚɥɢɡɚ ɮɭɧɤɰɢɨɧɚɥɚ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɜɜɟɞɟɦ ɦɟɪɭ
ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɫɨɩɨɫɬɚɜɥɟɧɢɹ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɨɩɪɟɞɟɥɢɦ ɫɤɚɥɹɪɧɨɟ ɩɪɨɢɡɜɟɞɟɧɢɟ
ɩɪɨɢɡɜɨɥɶɧɨɣ ɩɚɪɵ ɜɟɤɬɨɪɨɜ f1, f2  F ɜ ɮɨɪɦɟ:
(f1, f2)F = f2T CF-1 f1,
(1)
ɝɞɟ ɦɚɬɪɢɰɚ ɤɨɜɚɪɢɚɰɢɢ CF ɢɦɟɟɬ ɞɢɚɝɨɧɚɥɶɧɭɸ ɫɬɪɭɤɬɭɪɭ,
ɩɨɫɤɨɥɶɤɭ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɥɢɧɟɣɧɚɹ ɧɟɡɚɜɢɫɢɦɨɫɬɶ ɢɡɦɟɪɟɧɢɣ.
ȿɟ ɞɢɚɝɨɧɚɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɪɨɢɡɜɟɞɟɧɢɟɦ
ɧɨɪɦɢɪɭɸɳɢɯ ɢ ɜɟɫɨɜɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ, ɜɜɨɞɢɦɵɯ ɞɥɹ
ɧɨɪɦɢɪɨɜɤɢ ɢ ɭɱɟɬɚ ɧɟɪɚɜɧɨɬɨɱɧɨɫɬɢ ɡɚɦɟɪɨɜ.
ȼɜɟɞɟɦ ɬɚɤɠɟ ɧɨɪɦɭ ɜɟɤɬɨɪɨɜ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (1):
1/2
|| fi ||F = (fi, fi )F .
Ɋɢɫ. 1. Ɉɛɳɚɹ ɫɯɟɦɚ ɩɪɨɰɟɞɭɪɵ ɩɨɞɛɨɪɚ
(2)
ɉɭɫɬɶ ɬɚɤɠɟ ɨɬɨɛɪɚɠɟɧɢɟ ɧɚ ɨɛɥɚɫɬɶ ɫɨɩɨɫɬɚɜɥɟɧɢɹ
ɢɡ ɩɪɨɫɬɪɚɧɫɬɜɚ ɞɚɧɧɵɯ ɜɵɩɨɥɧɹɟɬɫɹ ɨɩɟɪɚɬɨɪɨɦ
ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɢɡɦɟɪɟɧɢɣ T(d), ɚ ɢɡ ɩɪɨɫɬɪɚɧɫɬɜɚ
ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ – ɨɩɟɪɚɬɨɪɨɦ ɩɪɹɦɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ
M(F). Ʉɚɤ ɩɨɞɱɟɪɤɢɜɚɥɨɫɶ ɜɵɲɟ, ɞɚɧɧɵɟ ɨɩɟɪɚɬɨɪɵ
ɩɨɪɨɠɞɚɸɬ ɜ ɨɛɥɚɫɬɢ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɧɟɱɟɬɤɢɟ ɩɨɞɦɧɨɠɟɫɬɜɚ,
ɫɜɹɡɚɧɧɵɟ ɫ ɧɟɢɡɛɟɠɧɵɦɢ ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɢɡɦɟɪɟɧɢɣ ɢ
ɦɨɞɟɥɢɪɨɜɚɧɢɹ (ɪɢɫ. 1). ɏɚɪɚɤɬɟɪɢɡɭɹ ɷɬɢ ɨɲɢɛɤɢ
ɨɬɨɛɪɚɠɟɧɢɹ
ɞɢɚɦɟɬɪɚɦɢ
()
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɩɨɞɦɧɨɠɟɫɬɜ G f, ɦɨɠɧɨ ɮɨɪɦɚɥɶɧɨ ɡɚɩɢɫɚɬɶ ɩɪɨɰɟɞɭɪɵ
ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɢɡɦɟɪɟɧɢɣ ɜ ɨɩɟɪɚɬɨɪɧɨɣ
ɮɨɪɦɟ:
ɦɨɞɟɥɢɪɨɜɚɧɢɟ – {f^Gf^} = M(F);
ɬɪɚɧɫɮɨɪɦɚɰɢɹ ɢɡɦɟɪɟɧɢɣ – {f*Gf*} = T(d).
ɉɨɫɤɨɥɶɤɭ ɦɟɪɚ ɛɥɢɡɨɫɬɢ ɞɜɭɯ ɜɟɤɬɨɪɨɜ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɨɩɪɟɞɟɥɟɧɚ, ɦɨɠɧɨ ɜ
ɨɛɳɟɦ ɜɢɞɟ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɨɩɬɢɦɢɡɚɰɢɨɧɧɭɸ ɡɚɞɚɱɭ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
Ff = argmin [J(F)], ɝɞɟ J(F) = ||T(d) M(F)||F.
(3)
Ɉɱɟɜɢɞɧɨ, ɱɬɨ "ɢɞɟɚɥɶɧɨɟ" ɪɟɲɟɧɢɟ, ɞɨɫɬɚɜɥɹɸɳɟɟ ɧɭɥɟɜɨɟ ɪɚɫɯɨɠɞɟɧɢɟ, ɧɟɞɨɫɬɢɠɢɦɨ ɞɨ ɬɟɯ
ɩɨɪ, ɩɨɤɚ ɧɟ ɨɩɪɟɞɟɥɟɧɵ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɤɪɢɬɟɪɢɢ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɨɛɥɚɫɬɢ ɩɟɪɟɫɟɱɟɧɢɹ ɞɜɭɯ ɧɟɱɟɬɤɢɯ
ɨɬɨɛɪɚɠɟɧɢɣ {f^Gf^} ɢ {f*Gf*}, ɢɡ ɩɪɨɫɬɪɚɧɫɬɜɚ ɦɨɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɢ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢɡɦɟɪɟɧɢɣ,
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɛɭɞɟɦ ɩɪɟɞɩɨɥɚɝɚɬɶ ɪɚɜɧɨɦɟɪɧɵɣ ɡɚɤɨɧ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɧɭɬɪɢ ɥɸɛɨɝɨ
ɩɨɞɦɧɨɠɟɫɬɜɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɫɨɩɨɫɬɚɜɥɟɧɢɹ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɩɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɥɸɛɚɹ ɬɨɱɤɚ ɢɡ
ɩɪɨɫɬɪɚɧɫɬɜɚ ɦɨɞɟɥɟɣ ɥɢɛɨ ɞɚɧɧɵɯ ɨɬɨɛɪɚɠɚɟɬɫɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɨ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɜ ɜɢɞɟ ɧɟɤɨɬɨɪɨɝɨ
ɤɨɦɩɚɤɬɧɨɝɨ "ɩɹɬɧɚ" ɫ ɤɨɧɟɱɧɵɦɢ ɪɚɡɦɟɪɚɦɢ.
ɉɪɢ ɬɚɤɨɣ ɩɨɫɬɚɧɨɜɤɟ ɤɪɢɬɟɪɢɣ ɞɨɩɭɫɬɢɦɵɯ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɣ ɨɬɨɛɪɚɠɟɧɢɣ, ɬɪɚɧɫɮɨɪɦɢɪɭɟɦɵɯ
ɢɡ ɢɡɦɟɪɟɧɢɣ ɢ ɫɢɧɬɟɬɢɱɟɫɤɢɯ ɞɚɧɧɵɯ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɡɦɟɪɚɦɢ ɦɚɤɫɢɦɚɥɶɧɨɣ ɢɡ ɞɜɭɯ ɩɨɞɨɛɥɚɫɬɟɣ
ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ. ɍɫɥɨɜɢɟ, ɤɨɬɨɪɨɦɭ ɞɨɥɠɧɨ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɪɟɲɟɧɢɟ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ, ɜ ɬɟɪɦɢɧɚɯ
ɩɪɨɛɥɟɦɵ ɦɢɧɢɦɢɡɚɰɢɢ ɮɭɧɤɰɢɨɧɚɥɚ (3) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:
Ff  X = argmin (J(F)F = ||T(d) M(F)||F);
f^ Gf^  Gf*.
(3*)
ȼ ɷɬɨɣ ɫɢɬɭɚɰɢɢ ɜɨɡɦɨɠɧɵ ɬɪɢ ɜɚɪɢɚɧɬɚ:
{Gf*} {Gf^}  ɇɟɨɩɬɢɦɚɥɶɧɨɟ ɪɟɲɟɧɢɟ – ɦɨɞɟɥɶ ɫɥɢɲɤɨɦ ɝɪɭɛɚɹ
(4)
{Gf*} ! {Gf^}  ɇɟɨɩɬɢɦɚɥɶɧɨɟ ɪɟɲɟɧɢɟ – ɞɚɧɧɵɟ ɧɟɞɨɫɬɚɬɨɱɧɨ ɬɨɱɧɵ
{Gf*} # {Gf^}  Ɉɩɬɢɦɚɥɶɧɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɨɥɧɨɬɵ ɦɨɞɟɥɢ ɢ ɬɨɱɧɨɫɬɢ
ɞɚɧɧɵɯ
ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɨɬɨɛɪɚɠɟɧɢɹ {f^Gf^} = M(F) ɜɵɩɨɥɧɹɸɬɫɹ ɧɟɥɢɧɟɣɧɵɦ ɨɩɟɪɚɬɨɪɨɦ
ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ʉɪɨɦɟ ɬɨɝɨ, ɟɞɢɧɫɬɜɟɧɧɨɫɬɶ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɦɨɠɟɬ ɛɵɬɶ ɨɛɟɫɩɟɱɟɧɚ ɥɢɲɶ ɩɪɢ
ɜɵɩɨɥɧɟɧɢɢ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɚɩɪɢɨɪɧɵɯ ɨɝɪɚɧɢɱɟɧɢɣ ɜ ɨɛɥɚɫɬɢ ɜɚɪɢɚɰɢɢ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ. Ɉɛɥɚɫɬɶ
ɨɞɧɨɫɜɹɡɧɵɯ ɨɬɨɛɪɚɠɟɧɢɣ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɨɛɥɚɫɬɶɸ ɪɟɲɟɧɢɹ ɢ ɨɛɨɡɧɚɱɚɬɶ Xa  X. Ɍɨɝɞɚ ɢɡ ɜɫɟɯ
ɜɨɡɦɨɠɧɵɯ ɪɟɲɟɧɢɣ ɜ ɤɚɱɟɫɬɜɟ ɪɟɡɭɥɶɬɚɬɚ ɛɭɞɟɬ ɜɵɛɢɪɚɬɶɫɹ ɜɟɤɬɨɪ F, ɩɪɢɧɚɞɥɟɠɚɳɢɣ ɩɨɞɦɧɨɠɟɫɬɜɭ
92
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
Xa, ɨɞɧɨɡɧɚɱɧɨ ɨɬɨɛɪɚɠɚɟɦɨɦɭ ɧɚ ɨɛɥɚɫɬɶ ɫɨɩɨɫɬɚɜɥɟɧɢɹ (ɪɢɫ. 1). ɉɪɢ ɷɬɨɦ ɨɝɪɚɧɢɱɟɧɢɹ ɧɚ ɦɧɨɠɟɫɬɜɟ
Fa  F ɦɨɝɭɬ ɧɨɫɢɬɶ "ɠɟɫɬɤɢɣ" ɯɚɪɚɤɬɟɪ, ɤɨɝɞɚ ɜɟɤɬɨɪɚ, ɧɟ ɩɪɢɧɚɞɥɟɠɚɳɢɟ ɤɨɦɩɚɤɬɧɨɦɭ ɩɨɞɦɧɨɠɟɫɬɜɭ
Fa, ɩɪɨɫɬɨ ɨɬɛɪɚɫɵɜɚɸɬɫɹ, ɥɢɛɨ "ɦɹɝɤɢɣ" – ɤɨɝɞɚ ɩɪɢɛɥɢɠɟɧɢɟ ɢɡɧɭɬɪɢ ɤ ɝɪɚɧɢɰɚɦ Fa ɨɬɦɟɱɚɟɬɫɹ
ɜɜɟɞɟɧɢɟɦ ɲɬɪɚɮɧɵɯ ɮɭɧɤɰɢɣ, ɧɚɡɧɚɱɚɟɦɵɯ ɧɚ ɜɟɥɢɱɢɧɭ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ. Ɉɤɨɧɱɚɬɟɥɶɧɨ
ɫɬɚɛɢɥɢɡɢɪɨɜɚɧɧɵɣ ɩɨ ɨɛɥɚɫɬɢ ɩɨɢɫɤɚ ɚɥɝɨɪɢɬɦ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɨɞɛɨɪɚ ɦɨɠɟɬ ɛɵɬɶ ɫɯɟɦɚɬɢɱɟɫɤɢ
ɡɚɩɢɫɚɧ ɜ ɮɨɪɦɟ:
Ff  Xa  X = argmin(||f* f^||F),
f* Gf*,
f^ Gf^  Gf*.
(3**)
ɋɬɪɚɬɟɝɢɹ ɩɨɢɫɤɚ ɪɟɲɟɧɢɹ (3**) ɜ ɭɧɢɦɨɞɚɥɶɧɨɣ ɨɛɥɚɫɬɢ ɨɩɢɫɵɜɚɟɬɫɹ ɧɢɠɟ.
Ȼɚɡɨɜɵɟ ɭɪɚɜɧɟɧɢɹ ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ ɜɨ ɜɪɟɦɟɧɧɨɣ ɲɤɚɥɟ ɷɜɨɥɸɰɢɢ ɨɫɚɞɨɱɧɨɝɨ ɛɚɫɫɟɣɧɚ ɨɫɧɨɜɚɧɵ
ɧɚ ɩɪɢɧɰɢɩɟ ɤɨɧɫɟɪɜɚɰɢɢ ɦɚɫɫ ɢ ɡɚɤɨɧɟ Ⱦɚɪɫɢ, ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ ɨɩɢɫɵɜɚɸɳɟɦ ɞɢɜɟɪɝɟɧɰɢɸ ɩɨɬɨɤɚ
ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɜ ɭɩɥɨɬɧɹɸɳɟɣɫɹ ɩɨɪɢɫɬɨɣ ɫɪɟɞɟ (Bear, Bachmat, 1991) ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɝɪɚɞɢɟɧɬɚ
ɞɚɜɥɟɧɢɣ. Ɂɞɟɫɶ ɦɵ ɧɟ ɛɭɞɟɦ ɨɛɫɭɠɞɚɬɶ ɚɞɟɤɜɚɬɧɨɫɬɶ ɷɬɨɣ ɥɢɧɟɣɧɨɣ ɦɨɞɟɥɢ ɪɟɚɥɶɧɵɦ ɝɟɨɥɨɝɢɱɟɫɤɢɦ
ɩɪɨɰɟɫɫɚɦ, ɩɪɨɬɟɤɚɸɳɢɦ ɜɨ ɦɧɨɝɨɦ ɤɚɬɚɫɬɪɨɮɢɱɧɨ (Ɏɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɮɚɤɬɨɪ..., 1989). ɉɨɫɬɭɥɢɪɭɹ
ɡɚɤɨɧ Ⱦɚɪɫɢ ɜ ɤɚɱɟɫɬɜɟ ɩɨɞɬɜɟɪɠɞɟɧɧɨɣ ɩɪɚɤɬɢɤɨɣ ɦɨɞɟɥɢ ɦɟɞɥɟɧɧɨ ɩɪɨɬɟɤɚɸɳɢɯ ɩɪɨɰɟɫɫɨɜ ɭɩɥɨɬɧɟɧɢɹɦɢɝɪɚɰɢɢ ɮɥɸɢɞɚ, ɦɵ ɥɢɲɶ ɨɱɟɪɱɢɜɚɟɦ ɤɥɚɫɫ ɨɩɟɪɚɬɨɪɨɜ ɩɪɹɦɨɣ ɡɚɞɚɱɢ, ɤɚɤ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ
ɨɩɟɪɚɬɨɪɨɜ, ɨɩɢɫɵɜɚɸɳɢɯ ɧɟɩɪɟɪɵɜɧɨ ɦɟɧɹɸɳɢɟɫɹ ɩɪɨɰɟɫɫɵ, ɧɟ ɢɦɟɸɳɢɟ ɪɚɡɪɵɜɨɜ ɜ ɩɪɟɞɟɥɚɯ ɨɛɥɚɫɬɢ
ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ. Ɍɨɱɧɨ ɬɚɤ ɠɟ ɤɢɧɟɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɍȼ-ɝɟɧɟɪɚɰɢɢ ɦɨɝɭɬ ɛɵɬɶ ɨɩɢɫɚɧɵ ɜ ɤɥɚɫɫɟ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɨɩɟɪɚɬɨɪɨɜ (Tissot, Welte, 1978). ɉɨɫɥɟɞɧɢɟ ɫɜɹɡɵɜɚɸɬ ɬɟɦɩ ɢ ɫɨɫɬɚɜ ɮɚɡɨɜɵɯ
ɬɪɚɧɫɮɨɪɦɚɰɢɣ ɨɪɝɚɧɢɱɟɫɤɨɝɨ ɜɟɳɟɫɬɜɚ ɫ ɚɛɫɨɥɸɬɧɵɦ ɡɧɚɱɟɧɢɟɦ ɢ ɝɪɚɞɢɟɧɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨ ɜɫɟɦɭ ɪɹɞɭ
ɝɟɧɟɪɢɪɭɟɦɵɯ ɍȼ (ɨɬ ɚɫɮɚɥɶɬɨɜ ɞɨ ɦɟɬɚɧɚ).
Ɋɟɲɟɧɢɟ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɚɜɥɟɧɢɣ ɢ ɧɚɫɵɳɟɧɢɣ ɩɨɪɨɜɨɝɨ
ɮɥɸɢɞɚ ɭɝɥɟɜɨɞɨɪɨɞɚɦɢ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɨ ɜ ɭɡɥɚɯ ɫɟɬɤɢ ɫ ɬɨɱɧɨɫɬɶɸ, ɤɨɬɨɪɚɹ ɞɨɥɠɧɚ ɛɵɬɶ
ɫɨɝɥɚɫɨɜɚɧɚ ɫ ɪɟɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ (Madatov, Sereda, 1997). ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɤɚɥɢɛɪɨɜɤɚ ɦɨɞɟɥɢ
ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ, ɨɫɧɨɜɚɧɧɚɹ ɧɚ ɩɨɞɛɨɪɟ (3*), ɨɤɚɠɟɬɫɹ ɧɟɨɩɬɢɦɚɥɶɧɨɣ ɜ ɫɦɵɫɥɟ (4). ɉɨɩɭɬɧɨ ɫ
ɨɫɧɨɜɧɵɦɢ ɪɟɲɟɧɢɹɦɢ, ɜ ɤɚɠɞɨɦ ɭɡɥɟ ɫɟɬɤɢ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɩɨɪɢɫɬɨɫɬɢ ɢ ɩɪɨɧɢɰɚɟɦɨɫɬɢ, ɤɨɬɨɪɵɟ
ɮɨɪɦɚɥɶɧɨ ɬɚɤɠɟ ɞɨɥɠɧɵ ɛɵɬɶ ɭɜɹɡɚɧɵ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɞɚɧɧɵɦɢ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɤɚɱɟɫɬɜɟ "ɞɚɧɧɵɯ" ɩɪɢ ɤɚɥɢɛɪɨɜɤɟ ɞɨɥɠɧɵ ɜɵɫɬɭɩɚɬɶ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ, ɧɚɫɵɳɟɧɢɣ ɍȼ, ɩɨɪɢɫɬɨɫɬɟɣ ɢ ɩɪɨɧɢɰɚɟɦɨɫɬɟɣ, ɨɬɧɟɫɟɧɧɵɟ ɤ
ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɵɦ ɥɢɬɨ-ɫɬɪɚɬɢɝɪɚɮɢɱɟɫɤɢɦ ɷɥɟɦɟɧɬɚɦ ɪɚɡɪɟɡɚ. ɉɨɫɤɨɥɶɤɭ ɩɚɥɟɨɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɟ
ɞɨɫɬɭɩɧɵ ɢɡɦɟɪɟɧɢɹɦ, ɪɟɱɶ ɜɫɟɝɞɚ ɛɭɞɟɬ ɢɞɬɢ ɨ ɧɚɫɬɨɹɳɟɦ ɜɪɟɦɟɧɢ – ɤɨɧɰɟ ɜɪɟɦɟɧɧɨɣ ɲɤɚɥɵ
ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ. Ɂɚ ɢɫɤɥɸɱɟɧɢɟɦ ɝɪɭɛɨɣ ɥɢɬɨ-ɫɬɪɚɬɢɝɪɚɮɢɱɟɫɤɨɣ "ɪɚɡɛɢɜɤɢ" ɪɚɡɪɟɡɚ ɩɨ ɞɚɧɧɵɦ
ɫɟɣɫɦɨɪɚɡɜɟɞɤɢ, ɧɢ ɨɞɧɨ ɢɡ ɬɪɟɛɭɟɦɵɯ ɢɡɦɟɪɟɧɢɣ ɧɟ ɞɨɫɬɭɩɧɨ ɫ ɩɨɜɟɪɯɧɨɫɬɢ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɪɟɱɶ
ɜɫɟɝɞɚ ɢɞɟɬ ɨ ɫɟɬɢ ɤɚɥɢɛɪɨɜɨɱɧɵɯ ɞɚɧɧɵɯ, ɫɨɜɩɚɞɚɸɳɟɣ ɫ ɫɟɬɶɸ ɫɤɜɚɠɢɧ. ȼɨɩɪɨɫɚɦ ɢɡɦɟɪɟɧɢɹ
ɞɚɜɥɟɧɢɣ, ɧɚɫɵɳɟɧɢɣ, ɩɨɪɢɫɬɨɫɬɟɣ ɢ ɩɪɨɧɢɰɚɟɦɨɫɬɟɣ ɩɨɫɜɹɳɟɧɚ ɫɩɟɰɢɚɥɶɧɚɹ ɥɢɬɟɪɚɬɭɪɚ (ɫɦ.,
ɧɚɩɪɢɦɟɪ, Ⱥɜɱɚɧ ɢ ɞɪ., 1979; Magara, 1978). Ɍɚɦ ɠɟ ɦɨɠɧɨ ɩɨɡɧɚɤɨɦɢɬɶɫɹ ɫ ɨɛɪɚɛɨɬɤɨɣ ɤɨɦɩɥɟɤɫɨɜ
ɤɚɪɨɬɚɠɟɣ, ɩɪɨɦɵɫɥɨɜɵɯ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɛɭɪɟɧɢɹ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɞɥɹ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɜ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɲɤɚɥɵ, ɬ.ɟ. ɫɨɫɬɚɜɢɬɶ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨɛ ɨɩɟɪɚɬɨɪɚɯ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɞɚɧɧɵɯ ɢɡɦɟɪɟɧɢɣ
T(d) ɢ ɢɯ ɩɨɝɪɟɲɧɨɫɬɹɯ (Ɇɭɯɟɪ, ɒɚɤɢɪɨɜ, 1992).
Ƚɟɨɮɥɸɢɞɚɥɶɧɵɟ ɞɚɜɥɟɧɢɹ ɞɨɫɬɭɩɧɵ ɞɥɹ ɢɡɦɟɪɟɧɢɣ ɜ ɱɪɟɡɜɵɱɚɣɧɨ ɨɝɪɚɧɢɱɟɧɧɵɯ ɡɨɧɚɯ
ɫɤɜɚɠɢɧ, ɫɜɹɡɚɧɧɵɯ ɫ ɯɨɪɨɲɨ ɩɪɨɧɢɰɚɟɦɵɦɢ ɪɚɡɧɨɫɬɹɦɢ ɩɨɪɨɞ, ɤɚɤ ɩɪɚɜɢɥɨ – ɰɟɥɟɜɵɦɢ ɤɨɥɥɟɤɬɨɪɚɦɢ.
Ɍɚɦ ɠɟ, ɯɨɬɹ ɢ ɡɧɚɱɢɬɟɥɶɧɨ ɪɟɠɟ, ɩɪɨɢɡɜɨɞɹɬɫɹ ɢɡɦɟɪɟɧɢɹ ɩɪɨɧɢɰɚɟɦɨɫɬɟɣ. ȼɫɹ ɨɫɬɚɥɶɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɨ
ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɹɯ (ɬ.ɟ. ɞɥɹ ɩɥɨɯɨ ɩɪɨɧɢɰɚɟɦɨɣ ɱɚɫɬɢ ɩɨɪɨɞ, ɤɨɬɨɪɚɹ, ɤɚɤ ɩɪɚɜɢɥɨ, ɩɪɟɨɛɥɚɞɚɟɬ
ɩɨ ɪɚɡɪɟɡɭ) ɦɨɠɟɬ ɩɨɫɬɭɩɚɬɶ ɢɡ ɤɨɫɜɟɧɧɵɯ ɢɫɬɨɱɧɢɤɨɜ, ɬɚɤɢɯ ɤɚɤ D-ɷɤɫɩɨɧɟɧɬɚ, V-ɤɚɪɨɬɚɠ ɢ ɬ.ɩ.
(Mouchet, Mitchell, 1989). ɉɪɢ ɚɤɤɭɪɚɬɧɨɦ ɫɨɛɥɸɞɟɧɢɢ ɬɟɯɧɨɥɨɝɢɢ ɛɭɪɟɧɢɢ (ɬ.ɟ. ɩɪɢ ɩɨɞɞɟɪɠɚɧɢɢ
ɛɚɥɚɧɫɚ ɭɞɟɥɶɧɨɝɨ ɜɟɫɚ ɛɭɪɨɜɨɝɨ ɪɚɫɬɜɨɪɚ ɫ ɝɪɚɞɢɟɧɬɨɦ ɮɨɪɦɚɰɢɨɧɧɵɯ ɞɚɜɥɟɧɢɣ), ɯɨɪɨɲɢɦ
ɩɨɤɚɡɚɬɟɥɟɦ ɞɚɜɥɟɧɢɣ (ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɞɥɹ ɦɚɤɫɢɦɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ) ɫɥɭɠɢɬ ɭɞɟɥɶɧɵɣ ɜɟɫ ɛɭɪɨɜɨɝɨ
ɪɚɫɬɜɨɪɚ.
ɇɚɫɵɳɟɧɢɹ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɍȼ ɦɨɝɭɬ ɛɵɬɶ ɨɰɟɧɟɧɵ ɧɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ ɝɚɡɨɜɨɝɨ
ɤɚɪɨɬɚɠɚ (Ɇɭɯɟɪ, ɒɚɤɢɪɨɜ, 1992), ɤɨɬɨɪɵɣ, ɤɚɤ ɩɪɚɜɢɥɨ, ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɜɫɟɦɭ ɡɚɛɨɸ ɜ ɩɪɨɰɟɫɫɟ
ɛɭɪɟɧɢɹ. ɋɥɟɞɭɟɬ ɥɢɲɶ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɩɪɚɜɤɢ ɡɚ ɫɤɨɪɨɫɬɶ ɛɭɪɟɧɢɹ ɢ ɩɪɨɦɵɜɤɢ,
ɤɚɜɟɪɧɨɦɟɬɪɢɸ ɢ ɫɨɫɬɚɜ ɛɭɪɨɜɨɝɨ ɪɚɫɬɜɨɪɚ ɫɥɟɞɭɟɬ ɞɨɩɨɥɧɢɬɶ ɩɨɩɪɚɜɤɚɦɢ ɧɚ ɮɚɡɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɫɦɟɫɢ
ɧɚ ɡɚɛɨɟ. ɏɪɨɦɚɬɨɝɪɚɮɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɜɵɩɨɥɧɹɟɬɫɹ ɥɢɲɶ ɜ ɡɨɧɚɯ ɨɬɛɨɪɚ ɩɪɨɛ ɧɚ ɧɟɮɬɶ ɢ ɝɚɡ. Ɍɚɤɢɦ
ɨɛɪɚɡɨɦ, ɤɚɥɢɛɪɨɜɨɱɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɤɪɚɣɧɟ ɧɟɪɚɜɧɨɬɨɱɧɚ ɢ ɧɟɪɚɜɧɨɦɟɪɧɚ ɞɚɠɟ ɜ ɩɪɟɞɟɥɚɯ ɨɞɧɨɝɨ
ɫɬɜɨɥɚ. Ⱦɨɩɨɥɧɢɬɟɥɶɧɨ ɤ ɝɚɡɨɜɨɦɭ ɤɚɪɨɬɚɠɭ, ɜɚɠɧɭɸ ɢɧɮɨɪɦɚɰɢɸ ɨ ɞɨɫɬɢɝɧɭɬɨɣ ɫɬɚɞɢɢ ɡɪɟɥɨɫɬɢ
93
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɧɟɮɬɟɝɚɡɨɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ ɧɟɫɭɬ ɢɡɦɟɪɟɧɢɹ ɨɬɪɚɠɚɬɟɥɶɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɜɢɬɪɢɧɢɬɚ, ɤɨɬɨɪɵɟ
ɜɵɩɨɥɧɹɸɬɫɹ ɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɥɨɜɢɹɯ (Ungerer, 1993).
Ɉɬɤɪɵɬɚɹ ɩɨɪɢɫɬɨɫɬɶ ɬɚɤɠɟ ɦɨɠɟɬ ɛɵɬɶ ɢɡɦɟɪɟɧɚ ɧɚ ɨɛɪɚɡɰɚɯ ɤɟɪɧɚ. Ɉɞɧɚɤɨ ɞɥɹ ɦɚɫɫɨɜɵɯ
ɪɚɫɱɟɬɨɜ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɟɪɟɫɱɟɬɵ ɢɡ ɚɤɭɫɬɢɱɟɫɤɨɝɨ, ɩɥɨɬɧɨɫɬɧɨɝɨ ɥɢɛɨ Ʉɋ ɤɚɪɨɬɚɠɟɣ (Ʉɨɬɹɯɨɜ, 1977).
Ɋɚɡɥɢɱɧɵɟ ɮɨɪɦɭɥɵ, ɭɫɬɚɧɨɜɥɟɧɧɵɟ ɷɦɩɢɪɢɱɟɫɤɢ ɞɥɹ ɩɟɫɱɚɧɢɫɬɵɯ, ɤɚɪɛɨɧɚɬɧɵɯ ɢ ɝɥɢɧɢɫɬɵɯ ɪɚɡɧɨɫɬɟɣ
ɩɨɪɨɞ, ɢɦɟɸɬ, ɤɚɤ ɩɪɚɜɢɥɨ, ɞɨɫɬɚɬɨɱɧɨ ɥɨɤɚɥɶɧɭɸ ɨɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɢ ɬɪɟɛɭɸɬ ɩɨɩɪɚɜɨɤ ɡɚ
ɦɢɧɟɪɚɥɢɡɚɰɢɸ ɩɨɪɨɜɨɣ ɠɢɞɤɨɫɬɢ, ɫɨɫɬɚɜ ɰɟɦɟɧɬɚ, ɝɥɢɧɢɫɬɨɫɬɶ ɢ ɬ.ɞ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɦɟɫɬɧɟɟ
ɝɨɜɨɪɢɬɶ ɧɟ ɨɛ ɚɛɫɨɥɸɬɧɵɯ ɡɧɚɱɟɧɢɹɯ ɨɬɤɪɵɬɨɣ ɩɨɪɢɫɬɨɫɬɢ, ɚ ɫɤɨɪɟɟ ɨ ɧɟɤɨɣ ɬɪɚɧɫɮɨɪɦɚɧɬɟ,
ɤɨɪɪɟɥɢɪɭɟɦɨɣ ɫ ɞɚɧɧɵɦ ɩɚɪɚɦɟɬɪɨɦ.
ɉɪɨɧɢɰɚɟɦɨɫɬɶ ɫɥɟɞɭɟɬ ɨɬɧɟɫɬɢ, ɩɨ ɧɚɲɟɦɭ ɦɧɟɧɢɸ, ɤ ɩɚɪɚɦɟɬɪɭ, ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɞɨɫɬɭɩɧɨɦɭ
ɞɥɹ ɰɟɥɟɣ ɤɚɥɢɛɪɨɜɤɢ, ɜ ɫɜɹɡɢ ɫ ɬɪɭɞɧɨɫɬɶɸ ɟɝɨ ɢɡɦɟɪɟɧɢɣ ɢ ɪɟɞɤɨɫɬɶɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɨɩɵɬɨɤ ɜ
ɪɚɡɜɟɞɨɱɧɨɣ ɩɪɚɤɬɢɤɟ.
Ɉɛɳɢɣ ɜɵɜɨɞ ɩɨ ɧɚɥɢɱɢɸ ɢ ɤɚɱɟɫɬɜɭ ɞɨɫɬɭɩɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɞɥɹ ɰɟɥɟɣ ɤɚɥɢɛɪɨɜɤɢ ɦɨɞɟɥɟɣ
ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ ɫɨɫɬɨɢɬ ɜ ɫɥɟɞɭɸɳɟɦ:
Ⱦɥɹ ɤɚɥɢɛɪɨɜɤɢ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɚɧɧɵɟ ɩɪɹɦɵɯ ɡɚɦɟɪɨɜ ɢ ɬɪɚɧɫɮɨɪɦɚɰɢɣ ɜ ɲɤɚɥɵ
ɞɚɜɥɟɧɢɣ, ɍȼ-ɧɚɫɵɳɟɧɢɣ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɢ ɩɨɪɢɫɬɨɫɬɟɣ, ɩɪɢɜɹɡɚɧɧɵɟ ɤ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɵɦ
ɷɥɟɦɟɧɬɚɦ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ.
ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɫɟɬɤɚ, ɧɚ ɤɨɬɨɪɨɣ ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɵ ɞɚɧɧɵɟ, ɫɜɹɡɚɧɚ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɫ
ɩɨɥɨɠɟɧɢɟɦ ɫɤɜɚɠɢɧ. ɇɨ ɢ ɬɚɦ ɨɧɚ ɤɪɚɣɧɟ ɧɟɪɚɜɧɨɦɟɪɧɚ. ɇɚɢɛɨɥɟɟ ɨɫɜɟɳɟɧɧɵɦɢ ɩɚɪɚɦɟɬɪɢɱɟɫɤɨɣ
ɢɧɮɨɪɦɚɰɢɟɣ ɫɥɟɞɭɟɬ ɫɱɢɬɚɬɶ ɰɟɥɟɜɵɟ ɢɧɬɟɪɜɚɥɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɨɡɦɨɠɧɨ-ɩɪɨɞɭɤɬɢɜɧɵɦɢ
ɪɟɡɟɪɜɭɚɪɚɦɢ ɧɟɮɬɢ ɢ ɝɚɡɚ.
Ɍɨɱɧɨɫɬɶ ɬɪɚɧɫɮɨɪɦɚɰɢɣ ɤɚɪɨɬɚɠɧɨɣ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɢɧɮɨɪɦɚɰɢɢ ɜ ɬɪɟɛɭɟɦɵɟ ɲɤɚɥɵ ɢɡɦɟɧɹɟɬɫɹ ɨɬ
ɟɞɢɧɢɰ ɞɨ ɞɟɫɹɬɤɨɜ ɩɪɨɰɟɧɬɨɜ (ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɨɝɪɟɲɧɨɫɬɢ), ɢ ɡɚɱɚɫɬɭɸ ɩɪɟɨɛɪɚɡɨɜɚɧɧɵɟ ɞɚɧɧɵɟ ɩɪɢɝɨɞɧɵ
ɥɢɲɶ ɞɥɹ ɤɚɱɟɫɬɜɟɧɧɵɯ ɥɢɛɨ ɨɪɢɟɧɬɢɪɨɜɨɱɧɵɯ ɨɰɟɧɨɤ ɩɪɟɞɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ, ɤɚɤ, ɧɚɩɪɢɦɟɪ, ɭɞɟɥɶɧɵɣ ɜɟɫ
ɩɪɨɦɵɜɨɱɧɨɣ ɠɢɞɤɨɫɬɢ ɜ ɩɪɢɦɟɧɟɧɢɢ ɤ ɞɚɧɧɵɦ ɨ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɹɯ.
ɉɨɞɨɛɧɵɣ ɜɵɜɨɞ ɧɢ ɜ ɤɨɟɣ ɦɟɪɟ ɧɟ ɞɨɥɠɟɧ ɫɥɭɠɢɬɶ ɨɫɧɨɜɚɧɢɟɦ ɞɥɹ ɨɬɤɚɡɚ ɨɬ ɩɨɩɵɬɤɢ
ɤɚɥɢɛɪɨɜɤɢ ɛɚɫɫɟɣɧɨɜɨɣ ɦɨɞɟɥɢ ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ. ȼɫɟ, ɱɬɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɞɩɪɢɧɹɬɶ – ɷɬɨ ɥɢɲɶ
ɭɩɪɨɫɬɢɬɶ ɦɨɞɟɥɶ ɞɨ ɬɚɤɨɣ ɫɬɟɩɟɧɢ, ɱɬɨɛɵ ɟɟ ɤɚɱɟɫɬɜɨ ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɨ ɤɚɱɟɫɬɜɭ ɞɚɧɧɵɯ, ɧɚ ɤɨɬɨɪɵɯ ɨɧɚ
ɛɭɞɟɬ ɤɚɥɢɛɪɨɜɚɬɶɫɹ. ɋɭɳɟɫɬɜɭɸɳɟɟ ɩɨɥɨɠɟɧɢɟ ɜɟɳɟɣ ɫ ɛɚɫɫɟɣɧɨɜɵɦ ɦɨɞɟɥɢɪɨɜɚɧɢɟɦ ɧɚɦɧɨɝɨ ɯɭɠɟ,
ɯɨɬɹ ɱɚɫɬɨ ɬɚɤɨɜɵɦ ɢ ɧɟ ɨɫɨɡɧɚɟɬɫɹ.
ȼ ɫɚɦɨɦ ɞɟɥɟ, ɬɪɟɯɦɟɪɧɵɟ ɦɧɨɝɨɮɚɡɧɵɟ ɩɪɹɦɵɟ ɡɚɞɚɱɢ ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ ɞɥɹ ɲɤɚɥ
ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ ɪɟɚɥɢɡɨɜɚɧɵ ɜ ɜɢɞɟ ɞɨɫɬɚɬɨɱɧɨ "ɬɹɠɟɥɵɯ" ɜ ɜɵɱɢɫɥɢɬɟɥɶɧɨɦ ɫɦɵɫɥɟ ɢ
ɫɟɪɜɢɫɧɨɦ ɢɫɩɨɥɧɟɧɢɢ ɩɚɤɟɬɨɜ ɩɪɨɝɪɚɦɦ. ɉɪɢ ɷɬɨɦ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɱɟɪɩɚɸɬɫɹ ɢɡ
ɧɟɤɢɯ ɬɚɛɥɢɰ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ, ɫɨɫɬɚɜɥɟɧɧɵɯ ɩɨ ɨɛɨɛɳɟɧɢɸ ɩɟɬɪɨɮɢɡɢɱɟɫɤɨɣ ɢɧɮɨɪɦɚɰɢɢ,
ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɢ ɬ.ɞ. ɇɢɤɚɤ ɧɟ ɩɪɢɜɹɡɚɧɧɵɟ ɤ ɪɟɚɥɶɧɵɦ ɞɚɧɧɵɦ ɨ ɩɟɬɪɨɮɢɡɢɤɟ
ɢɫɫɥɟɞɭɟɦɨɝɨ ɪɚɣɨɧɚ, ɩɨɞɨɛɧɵɟ ɦɨɞɟɥɢ ɢɦɟɸɬ ɫɤɨɪɟɟ ɞɟɦɨɧɫɬɪɚɰɢɨɧɧɵɣ, ɱɟɦ ɩɪɢɤɥɚɞɧɨɣ ɫɦɵɫɥ.
ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɢɯ ɞɥɹ ɩɪɨɝɧɨɡɨɜ "ɩɨɜɢɫɚɟɬ ɜ ɩɭɫɬɨɬɟ". ɉɨɩɵɬɤɢ ɤɚɥɢɛɪɨɜɤɢ ɭɩɢɪɚɸɬɫɹ ɜ ɤɪɚɣɧɸɸ
ɧɟɷɮɮɟɤɬɢɜɧɨɫɬɶ ɨɩɬɢɦɢɡɚɰɢɨɧɧɨɣ ɡɚɞɚɱɢ ɩɨɞɛɨɪɚ ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɪɟɚɥɢɡɭɸɬɫɹ, ɩɨɫɤɨɥɶɤɭ ɢɧɜɟɪɫɢɹ
ɫɬɨɥɶ "ɬɹɠɟɥɵɯ" ɜ ɜɵɱɢɫɥɢɬɟɥɶɧɨɦ ɫɦɵɫɥɟ ɦɨɞɟɥɶɧɵɯ ɨɩɟɪɚɬɨɪɨɜ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɭɫɩɟɲɧɨɣ ɜ
ɜɵɱɢɫɥɢɬɟɥɶɧɨɦ ɨɬɧɨɲɟɧɢɢ.
Ɉɱɟɜɢɞɧɨ, ɱɟɦ ɜɵɲɟ ɪɚɡɦɟɪɧɨɫɬɶ ɦɨɞɟɥɶɧɨɝɨ ɛɚɡɢɫɚ, ɬɟɦ, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɛɨɥɟɟ ɞɟɬɚɥɶɧɨ
ɨɩɢɫɵɜɚɟɬɫɹ ɫɪɟɞɚ. ȼɦɟɫɬɟ ɫ ɬɟɦ ɜɫɹ ɢɞɟɹ ɩɪɨɝɧɨɡɚ ɨɫɧɨɜɚɧɚ ɧɚ ɜɵɱɥɟɧɟɧɢɢ ɤɥɸɱɟɜɵɯ ɮɚɤɬɨɪɨɜ,
ɨɤɚɡɵɜɚɸɳɢɯ ɞɨɦɢɧɚɧɬɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɪɟɡɭɥɶɬɚɬ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜ ɨɛɥɚɫɬɢ ɫɨɩɨɫɬɚɜɥɟɧɢɹ. ȼ ɢɞɟɚɥɟ
ɧɚɛɨɪ ɧɚɢɛɨɥɟɟ ɱɭɜɫɬɜɢɬɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ ɫɪɟɞɵ, ɤɨɬɨɪɵɟ ɤ ɬɨɦɭ ɠɟ ɹɜɥɹɸɬɫɹ
ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɦɢ (ɬ.ɟ. ɫɥɚɛɨ ɜɚɪɶɢɪɭɟɦɵɦɢ) ɩɚɪɚɦɟɬɪɚɦɢ ɪɚɡɪɟɡɚ, ɹɜɥɹɟɬɫɹ ɰɟɥɟɜɵɦ ɛɚɡɢɫɨɦ
ɩɪɨɝɧɨɡɚ, ɬ.ɟ. ɬɚɤɢɦ ɩɨɞɦɧɨɠɟɫɬɜɨɦ Xɫ  X, ɤɨɬɨɪɨɟ ɩɪɢ ɦɢɧɢɦɚɥɶɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ ɫɨɯɪɚɧɹɥɨ ɛɵ
ɫɜɨɣɫɬɜɚ ɦɨɞɟɥɶɧɨɝɨ ɨɬɨɛɪɚɠɟɧɢɹ ɜɟɤɬɨɪɚ ɫɢɧɬɟɬɢɱɟɫɤɢɯ ɞɚɧɧɵɯ ɧɚ ɨɛɥɚɫɬɶ ɫɨɩɨɫɬɚɜɥɟɧɢɹ. Ʉ
ɫɨɠɚɥɟɧɢɸ, ɡɚɪɚɧɟɟ ɜɵɱɥɟɧɢɬɶ ɟɝɨ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟɜɨɡɦɨɠɧɨ. ɉɨɷɬɨɦɭ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨ
ɧɚɱɢɧɚɬɶ ɚɧɚɥɢɡ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɢ ɫ ɧɚɢɛɨɥɟɟ ɞɟɬɚɥɶɧɨɣ ɦɨɞɟɥɢ, ɩɨɫɬɟɩɟɧɧɨ "ɡɚɝɪɭɛɥɹɹ" ɟɟ ɩɭɬɟɦ
ɨɬɛɪɚɫɵɜɚɧɢɹ (ɡɚɤɪɟɩɥɟɧɢɹ) ɧɟɱɭɜɫɬɜɢɬɟɥɶɧɵɯ ɤ ɪɟɲɟɧɢɸ ɩɚɪɚɦɟɬɪɨɜ.
ȼ ɩɪɢɥɨɠɟɧɢɢ ɤ ɦɨɞɟɥɹɦ ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ, ɧɟɨɛɯɨɞɢɦɨ, ɜ ɱɚɫɬɧɨɫɬɢ, ɨɩɪɟɞɟɥɢɬɶɫɹ ɫ
ɪɚɡɦɟɪɧɨɫɬɶɸ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɫɟɬɤɢ ɢ ɫ ɞɟɬɚɥɶɧɨɫɬɶɸ ɩɨɞɪɚɡɞɟɥɟɧɢɹ ɪɚɡɪɟɡɚ ɧɚ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɵɟ
ɝɟɨɥɨɝɢɱɟɫɤɢɟ ɨɛɴɟɤɬɵ. Ɍɪɟɯɦɟɪɧɵɟ ɷɤɜɢɞɢɫɬɚɧɬɧɵɟ ɫɟɬɤɢ, ɨɱɟɜɢɞɧɨ, ɞɨɥɠɧɵ ɛɵɬɶ ɡɚɦɟɧɟɧɵ ɧɚ
ɬɪɢɚɧɝɭɥɹɰɢɨɧɧɵɟ ɫ ɭɡɥɚɦɢ, ɫɨɜɩɚɞɚɸɳɢɦɢ ɫ ɤɚɥɢɛɪɨɜɨɱɧɵɦɢ ɫɤɜɚɠɢɧɚɦɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɷɜɨɥɸɰɢɨɧɧɵɟ
ɬɪɟɯɦɟɪɧɵɟ ɦɨɞɟɥɢ ɭɩɥɨɬɧɟɧɢɹ ɩɨɬɪɟɛɭɸɬ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɬɪɟɯɦɟɪɧɨɝɨ ɠɟ ɩɨɥɹ ɧɚɩɪɹɠɟɧɢɣ
ɨɫɚɞɨɱɧɨɝɨ ɱɟɯɥɚ ɜ ɩɪɨɰɟɫɫɟ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ. ȼɨɫɫɬɚɧɨɜɥɟɧɢɟ ɠɟ ɩɚɥɟɨɝɟɨɦɟɬɪɢɢ ɩɨ ɞɚɧɧɵɦ
ɫɟɣɫɦɨɪɚɡɜɟɞɤɢ ɹɜɥɹɟɬɫɹ ɫɤɨɪɟɟ ɨɛɥɚɫɬɶɸ ɢɧɬɭɢɰɢɢ, ɱɟɦ ɫɬɪɨɝɨɝɨ ɪɚɫɱɟɬɚ, ɞɚɠɟ ɜ ɫɥɭɱɚɟ ɧɟɩɪɟɪɵɜɧɨɝɨ
94
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɩɨɝɪɭɠɟɧɢɹ ɛɚɫɫɟɣɧɚ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɨ ɦɟɪɟ "ɫɬɚɪɟɧɢɹ" ɨɫɚɞɨɱɧɨɣ ɬɨɥɳɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ
ɧɟɟɞɢɧɫɬɜɟɧɧɨɫɬɶ ɩɪɨɞɜɢɠɟɧɢɹ ɨɛɪɚɬɧɨ ɜ ɝɟɨɥɨɝɢɱɟɫɤɨɦ ɜɪɟɦɟɧɢ, ɤɨɬɨɪɚɹ ɫɬɚɧɨɜɢɬɫɹ
ɤɚɬɚɫɬɪɨɮɢɱɟɫɤɨɣ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɢɫɥɚ ɩɟɪɟɪɵɜɨɜ ɜ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɪɟɯɦɟɪɧɚɹ
ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɚ ɟɫɬɟɫɬɜɟɧɧɵɦ ɨɛɪɚɡɨɦ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɪɟɲɟɧɚ ɟɞɢɧɫɬɜɟɧɧɨ.
Ɉɞɧɚɤɨ ɱɢɫɬɨ ɨɞɧɨɦɟɪɧɚɹ ɩɨɫɬɚɧɨɜɤɚ ɧɟ ɩɨɡɜɨɥɹɟɬ ɫɢɧɬɟɡɢɪɨɜɚɬɶ ɜɫɟ ɪɚɡɧɨɨɛɪɚɡɢɟ
ɧɚɛɥɸɞɚɟɦɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɞɚɧɧɵɯ ɩɨ ɫɤɜɚɠɢɧɚɦ. Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ɫɩɚɞ ɭɪɨɜɧɹ ȺȼɉȾ, ɱɚɫɬɨ
ɧɚɛɥɸɞɚɟɦɵɣ ɩɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɝɪɚɧɢɰɵ "ɍȼ-ɝɟɧɟɪɢɪɭɸɳɚɹ ɩɨɤɪɵɲɤɚ – ɪɟɡɟɪɜɭɚɪ", ɧɟ ɦɨɠɟɬ ɛɵɬɶ
ɫɢɧɬɟɡɢɪɨɜɚɧ ɛɟɡ ɭɱɟɬɚ ɥɚɬɟɪɚɥɶɧɨɝɨ ɞɪɟɧɚɠɚ ɮɥɸɢɞɚ ɩɨ ɩɪɨɧɢɰɚɟɦɨɦɭ ɤɨɥɥɟɤɬɨɪɭ.
ɇɚɦɢ ɛɵɥ ɩɪɟɞɥɨɠɟɧ ɢ ɪɚɡɪɚɛɨɬɚɧ ɩɨɞɯɨɞ ɤ ɢɧɜɟɪɫɢɢ, ɨɫɧɨɜɚɧɧɵɣ ɧɚ ɷɮɮɟɤɬɢɜɧɨɣ 1.5D ɦɨɞɟɥɢ
ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ ɝɟɨɮɥɸɢɞɨɜ, ɤɚɤ ɨɫɧɨɜɚ ɤɚɥɢɛɪɨɜɚɧɢɹ ɬɪɚɧɫɩɨɪɬɧɨ-ɟɦɤɨɫɬɧɵɯ ɫɜɨɣɫɬɜ ɨɫɚɞɨɱɧɵɯ
ɩɨɪɨɞ (Madatov et al., 1996; 1997; 1998). ɇɢɠɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɪɚɡɪɚɛɨɬɤɢ ɦɨɞɟɥɢ ɭɩɥɨɬɧɟɧɢɹɦɢɝɪɚɰɢɢ, ɤɨɬɨɪɚɹ ɨɛɟɫɩɟɱɢɜɚɟɬ ɨɩɬɢɦɚɥɶɧɨɫɬɶ ɩɨɞɛɨɪɚ ɜ ɫɦɵɫɥɟ (4) ɢ ɩɪɢ ɷɬɨɦ ɹɜɥɹɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɩɪɨɫɬɨɣ ɜ ɜɵɱɢɫɥɢɬɟɥɶɧɨɦ ɨɬɧɨɲɟɧɢɢ. ɋɦɵɫɥ ɫɢɦɜɨɥɚ "1.5D" ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɷɮɮɟɤɬɵ, ɜɵɡɜɚɧɧɵɟ
ɧɟɜɟɪɬɢɤɚɥɶɧɵɦɢ ɤɨɦɩɨɧɟɧɬɚɦɢ ɫɬɪɟɫɫɚ ɩɪɢ ɭɩɥɨɬɧɟɧɢɢ-ɦɢɝɪɚɰɢɢ, ɭɱɢɬɵɜɚɸɬɫɹ ɷɮɮɟɤɬɢɜɧɨ ɩɭɬɟɦ
ɜɜɟɞɟɧɢɹ ɫɪɟɞɧɟɝɨ ɡɚ ɲɚɝ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɬɟɦɩɚ ɨɬɬɨɤɚ-ɩɪɢɬɨɤɚ ɝɟɨɮɥɸɢɞɚ ɢɡ ɨɞɧɨɦɟɪɧɨɣ ɫɢɫɬɟɦɵ ɜ
ɥɚɬɟɪɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ɉɪɢ ɷɬɨɦ ɩɪɚɤɬɢɱɟɫɤɢ ɡɧɚɱɢɦɵɟ ɩɨɬɨɤɢ ɮɥɸɢɞɚ ɜɨɡɦɨɠɧɵ ɥɢɲɶ ɜɞɨɥɶ
ɯɨɪɨɲɨ ɩɪɨɜɨɞɹɳɢɯ ɤɨɥɥɟɤɬɨɪɨɜ ɫ ɭɪɨɜɧɟɦ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɟɞɢɧɢɰɵ-ɫɨɬɧɢ ɦɢɥɥɢɞɚɪɫɢ (Verweij, 1993).
3. ɉɪɹɦɚɹ ɡɚɞɚɱɚ ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ ɞɥɹ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɨɛɴɟɦɚ ɭɩɥɨɬɧɹɸɳɟɣɫɹ ɩɨɪɢɫɬɨɣ ɩɨɪɨɞɵ ɜ
ɦɚɫɲɬɚɛɟ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ
ɇɚɲɚ ɡɚɞɚɱɚ ɜ ɷɬɨɦ ɪɚɡɞɟɥɟ ɛɭɞɟɬ ɫɨɫɬɨɹɬɶ ɜ ɪɚɡɪɚɛɨɬɤɟ ɬɚɤɨɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ
ɭɩɥɨɬɧɟɧɢɹ ɨɫɚɞɨɱɧɵɯ ɩɨɪɨɞ – ɦɢɝɪɚɰɢɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ (ɜɤɥɸɱɚɹ ɩɟɪɜɢɱɧɭɸ ɦɢɝɪɚɰɢɸ ɍȼ ɢɡ
ɝɟɧɟɪɢɪɭɸɳɢɯ ɬɨɥɳ), ɤɨɬɨɪɚɹ ɭɞɨɜɥɟɬɜɨɪɢɥɚ ɛɵ ɬɪɟɛɨɜɚɧɢɹ ɩɨ ɨɩɬɢɦɚɥɶɧɨɫɬɢ, ɜɵɞɜɢɧɭɬɵɟ ɜ
ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ. ɋɮɨɪɦɭɥɢɪɭɟɦ ɷɬɢ ɬɪɟɛɨɜɚɧɢɹ ɞɟɬɚɥɶɧɟɟ.
1. Ɉɩɟɪɚɬɨɪ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɞɨɥɠɟɧ ɛɚɡɢɪɨɜɚɬɶɫɹ ɧɚ ɪɟɲɟɧɢɢ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɤɨɧɫɟɪɜɚɰɢɢ
ɦɚɫɫ ɢ ɧɟɩɪɟɪɵɜɧɨɫɬɢ ɦɢɝɪɚɰɢɢ ɮɥɸɢɞɚ.
2. Ɋɟɩɪɟɡɟɧɬɚɬɢɜɧɵɣ ɷɥɟɦɟɧɬ ɨɛɴɟɦɚ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ ɞɨɥɠɟɧ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶɫɹ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɦɢ
ɮɢɡɢɱɟɫɤɢɦɢ ɫɜɨɣɫɬɜɚɦɢ ɦɚɬɪɢɰɵ ɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ, ɚ ɬɚɤɠɟ ɢɧɬɟɪɜɚɥɨɦ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ, ɜ
ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɨɧ ɨɬɥɚɝɚɥɫɹ.
3. Ɉɩɟɪɚɬɨɪ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɞɨɥɠɟɧ ɧɟɩɪɟɪɵɜɧɨ ɢ ɨɞɧɨɡɧɚɱɧɨ ɨɬɨɛɪɚɠɚɬɶ ɜɟɤɬɨɪ ɦɨɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɧɚ
ɨɛɥɚɫɬɶ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɜ ɲɤɚɥɚɯ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ, ɍȼ-ɧɚɫɵɳɟɧɢɣ ɢ ɩɨɪɢɫɬɨɫɬɟɣ.
4. ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɫɟɬɤɚ, ɧɚ ɤɨɬɨɪɭɸ ɨɬɨɛɪɚɠɚɸɬɫɹ ɫɢɧɬɟɡɢɪɨɜɚɧɧɵɟ ɞɚɧɧɵɟ, ɞɨɥɠɧɚ ɫɨɜɩɚɞɚɬɶ ɫ
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɫɟɬɤɨɣ, ɧɚ ɤɨɬɨɪɨɣ ɷɬɢ ɞɚɧɧɵɟ ɢɡɦɟɪɹɸɬɫɹ;
5. Ʉɚɠɞɵɣ ɢɧɞɢɜɢɞɭɚɥɶɧɵɣ ɫɢɧɬɟɬɢɱɟɫɤɢɣ ɨɞɧɨɦɟɪɧɵɣ (ɜɟɪɬɢɤɚɥɶɧɵɣ) ɩɪɨɮɢɥɶ, ɫɨɩɨɫɬɚɜɥɹɟɦɵɣ ɫ
ɞɚɧɧɵɦɢ ɩɨ ɤɚɥɢɛɪɨɜɨɱɧɨɣ ɫɤɜɚɠɢɧɟ, ɞɨɥɠɟɧ ɷɮɮɟɤɬɢɜɧɨ ɜɤɥɸɱɚɬɶ 3D ɷɮɮɟɤɬɵ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɢɡɥɨɠɟɧɢɟ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ ɨɫɧɨɜ ɬɟɨɪɢɢ ɭɩɥɨɬɧɟɧɢɹ, ɍȼɝɟɧɟɪɚɰɢɢ ɢ ɦɢɝɪɚɰɢɢ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɪɹɞɟ ɢɡɜɟɫɬɧɵɯ ɦɨɧɨɝɪɚɮɢɣ (Verweij, 1993; Magara, 1978; Bear,
Bachmat, 1991; Tissot, Welte, 1978). ɉɨɫɤɨɥɶɤɭ ɧɚɲɚ ɡɚɞɚɱɚ ɫɨɫɬɨɢɬ ɜ ɨɩɢɫɚɧɢɢ ɦɨɞɟɥɢ, ɩɪɢɝɨɞɧɨɣ ɞɥɹ
ɤɚɥɢɛɪɨɜɤɢ ɢ ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɣ ɬɪɟɛɨɜɚɧɢɹɦ "1.5D", ɦɵ ɱɚɫɬɢɱɧɨ ɩɨɜɬɨɪɢɦ ɨɫɧɨɜɧɵɟ ɨɬɩɪɚɜɧɵɟ
ɩɭɧɤɬɵ ɢ ɷɬɚɩɵ ɜɵɜɨɞɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɭɪɚɜɧɟɧɢɣ. ɉɪɢ ɷɬɨɦ ɚɤɰɟɧɬ ɛɭɞɟɬ ɫɞɟɥɚɧ ɧɚ ɨɬɥɢɱɢɬɟɥɶɧɵɯ
ɨɫɨɛɟɧɧɨɫɬɹɯ ɞɚɧɧɨɣ ɦɨɞɟɥɢ ɢ ɟɟ ɨɝɪɚɧɢɱɟɧɢɹɯ, ɚ ɤɨɧɟɱɧɵɟ ɮɨɪɦɭɥɵ ɛɭɞɭɬ ɧɟɫɤɨɥɶɤɨ ɨɬɥɢɱɚɬɶɫɹ ɨɬ
ɬɪɢɜɢɚɥɶɧɵɯ.
95
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
Ⱦɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɚ ɭɩɥɨɬɧɟɧɢɹ ɜɜɟɞɟɦ ɞɜɟ
ɞɟɤɚɪɬɨɜɵɯ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ: ɜɧɟɲɧɸɸ ɢ ɜɧɭɬɪɟɧɧɸɸ (ɪɢɫ. 2).
ȼɧɟɲɧɹɹ ɫɨɞɟɪɠɢɬ ɞɜɟ ɤɨɨɪɞɢɧɚɬɧɵɯ ɨɫɢ: ɚɛɫɨɥɸɬɧɨɝɨ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ
ɜɪɟɦɟɧɢ ɢ ɝɥɭɛɢɧɵ. Ɉɫɶ ɝɥɭɛɢɧ ɧɚɱɢɧɚɟɬɫɹ ɨɬ ɭɪɨɜɧɹ ɦɨɪɹ ɢ ɢɡɦɟɪɹɟɬ
ɜɟɪɬɢɤɚɥɶɧɵɟ ɞɜɢɠɟɧɢɹ ɞɧɚ ɝɢɩɨɬɟɬɢɱɟɫɤɨɝɨ ɛɚɫɫɟɣɧɚ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ,
ɝɞɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɫɨɜɩɚɞɚɟɬ ɫ ɩɨɝɪɭɠɟɧɢɟɦ. ȼɪɟɦɟɧɧɚɹ ɨɫɶ
ɧɚɱɢɧɚɟɬɫɹ ɜ ɧɟɤɨɬɨɪɨɣ ɫɬɚɪɬɨɜɨɣ ɬɨɱɤɟ ɢɫɬɨɪɢɢ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ ɢ
ɫɨɜɩɚɞɚɟɬ ɫ ɜɨɡɪɚɫɬɨɦ ɞɪɟɜɧɟɣɲɟɣ ɮɨɪɦɚɰɢɢ – ɭɫɥɨɜɧɨɝɨ ɮɭɧɞɚɦɟɧɬɚ.
ȼɨ ɜɧɟɲɧɟɣ, ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɜɜɟɞɟɦ ɜ
ɪɚɫɫɦɨɬɪɟɧɢɟ ɷɥɟɦɟɧɬɚɪɧɵɣ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɵɣ ɨɛɴɟɦ U – ɬɚɤɨɣ
ɤɜɚɡɢɨɞɧɨɪɨɞɧɵɣ ɷɥɟɦɟɧɬ ɨɫɚɞɨɱɧɨɣ ɝɨɪɧɨɣ ɩɨɪɨɞɵ, ɜ ɩɪɟɞɟɥɚɯ
ɤɨɬɨɪɨɝɨ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɥɨɤɚɥɶɧɵɦɢ ɜɚɪɢɚɰɢɹɦɢ ɫɜɨɣɫɬɜ
ɦɢɧɟɪɚɥɶɧɨɝɨ ɫɤɟɥɟɬɚ ɢ ɧɚɩɨɥɧɹɸɳɟɝɨ ɟɝɨ ɮɥɸɢɞɚ. Ʉɚɤ ɢɡɜɟɫɬɧɨ,
ɨɩɪɟɞɟɥɟɧɢɟ ɬɚɤɢɯ ɦɚɤɪɨɫɜɨɣɫɬɜ ɨɫɚɞɨɱɧɵɯ ɩɨɪɨɞ, ɤɚɤ ɩɨɪɢɫɬɨɫɬɶ,
ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɢ ɍȼ-ɝɟɧɟɪɚɰɢɨɧɧɵɣ ɩɨɬɟɧɰɢɚɥ, ɨɫɧɨɜɚɧɨ ɧɚ
Ɋɢɫ. 2. ɋɯɟɦɚ ɭɩɥɨɬɧɟɧɢɹ-ɍȼɨɫɪɟɞɧɟɧɢɢ ɩɨ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɦɭ ɨɛɴɟɦɭ (Aziz, Settari, 1983).
ɝɟɧɟɪɚɰɢɢ ɞɥɹ ɩɨɝɪɭɠɚɸɳɟɝɨɫɹ
ɋɜɹɠɟɦ ɫ ɷɥɟɦɟɧɬɨɦ U ɥɨɤɚɥɶɧɭɸ, ɜɧɭɬɪɟɧɧɸɸ ɫɢɫɬɟɦɭ
ɷɥɟɦɟɧɬɚ ɩɨɪɨɞɵ U
ɤɨɨɪɞɢɧɚɬ, ɤɨɬɨɪɚɹ ɜɦɟɫɬɟ ɫ ɧɢɦ ɫɥɟɞɭɟɬ ɜɞɨɥɶ ɬɪɚɟɤɬɨɪɢɢ
ɩɨɝɪɭɠɟɧɢɹ (Z, t), ɩɨɞɜɟɪɝɚɹɫɶ ɜɨɡɞɟɣɫɬɜɢɸ ɫɬɪɟɫɫɚ ɢ ɬɟɦɩɟɪɚɬɭɪɵ. ȼɨɡɧɢɤɚɸɳɢɟ ɩɪɢ ɷɬɨɦ ɷɮɮɟɤɬɵ
ɭɩɥɨɬɧɟɧɢɹ ɢ ɮɚɡɨɜɵɯ ɩɪɟɜɪɚɳɟɧɢɣ ɤɨɧɬɪɨɥɢɪɭɸɬɫɹ ɪɟɨɥɨɝɢɱɟɫɤɢɦɢ (Magara, 1978) ɢ ɤɢɧɟɬɢɱɟɫɤɢɦɢ
(Tissot, Welte, 1978) ɫɨɨɬɧɨɲɟɧɢɹɦɢ, ɭɫɬɚɧɨɜɥɟɧɧɵɦɢ ɷɦɩɢɪɢɱɟɫɤɢ ɞɥɹ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ
ɥɢɬɨɥɨɝɢɱɟɫɤɨɝɨ ɬɢɩɚ. ɉɨɫɥɟɞɧɢɟ ɨɞɧɨɡɧɚɱɧɨ ɫɜɹɡɵɜɚɸɬ ɦɚɤɪɨɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ ɫ
ɝɥɭɛɢɧɨɣ (Z), ɢɥɢ ɜɟɪɬɢɤɚɥɶɧɵɦ ɫɬɪɟɫɫɨɦ (V), ɢ/ɢɥɢ ɬɟɦɩɟɪɚɬɭɪɨɣ (T), ɤɨɬɨɪɵɯ ɞɨɫɬɢɝ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ
ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɵɣ ɨɛɴɟɦ (ɪɢɫ. 2ɛ). Ɂɚɦɟɬɢɦ, ɱɬɨ ɷɮɮɟɤɬɵ ɭɩɥɨɬɧɟɧɢɹ, ɜ ɪɚɦɤɚɯ ɬɟɨɪɢɢ ɩɥɚɫɬɢɱɧɵɯ
ɞɟɮɨɪɦɚɰɢɣ ɝɨɪɧɵɯ ɩɨɪɨɞ, ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ, ɤɚɤ ɧɟɨɛɪɚɬɢɦɵɟ. Ɍ.ɟ. ɬɪɚɟɤɬɨɪɢɢ ɩɨɞɴɟɦɚ ɜ ɛɚɫɫɟɣɧɨɜɨɣ
ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɥɚɬɨ ɧɚ ɬɪɟɧɞɟ ɭɩɥɨɬɧɟɧɢɹ. ɗɮɮɟɤɬɵ ɜɬɨɪɢɱɧɨɣ ɬɪɟɳɢɧɨɜɚɬɨɫɬɢ,
ɪɚɜɧɨ ɤɚɤ ɢ ɰɟɦɟɧɬɚɰɢɢ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɨɩɢɫɵɜɚɸɬɫɹ, ɤɚɤ ɩɪɚɜɢɥɨ, ɝɨɪɚɡɞɨ ɛɨɥɟɟ ɫɥɨɠɧɵɦɢ
ɷɦɩɢɪɢɱɟɫɤɢɦɢ ɫɨɨɬɧɨɲɟɧɢɹɦɢ, ɡɧɚɱɢɦɵɦɢ ɧɚ ɥɨɤɚɥɶɧɨɦ ɭɪɨɜɧɟ (Ʉɨɬɹɯɨɜ, 1977). ɋ ɧɚɲɟɣ ɬɨɱɤɢ
ɡɪɟɧɢɹ, ɨɧɢ ɞɨɥɠɧɵ ɜɤɥɸɱɚɬɶɫɹ ɜ ɷɦɩɢɪɢɱɟɫɤɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɪɟɨɥɨɝɢɢ ɢ ɤɢɧɟɬɢɤɢ ɞɚɧɧɨɝɨ
ɥɢɬɨɬɢɩɚ ɢ ɭɬɨɱɧɹɬɶɫɹ ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɫɥɭɱɚɟ ɜ ɯɨɞɟ ɤɚɥɢɛɪɨɜɤɢ ɦɨɞɟɥɟɣ ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ.
ɉɨɫɤɨɥɶɤɭ ɧɢ ɬɪɚɟɤɬɨɪɢɹ ɩɨɝɪɭɠɟɧɢɹ, ɧɢ ɬɪɟɧɞ ɭɩɥɨɬɧɟɧɢɹ ɧɟ ɢɦɟɸɬ ɩɟɬɟɥɶ, ɞɚɧɧɚɹ ɦɨɞɟɥɶ ɢɦɟɟɬ
ɬɟɧɞɟɧɰɢɸ ɧɟɩɪɟɪɵɜɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɨɛɴɟɦɚ.
Ʉɨɧɜɟɪɫɢɹ ɱɚɫɬɢ ɬɜɟɪɞɨɣ ɮɚɡɵ ɜ ɠɢɞɤɢɟ ɢ ɝɚɡɨɨɛɪɚɡɧɵɟ ɍȼ ɜɟɞɟɬ ɤ ɩɨɜɵɲɟɧɢɸ ɩɨɪɢɫɬɨɫɬɢ ɢ
ɮɨɪɦɚɥɶɧɨ ɦɨɠɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ, ɤɚɤ "ɪɚɡɭɩɥɨɬɧɟɧɢɟ". Ɉɞɧɚɤɨ ɪɚɡɧɢɰɚ ɩɥɨɬɧɨɫɬɟɣ ɤɨɧɜɟɪɬɢɪɭɟɦɨɣ
ɬɜɟɪɞɨɣ ɮɚɡɵ ɢ ɧɟɮɬɢ ɧɟɡɧɚɱɢɬɟɥɶɧɚ (ɬɢɩɢɱɧɚɹ ɩɥɨɬɧɨɫɬɶ ɤɟɪɨɝɟɧɚ ɧɟ ɩɪɟɜɵɲɚɟɬ 1100 ɤɝ/ɦ3, ɬ.ɟ.
ɧɟɧɚɦɧɨɝɨ ɜɵɲɟ ɩɥɨɬɧɨɫɬɢ ɩɨɪɨɜɨɣ ɜɨɞɵ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɵɜɟɞɟɧɢɟ ɢɡ ɦɚɬɪɢɰɵ ɤɟɪɨɝɟɧɚ ɩɭɬɟɦ
ɩɟɪɜɢɱɧɨɣ ɦɢɝɪɚɰɢɢ ɍȼ, ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɩɥɨɬɧɟɧɢɹ ɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ, ɷɤɜɢɜɚɥɟɧɬɧɨ ɜɵɜɟɞɟɧɢɸ
ɩɨɪɨɜɨɣ ɜɨɞɵ (Ungerer, 1993)), ɚ ɜ ɫɥɭɱɚɟ ɝɟɧɟɪɚɰɢɢ ɝɚɡɚ ɜɨɡɧɢɤɚɸɳɢɣ ɩɪɢ ɷɬɨɦ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ
ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɨɛɟɫɩɟɱɢɜɚɟɬ ɧɟɦɟɞɥɟɧɧɵɣ ɜɵɜɨɞ ɜɧɨɜɶ ɨɛɪɚɡɭɸɳɟɝɨɫɹ ɮɥɸɢɞɚ ɢɡ
ɨɛɴɟɦɚ, ɝɞɟ ɨɧ ɝɟɧɟɪɢɪɭɟɬɫɹ – ɩɟɪɜɢɱɧɭɸ ɍȼ-ɦɢɝɪɚɰɢɸ (ɀɭɡɟ, 1986). ɉɨɷɬɨɦɭ ɹɜɥɟɧɢɟ ɍȼ-ɝɟɧɟɪɚɰɢɢ
ɞɨɥɠɧɨ ɭɱɢɬɵɜɚɬɶɫɹ ɩɪɢ ɚɧɚɥɢɡɟ ɞɢɧɚɦɢɤɢ ɛɚɥɚɧɫɚ ɦɚɫɫ, ɧɨ ɧɟ ɜɨɡɦɭɳɚɟɬ ɬɪɟɧɞɚ ɧɨɪɦɚɥɶɧɨɝɨ
ɭɩɥɨɬɧɟɧɢɹ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɛɚɥɚɧɫ ɦɚɫɫ ɜ ɩɪɨɢɡɜɨɥɶɧɨɦ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɦ ɨɛɴɟɦɟ U ɤɨɧɬɪɨɥɢɪɭɟɬɫɹ
ɫɤɨɪɨɫɬɶɸ ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɩɨɬɨɤɚ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɨɤɚɥɶɧɨɣ, ɞɜɢɠɭɳɟɣɫɹ ɫɢɫɬɟɦɵ
ɤɨɨɪɞɢɧɚɬ ɜ ɤɚɠɞɵɣ ɬɟɤɭɳɢɣ ɦɨɦɟɧɬ ɢɫɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ, ɬ.ɟ. ɞɥɹ ɤɚɠɞɨɝɨ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɩɨɥɨɠɟɧɢɹ
ɷɥɟɦɟɧɬɚ U ɧɚ ɜɧɟɲɧɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
ɉɪɟɠɞɟ, ɱɟɦ ɡɚɩɢɫɚɬɶ ɢɫɯɨɞɧɵɟ ɭɪɚɜɧɟɧɢɹ, ɧɟɨɛɯɨɞɢɦɨ ɭɞɨɜɥɟɬɜɨɪɢɬɶ ɭɫɥɨɜɢɸ 5, ɜɵɞɜɢɧɭɬɨɦɭ
ɜ ɧɚɱɚɥɟ ɪɚɡɞɟɥɚ.
Ɂɞɟɫɶ ɦɵ ɜɵɧɭɠɞɟɧɵ ɜɜɟɫɬɢ ɫɟɪɶɟɡɧɨɟ ɨɝɪɚɧɢɱɟɧɢɟ ɧɚ ɪɚɡɦɟɪɧɨɫɬɶ ɥɨɤɚɥɶɧɨɣ ɦɨɞɟɥɢ ɪɚɡɝɪɭɡɤɢ
ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ, ɱɬɨɛɵ ɨɛɟɫɩɟɱɢɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɟɟ ɢɧɜɟɪɫɢɢ ɜ ɨɛɥɚɫɬɶ ɤɨɧɬɪɨɥɶɧɵɯ ɮɢɡɢɱɟɫɤɢɯ
ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɦɟɧɬɚ U. ɇɟɨɛɯɨɞɢɦɨɫɬɶ ɨɝɪɚɧɢɱɟɧɢɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ ɥɨɤɚɥɶɧɨɣ ɫɢɫɬɟɦɵ
ɬɨɥɶɤɨ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɶɸ ɜɵɬɟɤɚɟɬ ɟɳɟ ɢ ɢɡ ɬɨɝɨ ɮɚɤɬɚ, ɱɬɨ ɡɚɤɨɧɵ ɭɩɥɨɬɧɟɧɢɹ ɞɚɧɵ ɧɚɦ ɜɨ ɜɧɟɲɧɟɣ
ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɬɨɠɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɥɢɲɶ ɨɬ ɝɥɭɛɢɧɵ, ɥɢɛɨ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɫɬɪɟɫɫɚ (Magara, 1978).
ɉɪɢ ɷɬɨɦ ɢɝɧɨɪɢɪɨɜɚɬɶ ɥɚɬɟɪɚɥɶɧɵɟ ɨɬɬɨɤɢ ɢɡ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɨɛɴɟɦɚ ɦɵ ɧɟ ɛɭɞɟɦ, ɧɨ ɥɢɲɶ ɭɣɞɟɦ ɨɬ
ɧɟɜɨɫɫɬɚɧɨɜɢɦɵɯ ɥɚɬɟɪɚɥɶɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɝɨɪɧɨɝɨ ɞɚɜɥɟɧɢɹ. Ⱦɥɹ ɩɪɨɫɬɨɬɵ ɫɬɚɪɬɨɜɵɣ
ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɵɣ ɨɛɴɟɦ ɩɨɦɟɫɬɢɦ ɜ ɜɨɨɛɪɚɠɚɟɦɵɣ ɰɢɥɢɧɞɪ ɫ ɨɫɧɨɜɚɧɢɹɦɢ ɟɞɢɧɢɱɧɨɣ ɩɥɨɳɚɞɢ ɢ
ɜɵɫɨɬɨɣ h. Ɍɨɝɞɚ ɦɟɪɚ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ 'U/U ɛɭɞɟɬ ɫɨɜɩɚɞɚɬɶ ɫ ɦɟɪɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ
96
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɥɢɧɟɣɧɨɝɨ ɫɠɚɬɢɹ 'h/h ɩɨ ɜɟɪɬɢɤɚɥɢ. Ⱦɚɧɧɨɟ ɨɝɪɚɧɢɱɟɧɢɟ ɫɨɜɩɚɞɚɟɬ, ɩɨ ɫɭɳɟɫɬɜɭ, ɫ ɜɜɟɞɟɧɢɟɦ
ɬɪɚɧɫɜɟɪɫɚɥɶɧɨɣ ɢɡɨɬɪɨɩɧɨɫɬɢ ɞɥɹ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ. ɉɪɢ ɷɬɨɦ, ɨɱɟɜɢɞɧɨ, ɥɢɧɟɣɧɚɹ ɩɥɨɬɧɨɫɬɶ ɜɟɳɟɫɬɜɚ
ɱɢɫɥɟɧɧɨ ɫɨɜɩɚɞɚɟɬ ɫ ɨɛɵɱɧɨɣ ɢ ɨɬɥɢɱɚɟɬɫɹ ɥɢɲɶ ɪɚɡɦɟɪɧɨɫɬɶɸ. Ɂɞɟɫɶ ɢ ɞɚɥɟɟ ɦɵ ɧɟ ɛɭɞɟɦ ɞɟɥɚɬɶ
ɪɚɡɥɢɱɢɣ ɦɟɠɞɭ ɥɢɧɟɣɧɨɣ (ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ) ɢ ɨɛɵɱɧɨɣ ɩɥɨɬɧɨɫɬɶɸ.
Ɍɟɩɟɪɶ ɜɵɩɢɲɟɦ ɭɪɚɜɧɟɧɢɹ ɛɚɥɚɧɫɚ ɦɚɫɫ ɜ ɥɨɤɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ
ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɨɛɴɟɦɚ, ɫɥɟɞɭɸɳɟɝɨ ɩɨ ɬɪɚɟɤɬɨɪɢɹɦ ɩɨɝɪɭɠɟɧɢɹ – ɭɩɥɨɬɧɟɧɢɹ – ɮɚɡɨɜɵɯ
ɬɪɚɧɫɮɨɪɦɚɰɢɣ, ɚɩɪɢɨɪɧɨ ɡɚɞɚɧɧɵɯ ɧɚ ɜɧɟɲɧɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɦɚɫɫɚ ɬɜɟɪɞɨɣ ɮɚɡɵ ɩɨɪɨɞɵ ɩɨɬɟɧɰɢɚɥɶɧɨ ɦɨɠɟɬ ɥɢɲɶ ɩɟɪɟɯɨɞɢɬɶ ɜ
ɷɤɜɢɜɚɥɟɧɬɧɭɸ ɦɚɫɫɭ ɠɢɞɤɨɣ ɢɥɢ ɝɚɡɨɨɛɪɚɡɧɨɣ ɮɚɡɵ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɢɫɯɨɞɧɵɣ ɢ ɫɝɟɧɟɪɢɪɨɜɚɧɧɵɣ ɜ
ɩɨɝɪɭɠɚɸɳɟɦɫɹ ɷɥɟɦɟɧɬɟ h ɩɨɪɨɜɵɣ ɮɥɸɢɞ ɦɨɠɟɬ ɩɨɤɢɞɚɬɶ ɨɛɴɟɦ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɢ ɥɚɬɟɪɚɥɶɧɨɦ
(ɪɚɞɢɚɥɶɧɨɦ) ɧɚɩɪɚɜɥɟɧɢɹɯ ɜ ɜɢɞɟ ɩɨɬɨɤɚ Ⱦɚɪɫɢ. ɇɢɤɚɤɢɯ ɩɪɢɜɧɨɫɨɜ ɦɚɫɫ ɜɧɭɬɪɶ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ
ɨɛɴɟɦɚ ɢɡɜɧɟ ɧɟ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ. Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɹ ɤɨɧɫɟɪɜɚɰɢɢ ɦɚɫɫ ɞɥɹ ɫɥɭɱɚɹ n-ɤɨɦɩɨɧɟɧɬɧɨɝɨ
ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɦɨɝɭɬ ɛɵɬɶ ɡɚɩɢɫɚɧɵ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
U0 dh0 / dt = dM0 / dt
d(Qh0S1U1) / dt = dM1 / dt (Qh0 /I ) div(U1q1)
..........................................
d(Qh0Sn-1Un-1) / dt = dMn-1 / dt (Qh0 / I ) div(Un-1qn-1)
d(Qh0Sn Un) / dt = dMn / dt (Qh0 /I ) div(Un qn)
dM0 / dt = dM1 / dt + dM2 / dt + ... + dMn / dt
S1 + S2 + ... + Sn = 1
(5)
Ɂɞɟɫɶ dMn – ɞɢɮɮɟɪɟɧɰɢɚɥ ɦɚɫɫɵ n-ɣ ɤɨɦɩɨɧɟɧɬɵ ɮɥɸɢɞɚ, ɝɟɧɟɪɢɪɭɟɦɨɝɨ ɢɡ ɬɜɟɪɞɨɣ ɮɚɡɵ (0-ɣ ɢɧɞɟɤɫ ɜ
ɭɪɚɜɧɟɧɢɹɯ). Ȼɟɡɪɚɡɦɟɪɧɵɣ ɩɚɪɚɦɟɬɪ Q ɫɜɹɡɚɧ ɫ ɩɨɪɢɫɬɨɫɬɶɸ I ɫɨɨɬɧɨɲɟɧɢɟɦ: Q = I /(1-I). ɋɢɦɜɨɥɵ h0, Sn,
Un, qn ɨɛɨɡɧɚɱɚɸɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: ɜɵɫɨɬɭ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɰɢɥɢɧɞɪɚ, ɧɚɫɵɳɟɧɢɟ, ɩɥɨɬɧɨɫɬɶ (ɤɝ/ɦ3) ɢ
ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ [m/dt] ɩɨɬɨɤɚ n-ɣ ɮɚɡɨɜɨɣ ɤɨɦɩɨɧɟɧɬɵ, ɩɪɢɱɟɦ h0 = h(1-I), ɚ ɟɞɢɧɢɰɚ ɜɪɟɦɟɧɢ dt ɜɵɛɢɪɚɟɬɫɹ
ɡɞɟɫɶ ɢ ɞɚɥɟɟ, ɢɫɯɨɞɹ ɢɡ ɲɚɝɚ ɤɜɚɧɬɨɜɚɧɢɹ ɲɤɚɥɵ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ.
ɉɨɤɨɦɩɨɧɟɧɬɧɨɟ ɢɡɦɟɧɟɧɢɟ ɦɚɫɫɵ ɜ ɷɥɟɦɟɧɬɚɪɧɨɦ ɨɛɴɟɦɟ, ɤɚɤ ɜɢɞɧɨ ɢɡ ɩɟɪɜɵɯ n + 1 ɭɪɚɜɧɟɧɢɣ
ɫɢɫɬɟɦɵ, ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɝɟɧɟɪɚɰɢɨɧɧɨɝɨ ɢ ɦɢɝɪɚɰɢɨɧɧɨɝɨ ɱɥɟɧɚ. ɉɪɢ ɷɬɨɦ ɨɛɳɚɹ ɩɨɬɟɪɹ ɦɚɫɫɵ ɬɜɟɪɞɨɣ
ɮɚɡɵ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɞɨɛɚɜɨɤ ɜɨ ɜɫɟ ɦɟɧɟɟ ɩɥɨɬɧɵɟ ɮɚɡɵ. ɇɚɤɨɧɟɰ, ɫɭɦɦɚ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɜɤɥɚɞɨɜ ɤɚɠɞɨɣ
ɤɨɦɩɨɧɟɧɬɵ ɜ ɦɧɨɝɨɮɚɡɧɵɣ ɫɨɫɬɚɜ ɮɥɸɢɞɚ ɩɨɫɬɨɹɧɧɚ ɢ ɪɚɜɧɚ ɟɞɢɧɢɰɟ.
Ɏɨɪɦɚɥɶɧɨ ɤ ɹɜɥɟɧɢɹɦ ɤɨɧɜɟɪɫɢɢ ɬɜɟɪɞɨɣ ɮɚɡɵ ɜ ɩɨɪɨɜɵɣ ɮɥɸɢɞ ɨɬɧɨɫɹɬɫɹ ɥɸɛɵɟ
ɞɢɚɝɟɧɟɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɦɢɧɟɪɚɥɶɧɨɝɨ ɫɤɟɥɟɬɚ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɜ ɷɥɟɦɟɧɬɟ U ɜ ɩɪɨɰɟɫɫɟ ɟɝɨ
ɩɨɝɪɭɠɟɧɢɹ. Ɉɞɧɚɤɨ ɹɜɥɟɧɢɹɦɢ ɞɟɝɢɞɪɚɬɚɰɢɢ ɝɥɢɧɢɫɬɵɯ ɦɢɧɟɪɚɥɨɜ (ɧɚɩɪɢɦɟɪ, ɤɨɧɜɟɪɫɢɢ ɢɥɥɢɬɚ ɜ
ɦɨɧɬɦɨɪɢɥɨɧɢɬ), ɤɨɬɨɪɵɟ ɫɨɩɪɨɜɨɠɞɚɸɬɫɹ ɜɵɫɜɨɛɨɠɞɟɧɢɟɦ ɜɧɭɬɪɢɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣ ɜɨɞɵ, ɦɵ
ɩɪɟɧɟɛɪɟɝɚɟɦ. ɉɪɢ ɷɬɨɦ ɞɟɥɚɟɬɫɹ ɞɨɩɭɳɟɧɢɟ, ɱɬɨ ɩɟɪɟɯɨɞ ɜɨɞɵ ɢɡ ɜɧɭɬɪɢɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣ ɜ ɩɨɪɨɜɭɸ
ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɭɩɥɨɬɧɟɧɢɟɦ ɬɪɚɧɫɮɨɪɦɢɪɨɜɚɧɧɨɝɨ ɦɢɧɟɪɚɥɚ, ɬ.ɟ. ɭɪɚɜɧɟɧɢɟ ɛɚɥɚɧɫɚ ɦɚɫɫ ɧɟ ɧɚɪɭɲɚɟɬɫɹ.
ɑɬɨ ɤɚɫɚɟɬɫɹ ɢɡɦɟɧɟɧɢɹ ɮɥɸɢɞɨɩɪɨɜɨɞɹɳɢɯ ɫɜɨɣɫɬɜ ɦɚɬɪɢɰɵ, ɬɨ ɨɧɢ, ɨɱɟɜɢɞɧɨ, ɭɱɢɬɵɜɚɸɬɫɹ ɬɪɟɧɞɨɦ
ɭɩɥɨɬɧɟɧɢɹ-ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɝɥɢɧɢɫɬɵɯ ɥɢɬɨɬɢɩɨɜ.
ɉɪɢ ɤɨɧɜɟɪɫɢɢ ɠɟ ɱɚɫɬɢ ɛɨɝɚɬɨɣ ɨɪɝɚɧɢɤɨɣ, ɧɟɮɬɟɝɚɡɨɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ ɜ ɠɢɞɤɢɣ ɥɢɛɨ
ɝɚɡɨɨɛɪɚɡɧɵɣ ɭɝɥɟɜɨɞɨɪɨɞ ɜ ɨɛɥɚɫɬɢ ɢɡɦɟɪɹɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ (ɞɚɜɥɟɧɢɹ ɢ ɍȼ-ɧɚɫɵɳɟɧɢɹ) ɩɪɨɢɫɯɨɞɹɬ
ɬɚɤɢɟ ɢɡɦɟɧɟɧɢɹ, ɩɪɟɧɟɛɪɟɱɶ ɤɨɬɨɪɵɦɢ ɧɟɥɶɡɹ (Madatov et al., 1998). Ȼɨɥɟɟ ɬɨɝɨ, ɍȼ-ɝɟɧɟɪɚɰɢɹ ɹɜɥɹɟɬɫɹ
ɩɟɪɜɨɩɪɢɱɢɧɨɣ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɫɤɨɩɥɟɧɢɣ ɧɟɮɬɢ ɢ ɝɚɡɚ ɢ ɫ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɹɜɥɹɟɬɫɹ ɩɪɟɞɦɟɬɨɦ
ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ, ɬ.ɟ. ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɦɨɞɟɥɶ ɩɨɞɥɟɠɢɬ ɤɚɥɢɛɪɨɜɤɟ.
ɑɢɫɥɨ ɤɨɦɩɨɧɟɧɬ ɍȼ ɫɦɟɫɢ ɢ ɢɯ ɩɥɨɬɧɨɫɬɶ, ɜ ɫɥɭɱɚɟ ɡɚɤɪɵɬɨɣ ɞɥɹ ɩɪɢɜɧɨɫɚ ɢɡɜɧɟ
ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɦɚɫɫ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɫɢɫɬɟɦɵ, ɜɨɨɛɳɟ ɝɨɜɨɪɹ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɪɚɤɰɢɨɧɧɵɦ ɫɨɫɬɚɜɨɦ
ɩɟɪɜɢɱɧɨɣ ɍȼ-ɦɢɝɪɚɰɢɢ, ɬ.ɟ. ɬɢɩɨɦ ɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ, ɩɨɫɤɨɥɶɤɭ ɬɹɠɟɥɵɟ ɢ ɥɟɝɤɢɟ ɮɪɚɤɰɢɢ ɍȼ
ɜɡɚɢɦɧɨ ɪɚɫɬɜɨɪɹɸɬɫɹ ɞɪɭɝ ɜ ɞɪɭɝɟ, ɢ ɚɧɚɥɢɡ ɩɥɨɬɧɨɫɬɟɣ ɦɧɨɝɨɮɚɡɧɵɯ ɫɢɫɬɟɦ ɦɨɠɟɬ ɛɵɬɶ ɩɨɫɬɪɨɟɧ ɧɚ
ɡɚɤɨɧɟ "ɢɞɟɚɥɶɧɨɣ ɫɦɟɫɢ" (Aziz, Settari, 1983). C ɬɨɱɤɢ ɡɪɟɧɢɹ ɜɬɨɪɢɱɧɨɣ ɦɢɝɪɚɰɢɢ ɭɞɨɛɧɨ ɪɚɡɥɢɱɚɬɶ
ɥɢɲɶ ɠɢɞɤɭɸ ɢ ɝɚɡɨɨɛɪɚɡɧɭɸ ɮɚɡɵ. Ɍɨɝɞɚ ɫɢɫɬɟɦɚ (5) ɭɩɪɨɳɚɟɬɫɹ ɞɨ ɬɪɟɯ ɤɨɦɩɨɧɟɧɬ: 0 – ɬɜɟɪɞɚɹ ɮɚɡɚ:
ɫɤɟɥɟɬ ɨɫɚɞɨɱɧɨɣ ɩɨɪɨɞɵ, ɜ ɬɨɦ ɱɢɫɥɟ ɜɨɡɦɨɠɧɨ ɫɨɞɟɪɠɚɳɢɣ ɤɨɧɜɟɪɬɢɪɭɟɦɭɸ ɜ ɍȼ ɱɚɫɬɶ – ɤɟɪɨɝɟɧ, 1 –
ɠɢɞɤɚɹ ɮɚɡɚ: ɦɢɧɟɪɚɥɢɡɨɜɚɧɧɚɹ ɩɨɪɨɜɚɹ ɜɨɞɚ, 2 – ɍȼ ɫɦɟɫɶ, ɫɨɞɟɪɠɚɳɚɹ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɝɚɡɨɜɭɸ ɢ
ɧɟɮɬɹɧɭɸ ɤɨɦɩɨɧɟɧɬɭ, ɢɡɦɟɧɱɢɜɚɹ ɩɨ ɩɥɨɬɧɨɫɬɢ ɜ ɫɜɹɡɢ ɫ ɪɚɡɞɟɥɟɧɢɟɦ ɥɟɝɤɢɯ ɢ ɬɹɠɟɥɵɯ ɤɨɦɩɨɧɟɧɬ ɩɪɢ
ɩɚɞɟɧɢɢ ɞɚɜɥɟɧɢɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ.
dh0/dt = h0GG0
d(Qh0 (1-S)U1)/dt = (Qh0/I)div(U1q1)
97
(5*)
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
d(Qh0SU2)/dt = U0 h0GG0 + (Qh0/I)div(U2q2),
ɝɞɟ GG0 – ɬɟɦɩ ɍȼ-ɝɟɧɟɪɚɰɢɢ, ɹɜɥɹɸɳɢɣɫɹ ɛɟɡɪɚɡɦɟɪɧɨɣ (ɤɝ ɫɝɟɧɟɪɢɪɨɜɚɧɧɨɝɨ ɍȼ ɧɚ ɤɝ ɦɚɬɟɪɢɧɫɤɨɣ
ɩɨɪɨɞɵ) ɮɭɧɤɰɢɟɣ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɍȼ-ɩɨɬɟɧɰɢɚɥɚ ɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ (ɩɨɞɪɨɛɧɟɟ ɫɦ. ɪɚɡɞɟɥ 6).
ɉɥɨɬɧɨɫɬɶ ɦɢɧɟɪɚɥɨɝɢɱɟɫɤɨɝɨ ɫɤɟɥɟɬɚ U0 ɩɪɢɧɹɬɚ ɧɟɢɡɦɟɧɧɨɣ, ɬ.ɟ. ɞɢɚɝɟɧɟɬɢɱɟɫɤɢɟ ɢɡɦɟɧɟɧɢɹ
ɬɜɟɪɞɨɣ ɮɚɡɵ ɜ ɩɪɨɰɟɫɫɟ ɩɨɝɪɭɠɟɧɢɹ ɧɟ ɞɨɩɭɫɤɚɸɬɫɹ. ɉɨɷɬɨɦɭ U0 ɜ ɜɟɪɯɧɟɦ ɭɪɚɜɧɟɧɢɢ (5) ɛɵɥɨ
ɜɵɜɟɞɟɧɨ ɢɡ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨ ɜɪɟɦɟɧɢ ɢ ɫɨɤɪɚɳɟɧɨ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɬɟɪɹ ɦɚɫɫɵ ɬɜɟɪɞɨɣ ɮɚɡɵ ɷɥɟɦɟɧɬɚ
U ɞɨɩɭɫɤɚɟɬɫɹ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɍȼ-ɝɟɧɟɪɚɰɢɢ, ɚ ɟɝɨ ɩɥɨɬɧɨɫɬɶ ɜ ɤɚɠɞɨɣ ɬɨɱɤɟ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɵ
ɤɨɨɪɞɢɧɚɬ ɰɟɥɢɤɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɪɢɫɬɨɫɬɶɸ ɦɚɬɪɢɰɵ, ɩɪɢ ɢɡɜɟɫɬɧɵɯ ɩɥɨɬɧɨɫɬɹɯ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ.
ɉɥɨɬɧɨɫɬɶ ɠɢɞɤɨɣ ɢ ɜ ɨɫɨɛɟɧɧɨɫɬɢ ɝɚɡɨɨɛɪɚɡɧɨɣ ɮɚɡ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɦɟɧɹɟɬɫɹ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ
ɞɚɜɥɟɧɢɣ ɢ ɬɟɦɩɟɪɚɬɭɪɵ, ɩɨɷɬɨɦɭ ɜɦɟɫɬɟ ɫ ɭɞɟɥɶɧɵɦ ɧɚɫɵɳɟɧɢɟɦ (Qh0S) ɨɧɢ ɜɜɟɞɟɧɵ ɜ ɩɪɨɢɡɜɨɞɧɭɸ
ɦɚɫɫɵ ɩɨ ɜɪɟɦɟɧɢ.
ɋ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɫɢɫɬɟɦɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (5*), ɨɩɢɫɵɜɚɟɬ ɞɢɧɚɦɢɤɭ ɢɡɦɟɧɟɧɢɹ
ɩɥɨɬɧɨɫɬɢ ɷɥɟɦɟɧɬɚ ɜ ɫɜɹɡɢ ɫ ɦɟɯɚɧɢɡɦɚɦɢ ɩɨɬɟɪɶ ɢ ɝɟɧɟɪɚɰɢɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ. Ⱦɥɹ ɡɚɜɟɪɲɟɧɢɹ
ɩɨɫɬɪɨɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɧɟɨɛɯɨɞɢɦɨ ɞɨɩɨɥɧɢɬɶ ɤɨɧɫɬɪɭɤɰɢɸ (5*) ɭɪɚɜɧɟɧɢɹɦɢ, ɫɜɹɡɵɜɚɸɳɢɦɢ
ɩɥɨɬɧɨɫɬɶ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɢ ɩɨɪɢɫɬɨɫɬɶ ɷɥɟɦɟɧɬɚ U ɫ ɟɝɨ ɩɨɥɨɠɟɧɢɟɦ ɜɨ ɜɧɟɲɧɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɪɟɧɞɵ ɭɩɥɨɬɧɟɧɢɣ ɮɥɸɢɞɚ ɢ ɦɚɬɪɢɰɵ ɹɜɥɹɸɬɫɹ ɷɦɩɢɪɢɱɟɫɤɨɣ ɨɫɧɨɜɨɣ ɩɨɫɬɪɨɟɧɢɹ
ɩɪɹɦɨɣ ɡɚɞɚɱɢ, ɚ ɤɚɥɢɛɪɨɜɤɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɨɧɫɬɚɧɬ – ɩɪɟɞɦɟɬɨɦ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ. ɉɪɢ ɷɬɨɦ
ɱɚɫɬɶ ɤɨɧɫɬɚɧɬ ɦɨɠɟɬ ɛɵɬɶ ɚɩɪɢɨɪɧɨ ɢɡɜɟɫɬɧɚ ɧɚɫɬɨɥɶɤɨ ɬɨɱɧɨ, ɱɬɨ ɜ ɩɪɟɞɟɥɚɯ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɢ ɨɛɪɚɬɧɨɣ
ɡɚɞɚɱɢ ɧɟ ɩɨɬɪɟɛɭɟɬ ɤɚɥɢɛɪɨɜɤɢ.
ɉɥɨɬɧɨɫɬɶ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ, ɤɚɤ ɮɭɧɤɰɢɹ ɩɨɪɨɜɨɝɨ ɞɚɜɥɟɧɢɹ (Ɋ) ɢ ɬɟɦɩɟɪɚɬɭɪɵ (Ɍ)
ɤɨɧɬɪɨɥɢɪɭɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɮɚɡɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɭɪɚɜɧɟɧɢɟɦ ɫɨɫɬɨɹɧɢɹ (Verweij, 1993; Bear,
Bachmat, 1991), ɤɨɬɨɪɨɟ ɜ ɥɢɧɟɣɧɨɣ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
Uj dUj / dt = Jj dP / dt Ej dT / dt.
(6)
ɂɡɨɬɟɪɦɢɱɟɫɤɢɟ ɤɨɧɫɬɚɧɬɵ ɫɠɢɦɚɟɦɨɫɬɢ (J) ɢ ɢɡɨɛɚɪɢɱɟɫɤɢɟ ɤɨɧɫɬɚɧɬɵ ɪɚɫɲɢɪɟɧɢɹ (E) ɞɨɫɬɚɬɨɱɧɨ
ɭɫɬɨɣɱɢɜɵ ɢ ɯɨɪɨɲɨ ɢɡɭɱɟɧɵ ɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢ ɩɥɚɫɬɨɜɵɯ ɭɫɥɨɜɢɹɯ.
Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɟɩɪɟɪɵɜɧɨɫɬɢ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵ (5*) ɧɟɨɛɯɨɞɢɦɨ, ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ,
ɢɫɤɥɸɱɢɬɶ ɨɫɨɛɵɟ ɬɨɱɤɢ ɜɨ ɜɧɟɲɧɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɝɞɟ ɜɨɡɦɨɠɧɵ ɪɚɡɪɵɜɵ 1-ɝɨ ɩɨɪɹɞɤɚ ɜ
ɩɨɜɟɞɟɧɢɢ ɩɥɨɬɧɨɫɬɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ. Ɋɚɡɪɵɜɧɵɟ ɫɢɬɭɚɰɢɢ ɜɨɡɧɢɤɚɸɬ ɩɪɢ ɮɚɡɨɜɵɯ ɩɪɟɜɪɚɳɟɧɢɹɯ ɢ
ɨɬɦɟɱɚɸɬɫɹ ɤɪɢɬɢɱɟɫɤɢɦɢ ɬɨɱɤɚɦɢ ɧɚ ɞɢɚɝɪɚɦɦɚɯ ɮɚɡɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ. ȼ ɱɚɫɬɧɨɫɬɢ, ɨɧɢ ɢɦɟɸɬ ɦɟɫɬɨ
ɩɪɢ ɤɪɟɤɢɧɝɟ ɧɟɮɬɢ ɜ ɝɚɡ ɥɢɛɨ ɩɪɢ ɜɵɞɟɥɟɧɢɢ ɥɟɝɤɢɯ ɍȼ ɮɪɚɤɰɢɣ ɢɡ ɪɚɫɬɜɨɪɚ ɜ ɜɢɞɟ ɫɜɨɛɨɞɧɨɝɨ ɝɚɡɚ
(ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɝɟɨɥɨɝɢɢ..., 1984). ɂɡɦɟɧɟɧɢɹ ɠɟ ɩɥɨɬɧɨɫɬɢ ɨɬɞɟɥɶɧɨ ɠɢɞɤɨɣ ɢ ɝɚɡɨɨɛɪɚɡɧɨɣ ɤɨɦɩɨɧɟɧɬ
ɍȼ ɧɚ ɩɥɨɫɤɨɫɬɢ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɩɪɨɢɫɯɨɞɹɬ ɝɥɚɞɤɨ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ
ɧɟɩɪɟɪɵɜɧɨɫɬɢ ɪɟɲɟɧɢɹ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɨɛɯɨɞɢɦɨ ɞɨɩɨɥɧɢɬɶ ɭɪɚɜɧɟɧɢɹ (5*-6) ɞɢɚɝɪɚɦɦɨɣ ɩɪɟɞɟɥɶɧɨɝɨ
ɧɚɫɵɳɟɧɢɹ ɩɨɪɨɜɨɣ ɠɢɞɤɨɫɬɢ ɝɚɡɨɦ (ɫɦ., ɧɚɩɪɢɦɟɪ, ɧɨɦɨɝɪɚɦɦɵ Ⱦɠ. Ⱥɦɢɤɫɚ: ɋɩɪɚɜɨɱɧɢɤ ɩɨ
ɝɟɨɥɨɝɢɢ..., 1984) ɢ ɤɨɧɬɪɨɥɢɪɨɜɚɬɶ ɟɟ ɩɟɪɟɫɟɱɟɧɢɟ ɫ ɤɪɢɜɨɣ ɬɟɤɭɳɟɝɨ ɧɚɫɵɳɟɧɢɹ ɝɚɡɨɦ ɜ ɥɸɛɨɣ
ɩɪɨɢɡɜɨɥɶɧɨɣ ɬɨɱɤɟ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ. Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨ ɷɬɨɬ ɜɨɩɪɨɫ ɨɫɜɟɳɚɟɬɫɹ ɜ
ɫɥɟɞɭɸɳɟɦ ɪɚɡɞɟɥɟ.
ɉɨɪɢɫɬɨɫɬɶ ɷɥɟɦɟɧɬɚ U ɦɨɠɟɬ ɩɪɟɬɟɪɩɟɜɚɬɶ ɢɡɦɟɧɟɧɢɹ ɧɚ ɬɪɚɟɤɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ: ɩɪɢ ɟɝɨ
ɭɩɥɨɬɧɟɧɢɢ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɫɬɪɟɫɫɚ V ɢ/ɢɥɢ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ ɩɨɪɢɫɬɨɫɬɶ ɫɨɤɪɚɳɚɟɬɫɹ, ɚ ɩɪɢ ɤɨɧɜɟɪɫɢɢ
ɱɚɫɬɢ ɦɢɧɟɪɚɥɶɧɨɣ ɦɚɬɪɢɰɵ ɜ ɝɟɨɮɥɸɢɞɚɥɶɧɭɸ ɮɚɡɭ (GG0) – ɭɜɟɥɢɱɢɜɚɟɬɫɹ. ȼ ɫɚɦɨɦ ɨɛɳɟɦ ɜɢɞɟ:
dQ / dt = 1/ (1 I)2 [(1 I)GG0 dI(V,T) / dt].
(7)
Ɍɪɟɧɞɵ ɧɨɪɦɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ ɦɚɬɪɢɰ, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɯ ɥɢɬɨɬɢɩɚ, ɫɨɜɦɟɫɬɧɨ ɫ ɬɪɟɧɞɚɦɢ
ɩɪɨɧɢɰɚɟɦɨɫɬɟɣ ɮɨɪɦɢɪɭɸɬ ɨɛɨɛɳɟɧɧɵɟ ɦɨɞɟɥɢ ɭɩɥɨɬɧɟɧɢɹ, ɤɨɬɨɪɵɟ ɚɧɚɥɢɡɢɪɭɸɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ ɪɚɡɞɟɥɟ.
Ɍɟɦɩ ɝɟɧɟɪɚɰɢɢ ɍȼ ɜ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɦɨɞɟɥɢ Ɍɢɫɫɨ ɩɨɞɪɨɛɧɟɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɜ ɪɚɡɞɟɥɟ 6.
4. Ɇɨɞɟɥɶ ɭɩɥɨɬɧɟɧɢɹ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ
ȼ ɞɚɧɧɨɣ ɦɨɞɟɥɢ ɩɨɪɨɜɵɣ ɮɥɸɢɞ ɛɭɞɟɬ ɩɪɟɞɫɬɚɜɥɹɬɶɫɹ ɦɢɧɟɪɚɥɢɡɨɜɚɧɧɨɣ ɜɨɞɨɣ, ɧɚɫɵɳɟɧɧɨɣ ɜ
ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɟɤɨɬɨɪɨɣ ɦɚɫɫɨɣ ɭɝɥɟɜɨɞɨɪɨɞɨɜ. Ɋɚɫɬɜɨɪɟɧɢɟ ɩɨɫɥɟɞɧɢɯ ɜ ɜɨɞɟ ɤɨɧɬɪɨɥɢɪɭɟɬɫɹ ɤɪɢɜɨɣ
ɩɪɟɞɟɥɶɧɨɝɨ ɧɚɫɵɳɟɧɢɹ ɪɚɫɬɜɨɪɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ (ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɝɟɨɥɨɝɢɢ...,
1984). Ɏɢɡɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɨɪɨɜɨɝɨ ɪɚɫɬɜɨɪɚ, ɨɤɚɡɵɜɚɸɳɢɟ ɜɥɢɹɧɢɟ ɧɚ ɟɝɨ ɩɥɨɬɧɨɫɬɶ, ɜ ɩɪɚɤɬɢɤɟ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɡɚɤɨɧɭ "ɢɞɟɚɥɶɧɨɣ ɫɦɟɫɢ", ɬ.ɟ. ɫɭɦɦɨɣ ɫɜɨɣɫɬɜ ɱɢɫɬɵɯ ɤɨɦɩɨɧɟɧɬɨɜ, ɜɡɜɟɲɟɧɧɨɣ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɞɨɩɪɟɞɟɥɶɧɵɦɢ ɧɚɫɵɳɟɧɢɹɦɢ.
98
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɉɥɨɬɧɨɫɬɶ ɥɸɛɨɣ "ɱɢɫɬɨɣ" (ɛɟɡ ɪɚɫɬɜɨɪɟɧɧɵɯ ɩɪɢɦɟɫɟɣ)
ɠɢɞɤɨɣ ɮɚɡɵ ɨɩɪɟɞɟɥɹɟɬɫɹ, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ,
ɱɟɪɟɡ ɤɨɷɮɮɢɰɢɟɧɬɵ ɢɡɨɛɚɪɢɱɟɫɤɨɝɨ ɬɟɪɦɚɥɶɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɢ
ɢɡɨɬɟɪɦɚɥɶɧɨɣ ɫɠɢɦɚɟɦɨɫɬɢ ɩɨɞ ɞɚɜɥɟɧɢɟɦ (ɫɦ. ɬɚɛɥ. 1). Ⱦɥɹ
ɩɥɨɬɧɨɫɬɢ ɠɢɞɤɨɣ ɮɚɡɵ ɜ "ɪɚɛɨɱɟɦ" ɞɢɚɩɚɡɨɧɟ ɡɧɚɱɟɧɢɣ ɮɢɡɢɱɟɫɤɢɯ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɫɚɞɨɱɧɨɝɨ ɛɚɫɫɟɣɧɚ (Z = 0-5ɤɦ; T = 10-200qɋ; P = 0.150 Mɉɚ) ɞɨɫɬɚɬɨɱɧɨ ɬɨɱɧɚ ɥɢɧɟɣɧɚɹ ɦɨɞɟɥɶ ɜɢɞɚ
U1(P,T) = U1(P0,T0) [1+E1(T T0) + J1(P P0)],
Ɋɢɫ. 3. Ɂɚɜɢɫɢɦɨɫɬɶ ɩɥɨɬɧɨɫɬɢ
ɩɨɪɨɜɨɣ ɜɨɞɵ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɢ
ɪɚɡɥɢɱɧɵɯ
ɚɩɩɪɨɤɫɢɦɚɰɢɹɯ
ɨɛɴɟɦɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ
1 – ɩɚɪɚɛɨɥɢɱɟɫɤɚɹ:
E1 = (25.9 8.38T + 0.445T 2) 10-4
2 – ɩɚɪɚɛɨɥɢɱɟɫɤɚɹ ɫ ɩɨɩɪɚɜɤɨɣ
ɧɚ ɦɢɧɟɪɚɥɢɡɚɰɢɸ
3 – ɥɢɧɟɣɧɚɹ: E1 = 4.95 10-4T
(8)
ɝɞɟ Ɋ0, Ɍ0 – ɧɟɤɨɬɨɪɵɟ ɧɨɪɦɚɥɶɧɵɟ ɭɫɥɨɜɢɹ, ɜ ɤɨɬɨɪɵɯ ɞɨɫɬɭɩɧɵ
ɦɚɫɫɨɜɵɟ ɢɡɦɟɪɟɧɢɹ (ɧɢɠɟ ɜ ɪɚɫɱɟɬɚɯ P0 = 0.1 Mɉɚ, T0 = 15qC).
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɥɨɬɧɨɫɬɢ "ɱɢɫɬɨɣ" ɝɚɡɨɜɨɣ ɮɚɡɵ
ɢɫɩɨɥɶɡɭɟɬɫɹ ɭɪɚɜɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ (Denesh, 1998) ɫ
ɩɨɩɪɚɜɤɨɣ ɡɚ "ɧɟɢɞɟɚɥɶɧɨɟ" ɩɨɜɟɞɟɧɢɟ ɩɨɞ ɞɚɜɥɟɧɢɟɦ (Z-ɮɚɤɬɨɪ, ɩɨ
Ʉɚɰɭ – ɫɦ. ɪɢɫ. 5. ȼ ɮɨɪɦɭɥɟ (8*) ɨɧ ɨɛɨɡɧɚɱɟɧ ɱɟɪɟɡ O):
U2(P,T) = U2(P0,T0)[ (P/P0) (T0/OT) ].
(8*)
ȼ ɩɪɢɪɨɞɧɵɯ ɭɫɥɨɜɢɹɯ, ɨɞɧɚɤɨ, "ɱɢɫɬɵɟ" ɮɚɡɵ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɧɟ
ɧɚɛɥɸɞɚɸɬɫɹ. ɉɨɪɨɜɚɹ ɜɨɞɚ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɝɥɭɛɢɧɵ ɦɢɧɟɪɚɥɢɡɭɟɬɫɹ. ɉɪɢ
ɷɬɨɦ ɪɚɡɭɩɥɨɬɧɟɧɢɟ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɱɚɫɬɢɱɧɨ ɤɨɦɩɟɧɫɢɪɭɟɬ
ɷɬɨɬ ɷɮɮɟɤɬ. ȼ ɢɬɨɝɟ ɥɢɧɟɣɧɚɹ ɦɨɞɟɥɶ (8) ɨɤɚɡɵɜɚɟɬɫɹ ɞɚɠɟ ɬɨɱɧɟɟ, ɱɟɦ
ɩɚɪɚɛɨɥɢɱɟɫɤɚɹ (ɪɢɫ. 3).
Ʉɨɦɩɨɧɟɧɬɧɵɣ ɫɨɫɬɚɜ ɍȼ-ɫɦɟɫɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɢɩɨɦ
ɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ (ɫɦ. ɪɚɡɞɟɥ 6). ɉɪɢ ɷɬɨɦ ɠɢɞɤɚɹ ɮɚɡɚ
(ɧɟɮɬɶ) ɫɨɞɟɪɠɢɬ ɬɟɦ ɛɨɥɶɲɟ ɪɚɫɬɜɨɪɟɧɧɵɯ ɥɟɝɤɢɯ ɮɪɚɤɰɢɣ, ɱɟɦ
ɜɵɲɟ ɩɥɚɫɬɨɜɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɢ ɝɟɨɮɥɸɢɞɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ (Aziz,
Settari, 1983). ɇɚɥɢɱɢɟ ɢ ɫɨɫɬɚɜ ɫɜɨɛɨɞɧɨɝɨ ɝɚɡɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɢ
ɩɨɦɨɳɢ ɧɨɦɨɝɪɚɦɦ ɩɪɟɞɟɥɶɧɨɣ ɪɚɫɬɜɨɪɢɦɨɫɬɢ (ɧɚɩɪ.,
ɧɨɦɨɝɪɚɦɦɵ Ⱦɠ. Ⱥɦɢɤɫɚ: ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɝɟɨɥɨɝɢɢ..., 1984).
ɉɪɢɦɟɪ ɩɨ ɩɪɟɞɟɥɶɧɨɦɭ ɫɨɞɟɪɠɚɧɢɸ ɦɟɬɚɧɚ ɜ "ɱɟɪɧɨɣ" ɧɟɮɬɢ
ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 4. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɥɨɬɧɨɫɬɶ ɧɟɮɬɢ ɢ ɝɚɡɚ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɦɩɨɧɟɧɬɧɨɝɨ ɫɨɫɬɚɜɚ ɩɨ ɡɚɤɨɧɭ
"ɢɞɟɚɥɶɧɨɣ ɫɦɟɫɢ".
Ɋɢɫ. 4. Ɋɚɫɬɜɨɪɢɦɨɫɬɶ ɦɟɬɚɧɚ ɜ ɬɹɠɟɥɨɣ
ɏɚɪɚɤɬɟɪ ɩɨɜɟɞɟɧɢɹ ɩɥɨɬɧɨɫɬɟɣ ɩɨɪɨɜɨɣ ɜɨɞɵ, ɧɟɮɬɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɚɜɥɟɧɢɹ ɩɪɢ
"ɱɟɪɧɨɣ" ɧɟɮɬɢ ɢ ɝɚɡɚ (ɦɟɬɚɧɚ) ɫ ɝɥɭɛɢɧɨɣ ɥɟɝɤɨ ɨɰɟɧɢɬɶ, ɪɚɡɥɢɱɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ (ɱɢɫɥɚ ɭ ɤɪɢɜɵɯ).
ɢɫɩɨɥɶɡɭɹ ɥɢɧɟɣɧɨɟ ɧɚɪɚɫɬɚɧɢɟ ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ ɢ ɂɫɩɨɥɶɡɨɜɚɧɚ ɩɚɪɚɛɨɥ. ɚɩɩɪɨɤɫɢɦɚɰɢɹ
ɬɟɦɩɟɪɚɬɭɪɵ ɫ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɢɦ ɝɪɚɞɢɟɧɬɨɦ 10006.2 ɉɚ/ɦ ɢ ɞɚɧɧɵɯ ɩɨ ɧɨɦɨɝɪɚɦɦɟ Ⱦɠ. Ⱥɦɢɤɫɚ
(ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɝɟɨɥɨɝɢɢ..., 1984)
ɬɟɦɩɟɪɚɬɭɪɧɵɦ ɝɪɚɞɢɟɧɬɨɦ 0.03qC/ɦ.
Ɋɢɫ. 5.
Ɂɚɜɢɫɢɦɨɫɬɶ
Z-ɮɚɤɬɨɪɚ
(ɤɨɷɮ-ɬɚ
ɫɠɢɦɚɟɦɨɫɬɢ) ɞɥɹ ɦɟɬɚɧɚ ɨɬ ɝɟɨɮɥɸɢɞɚɥɶɧɨɝɨ
ɞɚɜɥɟɧɢɹ.
ɂɫɩɨɥɶɡɨɜɚɧɚ
ɩɚɪɚɛɨɥɢɱɟɫɤɚɹ
ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɩɨ ɞɚɧɧɵɦ D. Bus, R. Witing, 1962 (ɫɦ.
Denesh, 1998)
Ɋɢɫ. 6. ɉɨɜɟɞɟɧɢɟ ɩɥɨɬɧɨɫɬɟɣ ɪɚɡɥɢɱɧɵɯ ɮɚɡɨɜɵɯ
ɤɨɦɩɨɧɟɧɬ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ (ɦɢɧɟɪɚɥɢɡɨɜɚɧɧɚɹ
ɜɨɞɚ, ɬɹɠɟɥɚɹ ɧɟɮɬɶ, ɦɟɬɚɧ) ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɝɥɭɛɢɧɵ
ɩɪɢ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɦ ɞɚɜɥɟɧɢɢ ɢ ɬɟɦɩɟɪɚɬɭɪɧɨɦ
ɝɪɚɞɢɟɧɬɟ 0.03qC/ɦ
Ʉɚɤ ɜɢɞɧɨ ɢɡ ɪɢɫ. 6, ɩɨ ɦɟɪɟ ɧɚɪɚɫɬɚɧɢɹ ɞɚɜɥɟɧɢɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɩɥɨɬɧɨɫɬɶ ɧɟɮɬɢ ɩɪɢɛɥɢɠɚɟɬɫɹ
ɤ ɩɥɨɬɧɨɫɬɢ "ɫɭɯɨɝɨ" ɝɚɡɚ ɡɚ ɫɱɟɬ ɪɚɫɬɜɨɪɟɧɢɹ ɜɫɟ ɛɨɥɶɲɟɣ ɨɛɴɟɦɧɨɣ ɞɨɥɢ ɥɟɝɤɢɯ ɮɪɚɤɰɢɣ.
Ɋɚɡɭɩɥɨɬɧɟɧɢɟ ɜɨɞɵ ɩɨ ɦɟɪɟ ɬɟɪɦɚɥɶɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɢ ɪɚɫɬɜɨɪɟɧɢɹ ɜ ɧɟɣ ɱɚɫɬɢ ɭɝɥɟɜɨɞɨɪɨɞɨɜ
99
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɤɨɦɩɟɧɫɢɪɨɜɚɧɨ ɩɨɜɵɲɟɧɢɟɦ ɦɢɧɟɪɚɥɢɡɚɰɢɢ ɢ ɩɨɷɬɨɦɭ ɧɟ ɫɬɨɥɶ ɡɚɦɟɬɧɨ. Ɍɚɤɚɹ ɬɟɧɞɟɧɰɢɹ ɫɨɯɪɚɧɹɟɬɫɹ
ɞɥɹ ɥɸɛɨɝɨ ɤɨɦɩɨɧɟɧɬɧɨɝɨ ɫɨɫɬɚɜɚ ɝɟɨɮɥɸɢɞɚɥɶɧɨɣ ɫɦɟɫɢ.
Ɍɚɛɥɢɰɚ 1. Ɏɢɡɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɩɨɪɨɜɨɣ ɠɢɞɤɨɫɬɢ (ɩɨ ɞɚɧɧɵɦ: ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɝɟɨɥɨɝɢɢ..., 1984)
ɋɜɨɣɫɬɜɨ
Ʉɨɷɮɮ. ɢɡɨɛɚɪɢɱɟɫɤɨɝɨ ɬɟɪɦɚɥɶɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ
Ʉɨɷɮɮ. ɢɡɨɬɟɪɦɚɥɶɧɨɣ ɫɠɢɦɚɟɦɨɫɬɢ ɩɨɞ ɞɚɜɥɟɧɢɟɦ
ɉɥɨɬɧɨɫɬɶ ɩɪɢ ɧ.ɭ.
ɒɤɚɥɚ
1/qɋ
1/ɉɚ
ɤɝ/ɦ3
ɉɨɪɨɜɚɹ ɜɨɞɚ
5  10-4
4.78  10-10
1020
"ɑɟɪɧɚɹ" ɧɟɮɬɶ
7.2  10-4
3.2  10-10
850
5. Ɉɛɨɛɳɟɧɧɚɹ 1.5D ɦɨɞɟɥɶ ɭɩɥɨɬɧɟɧɢɹ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ ɩɨɪɨɞɵ
Ɇɨɞɟɥɢ ɭɩɥɨɬɧɟɧɢɹ ɨɫɚɞɨɱɧɵɯ ɝɨɪɧɵɯ ɩɨɪɨɞ, ɤɚɤ ɩɪɚɜɢɥɨ, ɩɪɟɞɫɬɚɜɥɹɸɬɫɹ ɷɦɩɢɪɢɱɟɫɤɢɦɢ
ɡɚɜɢɫɢɦɨɫɬɹɦɢ ɩɨɪɢɫɬɨɫɬɢ ɜɵɛɪɚɧɧɨɝɨ ɥɢɬɨɥɨɝɢɱɟɫɤɨɝɨ ɨɛɴɟɤɬɚ (ɥɢɬɨɬɢɩɚ) ɨɬ ɝɥɭɛɢɧɵ, ɫɬɪɟɫɫɚ ɢ/ɢɥɢ
ɬɟɦɩɟɪɚɬɭɪɵ (Magara, 1978). ɂɡɜɟɫɬɧɨ, ɱɬɨ ɞɚɠɟ ɜɟɫɶɦɚ ɫɥɨɠɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ, ɤɨɦɛɢɧɢɪɭɸɳɢɟ ɷɮɮɟɤɬɵ
ɦɟɯɚɧɢɱɟɫɤɢɯ (ɩɥɚɫɬɢɱɟɫɤɚɹ ɞɟɮɨɪɦɚɰɢɹ, ɪɚɫɬɪɟɫɤɢɜɚɧɢɟ, ɢ ɬ.ɞ.) ɢ ɞɢɚɝɟɧɟɬɢɱɟɫɤɢɯ (ɰɟɦɟɧɬɚɰɢɹ,
ɞɟɝɢɞɪɚɬɚɰɢɹ ɝɥɢɧɢɫɬɵɯ ɦɢɧɟɪɚɥɨɜ, ɪɚɫɬɜɨɪɟɧɢɟ ɩɨɞ ɞɚɜɥɟɧɢɟɦ ɢ ɬ.ɞ.) ɩɪɨɰɟɫɫɨɜ, ɩɪɢɜɨɞɹɳɢɯ ɤ
ɡɚɤɨɧɨɦɟɪɧɵɦ ɢɡɦɟɧɟɧɢɹɦ ɩɥɨɬɧɨɫɬɢ ɩɨɪɨɞ, ɡɚɜɟɞɨɦɨ ɹɜɥɹɸɬɫɹ ɭɩɪɨɳɟɧɢɟɦ ɪɟɚɥɶɧɵɯ ɩɪɨɰɟɫɫɨɜ,
ɩɪɨɬɟɤɚɸɳɢɯ ɧɚ ɦɢɤɪɨɭɪɨɜɧɟ (ɧɚ ɭɪɨɜɧɟ ɩɨɪ) (Verweij, 1993; Schneider et al., 1994).
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɪɚɡɛɪɨɫ ɞɚɧɧɵɯ ɩɨɥɟɜɵɯ ɢ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɡɦɟɪɟɧɢɣ ɩɨɪɢɫɬɨɫɬɢ ɢ ɫɜɹɡɚɧɧɵɯ ɫ
ɧɟɣ ɩɚɪɚɦɟɬɪɨɜ (ɝɥɢɧɢɫɬɨɫɬɶ, ɬɪɟɳɢɧɨɜɚɬɨɫɬɶ, ɤɚɥɶɰɢɬɢɡɚɰɢɹ ɢ ɬ.ɩ.) ɧɟ ɩɨɡɜɨɥɹɟɬ ɤɚɥɢɛɪɨɜɚɬɶ ɛɨɥɟɟ
ɫɥɨɠɧɵɟ ɦɨɞɟɥɢ, ɱɟɦ ɫɬɚɜɲɢɟ ɤɥɚɫɫɢɱɟɫɤɢɦɢ ɬɪɟɧɞɵ ɭɩɥɨɬɧɟɧɢɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɝɥɭɛɢɧɵ.
ȼ ɩɪɢɥɨɠɟɧɢɢ ɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɡɚɞɚɱɟ ɦɵ ɛɭɞɟɦ ɬɪɚɤɬɨɜɚɬɶ ɬɟɪɦɢɧ "Ɉɛɨɛɳɟɧɧɚɹ ɦɨɞɟɥɶ
ɭɩɥɨɬɧɟɧɢɹ" ɧɟɫɤɨɥɶɤɨ ɲɢɪɟ, ɱɟɦ ɜ ɫɬɚɧɞɚɪɬɧɨɦ ɩɨɞɯɨɞɟ (Magara, 1978), ɩɨɧɢɦɚɹ ɩɨɞ ɧɢɦ ɜɫɸ
ɫɨɜɨɤɭɩɧɨɫɬɶ ɩɪɨɰɟɫɫɨɜ, ɫɜɹɡɚɧɧɭɸ ɫ ɜɵɜɟɞɟɧɢɟɦ ɢɡɧɚɱɚɥɶɧɨɝɨ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɢɡ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ
ɨɛɴɟɦɚ ɜ ɩɪɨɰɟɫɫɟ ɟɝɨ ɩɪɨɞɜɢɠɟɧɢɹ ɩɨ ɷɜɨɥɸɰɢɨɧɧɨɣ ɬɪɚɟɤɬɨɪɢɢ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ.
Ɉɱɟɜɢɞɧɨ, ɷɬɚ ɫɨɜɨɤɭɩɧɨɫɬɶ ɜɤɥɸɱɚɟɬ ɦɚɤɪɨɦɟɯɚɧɢɡɦɵ ɩɨɬɟɪɢ ɩɨɪɢɫɬɨɫɬɢ ɫ ɝɥɭɛɢɧɨɣ (ɬɪɟɧɞɵ
"ɧɨɪɦɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ") ɢ ɦɟɯɚɧɢɡɦɵ ɦɢɝɪɚɰɢɢ ɮɥɸɢɞɚ, ɤɨɬɨɪɵɟ ɨɩɢɫɵɜɚɸɬɫɹ ɞɢɜɟɪɝɟɧɰɢɟɣ ɩɨɬɨɤɚ
ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɜ ɥɨɤɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ "ɧɨɪɦɚɥɶɧɨɟ ɭɩɥɨɬɧɟɧɢɟ" ɨɫɚɞɨɱɧɨɣ ɩɨɪɨɞɵ, ɤɨɬɨɪɨɟ ɹɜɥɹɟɬɫɹ
ɩɪɟɞɦɟɬɨɦ ɷɦɩɢɪɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ, ɩɪɟɞɩɨɥɚɝɚɟɬ ɜɵɬɟɫɧɟɧɢɟ ɢɡ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɦɚɬɪɢɰɵ
ɩɨɪɨɞɵ ɧɟɫɠɢɦɚɟɦɨɝɨ ɮɥɸɢɞɚ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɫɬɪɟɫɫɚ ɞɨ ɞɨɫɬɢɠɟɧɢɹ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɝɨ
ɪɚɜɧɨɜɟɫɢɹ. ɋɚɦ ɫɤɟɥɟɬ (ɦɚɬɪɢɰɚ ɩɨɪɨɞɵ) ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɧɟɫɠɢɦɚɟɦɵɦ. ɉɪɢ ɷɬɨɦ, ɪɟɡɭɥɶɬɚɬ – ɡɧɚɱɟɧɢɟ
ɩɨɪɢɫɬɨɫɬɢ ɧɚ ɞɚɧɧɨɣ ɝɥɭɛɢɧɟ – ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɪɚɟɤɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɨɛɴɟɦɚ ɜ
ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɢɲɶ ɟɝɨ ɥɢɬɨɬɢɩɨɦ.
ɂɫɫɥɟɞɨɜɚɧɢɹ ɧɚ ɨɛɪɚɡɰɚɯ (Schneider et al., 1994) ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɪɚɡɝɪɭɡɤɚ ɜɟɪɬɢɤɚɥɶɧɨɝɨ
ɫɬɪɟɫɫɚ, ɜɨɡɧɢɤɚɸɳɚɹ ɜɫɥɟɞɫɬɜɢɟ ɩɨɞɴɟɦɚ ɞɧɚ ɛɚɫɫɟɣɧɚ ɢ ɱɚɫɬɢɱɧɨɣ ɷɪɨɡɢɢ ɜɵɲɟɥɟɠɚɳɢɯ ɬɨɥɳ, ɧɟ
ɩɪɢɜɨɞɢɬ ɤ ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɭɬɟɪɹɧɧɨɣ ɩɨɪɢɫɬɨɫɬɢ. Ȼɨɥɟɟ ɬɨɝɨ, ɩɪɢ ɩɨɫɥɟɞɭɸɳɟɦ ɩɨɝɪɭɠɟɧɢɢ ɩɨɪɨɞɚ
ɧɚɱɧɟɬ ɭɩɥɨɬɧɹɬɶɫɹ ɜɧɨɜɶ ɥɢɲɶ ɩɨɫɥɟ ɩɪɨɯɨɠɞɟɧɢɹ ɬɨɱɤɢ, ɫ ɤɨɬɨɪɨɣ ɛɵɥ ɧɚɱɚɬ ɟɟ ɩɨɞɴɟɦ. ɋɥɨɠɧɟɟ
ɨɛɫɬɨɢɬ ɞɟɥɨ ɫ ɹɜɥɟɧɢɹɦɢ ɜɬɨɪɢɱɧɵɯ ɢɡɦɟɧɟɧɢɣ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ. Ɉɞɧɚɤɨ, ɫɱɢɬɚɹ ɢɯ ɜ ɨɫɧɨɜɧɨɦ
ɬɟɦɩɟɪɚɬɭɪɧɨ ɡɚɜɢɫɢɦɵɦɢ (Ʉɨɬɹɯɨɜ, 1977), ɦɨɠɧɨ ɩɪɟɞɩɨɥɨɠɢɬɶ ɩɨɞɨɛɧɭɸ ɦɨɞɟɥɶ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɤ
ɩɨɞɴɟɦɭ ɢ ɞɥɹ ɞɢɚɝɟɧɟɬɢɱɟɫɤɢɯ ɹɜɥɟɧɢɣ.
Ƚɟɨɥɨɝɢɱɟɫɤɢɣ ɬɟɦɩ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ ɪɟɞɤɨ ɩɪɟɜɵɲɚɟɬ 100-150 ɦ ɜɟɪɬɢɤɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ
ɨɫɚɞɤɨɜ ɫ ɧɚɱɚɥɶɧɨɣ ɩɨɪɢɫɬɨɫɬɶɸ 0.5-0.65 ɡɚ ɦɢɥɥɢɨɧ ɥɟɬ (Verweij, 1993). ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɩɪɢɦɟɧɢɬɶ
ɡɚɤɨɧ Ⱦɚɪɫɢ ɞɥɹ ɫɜɹɡɢ ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɚ ɮɥɸɢɞɚ ɢɡ ɭɩɥɨɬɧɹɸɳɟɝɨɫɹ ɷɥɟɦɟɧɬɚ ɫ ɞɟɣɫɬɜɭɸɳɢɦ ɧɚ ɧɟɝɨ
ɝɪɚɞɢɟɧɬɨɦ ɞɚɜɥɟɧɢɹ. Ɏɨɪɦɚɥɶɧɨ ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɫɬɪɟɫɫɚ ɬɚɤɠɟ ɜɵɡɵɜɚɸɬ ɭɩɥɨɬɧɟɧɢɟ
ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ, ɬ.ɟ. ɨɬɬɨɤ ɮɥɸɢɞɚ. ȿɫɥɢ ɪɚɫɩɪɨɫɬɪɚɧɢɬɶ ɡɚɤɨɧ Ⱦɚɪɫɢ ɢ ɧɚ ɧɢɯ, ɬɨ ɞɥɹ
ɞɢɜɟɪɝɟɧɰɢɢ ɩɨɬɨɤɚ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɨɛɨɛɳɟɧɧɵɦ ɧɚ ɫɥɭɱɚɣ 3D
ɩɪɟɞɫɬɚɜɥɟɧɢɟɦ ɜɢɞɚ (Bear, Bachmat, 1991; Aziz, Settari, 1983):
div(qj) =  ((Kj KL/Pj) fj),
(9)
ɝɞɟ qj, K j ɢ P j – ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ, ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɢ ɜɹɡɤɨɫɬɶ j-ɣ ɮɚɡɵ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ; KL
– ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɦɚɬɪɢɰɵ, ɨɩɪɟɞɟɥɟɧɧɚɹ ɤɚɤ ɮɭɧɤɰɢɹ ɩɨɪɢɫɬɨɫɬɢ ɞɥɹ L-ɝɨ ɥɢɬɨɬɢɩɚ ɜ ɪɚɛɨɱɟɦ
ɞɢɚɩɚɡɨɧɟ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ; fj = {rxx(Ɏj + Ugz), ryy(Ɏj + Ugz), rzz(Ɏj + Ugz)}, ɝɞɟ rx, ry, rz
– ɤɨɷɮɮɢɰɢɟɧɬɵ ɚɧɢɡɨɬɪɨɩɢɢ ɩɪɨɜɨɞɢɦɨɫɬɢ ɦɚɬɪɢɰɵ, U – ɩɥɨɬɧɨɫɬɶ ɩɨɪɨɜɨɣ ɜɨɞɵ, g – ɭɫɤɨɪɟɧɢɟ
ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ, Ɏj – ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ, ɢɦɟɸɳɢɣ ɪɚɡɦɟɪɧɨɫɬɶ ɞɚɜɥɟɧɢɣ ɢ ɜ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɮɚɡɵ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɪɚɜɧɵɣ (England et al., 1987):
Ɏj = P gzUj

Ɏj ! Capj
100
(10)
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
Ɏj = 0

ɫɬɪ.89-114
Ɏj d Capj
Ɏɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɨɩɪɟɞɟɥɹɟɬɫɹ, ɤɚɤ ɪɚɛɨɬɚ ɩɨ ɩɟɪɟɦɟɳɟɧɢɸ ɟɞɢɧɢɱɧɨɣ ɦɚɫɫɵ
ɮɥɸɢɞɚ ɢɡ ɛɟɫɤɨɧɟɱɧɨɫɬɢ (ɩɪɚɤɬɢɱɟɫɤɢ ɢɡ ɬɨɱɤɢ (Ɋ(0),Ɍ(0)) ɜ ɞɚɧɧɭɸ ɬɨɱɤɭ (Ɋ(z),Ɍ(z)) ɜɧɟɲɧɟɣ ɫɢɫɬɟɦɵ
ɤɨɨɪɞɢɧɚɬ. ɉɪɟɧɟɛɪɟɝɚɹ ɬɟɪɦɚɥɶɧɵɦ ɪɚɫɲɢɪɟɧɢɟɦ ɜɵɬɟɫɧɹɟɦɨɝɨ ɩɪɢ ɭɩɥɨɬɧɟɧɢɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ1,
ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɪɚɛɨɬɭ ɤ ɟɞɢɧɢɱɧɨɦɭ ɨɛɴɟɦɭ ɮɥɸɢɞɚ, ɢ ɬɨɝɞɚ ɫɨɩɨɫɬɚɜɥɹɬɶ ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ
ɩɨɬɟɧɰɢɚɥ ɫ ɝɟɨɮɥɸɢɞɚɥɶɧɵɦ ɞɚɜɥɟɧɢɟɦ P. ȼ ɱɚɫɬɧɨɫɬɢ, ɞɥɹ ɜɨɞɵ, ɤɚɤ ɫɥɟɞɭɟɬ ɢɡ (10), ɞɢɧɚɦɢɱɟɫɤɢɣ
ɩɨɬɟɧɰɢɚɥ ɨɬɥɢɱɟɧ ɨɬ ɧɭɥɹ ɩɪɢ ɝɟɨɮɥɸɢɞɚɥɶɧɨɦ ɞɚɜɥɟɧɢɢ, ɨɬɥɢɱɧɨɦ ɨɬ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɝɨ. Ⱦɥɹ ɛɨɥɟɟ
ɥɟɝɤɢɯ ɮɪɚɤɰɢɣ, ɞɜɢɠɭɳɢɯɫɹ ɜ ɡɚɩɨɥɧɟɧɧɨɦ ɜɨɞɨɣ ɩɨɪɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɟɫɥɢ ɢɯ ɪɚɫɫɦɚɬɪɢɜɚɬɶ, ɤɚɤ
ɫɚɦɨɫɬɨɹɬɟɥɶɧɭɸ ɮɚɡɭ ɍȼ, ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɜɨɡɧɢɤɚɟɬ ɩɨɬɟɧɰɢɚɥ ɜɫɩɥɵɬɢɹ. Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɫɥɭɱɚɟ
ɦɧɨɝɨɮɚɡɧɨɝɨ ɩɨɬɨɤɚ, ɞɜɢɠɟɧɢɟ ɧɟɜɨɞɧɨɣ ɮɚɡɵ ɜ ɩɨɪɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɦɨɠɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɥɢɲɶ ɫ
ɩɪɟɨɞɨɥɟɧɢɟɦ ɤɚɩɢɥɥɹɪɧɨɝɨ ɛɚɪɶɟɪɚ (ɢɥɢ "ɜɯɨɞɧɨɝɨ ɞɚɜɥɟɧɢɹ") ɩɨ ɞɚɧɧɨɣ ɮɚɡɟ – Capj, ɢɡɦɟɪɹɸɳɟɝɨɫɹ ɜ
ɲɤɚɥɟ ɞɚɜɥɟɧɢɣ (Aziz, Settari, 1983).
ɉɨɫɤɨɥɶɤɭ ɡɚɜɢɫɢɦɨɫɬɶ ɭɩɥɨɬɧɟɧɢɹ ɩɨɪɨɞ ɨɬ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɫɬɪɟɫɫɚ ɧɟ ɢɡɭɱɟɧɚ ɷɦɩɢɪɢɱɟɫɤɢ,
ɢ ɜɫɥɟɞɫɬɜɢɟ ɭɩɨɦɹɧɭɬɵɯ ɜɵɲɟ ɬɪɭɞɧɨɫɬɟɣ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɝɪɚɞɢɟɧɬɨɜ ɞɚɜɥɟɧɢɣ, ɞɥɹ
ɰɟɥɟɣ ɩɨɫɥɟɞɭɸɳɟɣ ɤɚɥɢɛɪɨɜɤɢ ɭɩɪɨɫɬɢɦ ɜɵɪɚɠɟɧɢɟ (9):
div(qj) = d/dz [ (Kj KL/Pj) rz (dɎj / dt)] + dQj / dt.
(9*)
Ɂɞɟɫɶ ɱɥɟɧ dQj /dt ɨɛɨɡɧɚɱɚɟɬ ɬɟɦɩ ɫɨɜɨɤɭɩɧɨɝɨ ɨɬɬɨɤɚ ɮɥɸɢɞɚ ɢɡ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɨɛɴɟɦɚ ɜ
ɥɚɬɟɪɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ – "ɫɬɨɤ". ɋɦɵɫɥ ɷɥɟɦɟɧɬɚ ɩɨɹɫɧɹɟɬ ɫɯɟɦɚ ɧɚ ɪɢɫ. 7.
ɇɟɪɚɜɧɨɦɟɪɧɨɟ ɩɨɝɪɭɠɟɧɢɟ ɞɧɚ ɛɚɫɫɟɣɧɚ ɢ
ɧɚɥɢɱɢɟ ɧɚ ɟɝɨ ɤɪɚɹɯ ɫɬɚɛɢɥɶɧɵɯ ɡɨɧ, ɧɟ
ɢɫɩɵɬɵɜɚɜɲɢɯ ɩɨɝɪɭɠɟɧɢɹ, ɫɨɡɞɚɸɬ ɩɪɟɞɩɨɫɵɥɤɢ
ɞɥɹ ɩɨɹɜɥɟɧɢɹ ɥɚɬɟɪɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɞɪɟɧɚɠɚ,
ɧɚɩɪɚɜɥɟɧɧɨɣ ɨɬ ɰɟɧɬɪɚ ɤ ɩɟɪɢɮɟɪɢɢ. ɗɮɮɟɤɬ
Ɋɢɫ. 7. ɋɯɟɦɚ ɥɚɬɟɪɚɥɶɧɨɣ ɪɚɡɝɪɭɡɤɢ ɞɚɜɥɟɧɢɣ ɥɚɬɟɪɚɥɶɧɨɣ ɦɢɝɪɚɰɢɢ ɨɫɨɛɟɧɧɨ ɡɧɚɱɢɦ ɞɥɹ ɥɟɝɤɢɯ
ɍȼ ɮɪɚɤɰɢɣ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɢɡ-ɡɚ ɤɚɩɢɥɥɹɪɧɵɯ
ɛɚɪɶɟɪɨɜ (ɩɨɤɪɵɲɟɤ) ɧɚ ɩɭɬɢ ɢɯ ɜɟɪɬɢɤɚɥɶɧɨɣ
ɦɢɝɪɚɰɢɢ (Verweij, 1993; ɀɭɡɟ, 1986). ȿɫɥɢ
ɫɨɜɦɟɫɬɢɬɶ
ɝɥɨɛɚɥɶɧɭɸ
ɡɨɧɭ
ɪɚɡɝɪɭɡɤɢ
ɫ
ɩɨɜɟɪɯɧɨɫɬɶɸ, ɬɨ, ɩɪɢ ɧɚɥɢɱɢɢ ɧɟɧɭɥɟɜɨɝɨ
ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɜ ɥɸɛɨɣ ɬɨɱɤɟ ɜ
ɩɪɟɞɟɥɚɯ ɨɛɥɚɫɬɢ ɤɚɥɢɛɪɨɜɤɢ (G), ɦɨɠɧɨ ɛɭɞɟɬ
ɨɰɟɧɢɬɶ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ, ɫɨɫɬɚɜɥɹɸɳɭɸ ɝɪɚɞɢɟɧɬɚ
ɩɨɬɟɧɰɢɚɥɚ – Ɏj /'. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɪɢ G << ' (ɪɢɫ. 7),
ɱɬɨ, ɤɚɤ ɩɪɚɜɢɥɨ, ɫɩɪɚɜɟɞɥɢɜɨ ɞɚɠɟ ɞɥɹ ɝɥɭɛɨɤɢɯ
ɝɪɚɛɟɧɨɜ, ɤɨ ɜɫɟɣ ɨɛɥɚɫɬɢ ɤɚɥɢɛɪɨɜɤɢ ɦɨɠɧɨ
ɩɪɢɦɟɧɢɬɶ ɨɞɧɨ ɢ ɬɨ ɠɟ ɫɪɟɞɧɟɟ ɭɞɚɥɟɧɢɟ ', ɢ ɬɚɤɢɦ
Ɋɢɫ. 8.
Ɂɚɜɢɫɢɦɨɫɬɶ
ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɨɛɪɚɡɨɦ ɭɱɟɫɬɶ ɥɚɬɟɪɚɥɶɧɵɣ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɣ ɜ
ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɦɚɬɪɢɰɵ ɨɬ ɫɨɞɟɪɠɚɧɢɹ ɝɚɡɚ ɜ ɫɨɫɬɚɜɥɹɸɳɟɣ wQ /wt – "ɫɬɨɤɟ" ɭɪɚɜɧɟɧɢɹ (9*). Ɍɨɝɞɚ
j
ɩɨɪɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ (ɩɨ ȼɢɤɨɜɭ-Ȼɨɬɫɟɬɭ ɪɚɡɥɢɱɢɹ ɜ ɡɧɚɱɟɧɢɹɯ ɷɬɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɨɬ ɨɞɧɨɣ
(ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɝɟɨɥɨɝɢɢ..., 1984))
1.5D ɦɨɞɟɥɢ ɭɩɥɨɬɧɟɧɢɹ-ɦɢɝɪɚɰɢɢ ɤ ɞɪɭɝɨɣ (ɨɬ
ɨɞɧɨɣ ɤɚɥɢɛɪɨɜɨɱɧɨɣ ɫɤɜɚɠɢɧɵ ɤ ɞɪɭɝɨɣ) ɛɭɞɭɬ ɰɟɥɢɤɨɦ ɨɬɪɚɠɚɬɶ ɥɨɤɚɥɶɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɥɚɬɟɪɚɥɶɧɨɣ
ɩɪɨɜɨɞɢɦɨɫɬɢ. ɗɬɢ ɨɫɨɛɟɧɧɨɫɬɢ ɛɭɞɭɬ, ɨɱɟɜɢɞɧɨ, ɜɤɥɸɱɚɬɶ ɜ ɫɟɛɹ ɬɚɤɠɟ ɷɤɪɚɧɢɪɭɸɳɢɟ ɫɜɨɣɫɬɜɚ
ɪɚɡɥɨɦɨɜ, ɥɟɠɚɳɢɯ ɧɚ ɩɭɬɢ ɥɚɬɟɪɚɥɶɧɨɝɨ ɞɪɟɧɚɠɚ. Ȼɨɥɟɟ ɩɨɞɪɨɛɧɨ ɜɨɩɪɨɫɵ ɤɚɥɢɛɪɨɜɤɢ "ɫɬɨɤɨɜɵɯ"
ɤɨɦɩɨɧɟɧɬ ɨɩɢɫɚɧɵ ɜ (Madatov et al., 1998). ȼ ɞɚɧɧɨɦ ɪɚɡɞɟɥɟ ɦɵ ɫɨɫɪɟɞɨɬɨɱɢɦɫɹ ɧɚ ɨɰɟɧɤɟ ɩɪɨɜɨɞɢɦɨɫɬɢ
ɢ ɩɚɪɚɦɟɬɪɨɜ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ ɦɚɬɪɢɰɵ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɨɛɴɟɦɚ. ɗɬɢ ɩɚɪɚɦɟɬɪɵ, ɜɦɟɫɬɟ ɫ
ɷɦɩɢɪɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ ɭɩɥɨɬɧɟɧɢɹ ɢ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɞɥɹ ɞɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ, ɨɩɪɟɞɟɥɹɸɬ ɜɚɠɧɟɣɲɢɟ
ɫɨɫɬɚɜɥɹɸɳɢɟ ɛɚɡɢɫɚ ɩɪɨɫɬɪɚɧɫɬɜɚ ɩɚɪɚɦɟɬɪɨɜ ɢɡɭɱɚɟɦɨɣ ɨɛɨɛɳɟɧɧɨɣ ɦɨɞɟɥɢ ɭɩɥɨɬɧɟɧɢɹ.
ɉɚɪɚɦɟɬɪɵ ɧɨɪɦɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ ɜɯɨɞɹɬ ɜ ɜɢɞɟ ɤɨɧɫɬɚɧɬ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɷɦɩɢɪɢɱɟɫɤɢɟ
ɬɪɟɧɞɵ, ɨɩɢɫɵɜɚɸɳɢɟ ɭɦɟɧɶɲɟɧɢɟ ɩɨɪɢɫɬɨɫɬɢ ɫ ɪɨɫɬɨɦ ɝɥɭɛɢɧɵ, ɫɬɪɟɫɫɚ ɢ/ɢɥɢ ɬɟɦɩɟɪɚɬɭɪɵ (ɪɢɫ. 9).
ɉɪɨɧɢɰɚɟɦɨɫɬɶ ɦɚɬɪɢɰɵ KL, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɥɹ ɞɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ
ɩɨɪɢɫɬɨɫɬɢ I ɢ ɤɨɧɫɬɚɧɬɵ ɩɪɨɧɢɰɚɟɦɨɫɬɢ OL, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɣ ɢɡɜɢɥɢɫɬɨɫɬɶ ɩɨɪɨɜɵɯ ɤɚɧɚɥɨɜ, ɥɢɛɨ
1
Xiaorong ɢ Vasseur (1992) ɩɨɤɚɡɚɥɢ, ɱɬɨ ɬɟɪɦɚɥɶɧɨɟ ɪɚɫɲɢɪɟɧɢɟ ɩɨɪɨɜɨɣ ɜɨɞɵ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɟɬ ɧɚ
ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɬɨɥɶɤɨ ɩɪɢ ɢɡɨɥɹɰɢɢ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɨɛɴɟɦɚ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɩɪɨɧɢɰɚɟɦɵɦɢ
ɩɨɪɨɞɚɦɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɜɩɪɨɱɟɦ, ɚɩɩɪɨɤɫɢɦɚɰɢɹ (10) ɜ ɜɢɞɟ ɡɚɤɨɧɚ Ⱦɚɪɫɢ ɬɚɤɠɟ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɞɨɩɭɫɬɢɦɨɣ.
101
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɭɞɟɥɶɧɭɸ ɩɥɨɳɚɞɶ ɜɧɭɬɪɟɧɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ (Ʉɨɬɹɯɨɜ, 1977) (ɪɢɫ. 10). ȼɹɡɤɨɫɬɶ Pj
ɞɚɧɧɨɣ ɝɟɨɮɥɸɢɞɚɥɶɧɨɣ ɮɚɡɵ j ɬɚɤɠɟ ɧɟɩɪɟɪɵɜɧɨ ɨɩɪɟɞɟɥɟɧɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ
ɷɦɩɢɪɢɱɟɫɤɢɦɢ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (Denesh, 1998) (ɪɢɫ. 11). ɇɚɤɨɧɟɰ, ɩɪɨɜɨɞɢɦɨɫɬɶ ɦɚɬɪɢɰɵ ɩɨ ɞɚɧɧɨɣ
ɝɟɨɮɥɸɢɞɚɥɶɧɨɣ ɮɚɡɟ j ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɥɹ ɞɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ L ɜ ɜɢɞɟ Kj KL /Pj. (Verweij, 1993; ɋɩɪɚɜɨɱɧɢɤ ɩɨ
ɝɟɨɥɨɝɢɢ..., 1984) ɢ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɬɟɦɩ ɦɢɝɪɚɰɢɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɢɡ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ ɩɪɢ
ɟɞɢɧɢɱɧɨɦ ɝɪɚɞɢɟɧɬɟ ɝɟɨɮɥɸɢɞɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ (ɪɢɫ. 12).
102
Ɋɢɫ. 9. ɗɦɩɢɪɢɱɟɫɤɢɟ ɬɪɟɧɞɵ "ɧɨɪɦɚɥɶɧɨɝɨ
ɭɩɥɨɬɧɟɧɢɹ" ɜ ɲɤɚɥɟ ɝɥɭɛɢɧɵ
(ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɝɪɚɞɢɟɧɬ 0.03 °C/m)
1. Ɍɟɪɪɢɝɟɧɧɵɣ ɥɢɧɨɬɢɩ
I = I0 exp(KZ)
I0 = 0.6; K = 0.0037 Ƚɥɢɧɢɫɬɵɟ ɦɚɬɪɢɰɵ;
I0 = 0.5; K = 0.0025 ɉɟɫɱɚɧɢɫɬɵɟ ɦɚɬɪɢɰɵ
2. Ʉɚɪɛɨɧɚɬɧɵɣ ɥɢɧɨɬɢɩ
I = I0 KZ, ɩɪɢ Z d Zcr, ɢɥɢ ɠɟ
I = (I0 KZcr) exp[30K(Z Zcr)]
Zcr = Tcr/GT; ɝɥɭɛɢɧɚ ɤɨɥɥɚɩɫɚ ɩɨɪɢɫɬɨɫɬɢ,
ɝɞɟ Tcr = 95°ɋ, GT = 0.03° ɋ/ɦ
I0 = 0.45; K = 0.00006 Ɇɟɥɨɜɵɟ ɦɚɬɪɢɰɵ
Ɋɢɫ. 10. ɗɦɩɢɪɢɱɟɫɤɢɟ ɬɪɟɧɞɵ ɩɪɨɧɢɰɚɟɦɨɫɬɢ
ɜ ɲɤɚɥɟ ɝɥɭɛɢɧɵ
(ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɝɪɚɞɢɟɧɬ 0.03°C/m)
Ɋɢɫ. 11. ɗɦɩɢɪɢɱɟɫɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɜɹɡɤɨɫɬɢ
ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɲɤɚɥɟ
ɝɥɭɛɢɧɵ (ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɝɪɚɞɢɟɧɬ 0.03°ɋ/m)
1. Ɍɟɪɪɢɝɟɧɧɵɣ ɥɢɧɨɬɢɩ (Ƚɥɢɧɢɫɬɵɟ ɦɚɬɪɢɰɵ)
ɄɆ = OɆ (0.2I 3Ɇ(Z)) / [1 IɆ(Z)]2),
ɝɞɟ OɆ = 10-16 ɦ2
1. ȼɨɞɚ
PW(Z) = 103^5.28 + 3.8A(Z) 0.28[A(Z)]3`-1,
ɝɞɟ A(Z) = [T(Z) 150]/100
2. Ɍɟɪɪɢɝɟɧɧɵɣ ɥɢɧɨɬɢɩ (ɉɟɫɱɚɧɢɫɬɵɟ ɦɚɬɪɢɰɵ)
ɄS = OS I 8S (Z) ɝɞɟ OS = 10-12 ɦ2
2. ɇɟɮɬɶ
P0(Z) = 1.4186  10-10  exp[6597/(237 + T(Z))]
3. Ʉɚɪɛɨɧɚɬɧɵɣ ɥɢɧɨɬɢɩ (Ɇɟɥɨɜɵɟ ɦɚɬɪɢɰɵ)
Ʉɋ = Oɋ 10[10.3IC(Z)7.6],
ɝɞɟ Oɋ = 3.1510-13 ɦ2
3. Ƚɚɡ
P(Z) = [10-5 + 1.510-6Z 2.2(T(Z) 15)]  10-7,
ɝɞɟ T(Z) = Ɍ0 + Z GɌ, Ɍ0 = 10°ɋ,
GɌ = 0.03°ɋ/ɦ
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
Ɋɢɫ. 12. ɍɞɟɥɶɧɚɹ (ɨɬɧɟɫɟɧɧɚɹ ɧɚ ɟɞɢɧɢɱɧɵɣ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɣ - 1Pa/m) ɝɟɨɮɥɸɢɞɚɥɶɧɚɹ
ɩɪɨɜɨɞɢɦɨɫɬɶ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɝɥɭɛɢɧɵ: (ɚ) ɞɥɹ ɩɟɫɱɚɧɢɫɬɨɣ ɦɚɬɪɢɰɵ ɩɨ ɪɚɡɥɢɱɧɨɦɭ ɬɢɩɭ
ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ; (ɛ) ɞɥɹ ɪɚɡɥɢɱɧɨɝɨ ɥɢɬɨɬɢɩɚ ɦɚɬɪɢɰɵ ɩɨ ɩɨɪɨɜɨɣ ɜɨɞɟ.Ɍɪɟɧɞɵ
ɪɚɫɫɱɢɬɚɧɵ ɧɚ ɨɫɧɨɜɚɧɢɢ ɞɚɧɧɵɯ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɧɚ ɪɢɫ. 9-11
ɍɯɭɞɲɟɧɢɟ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɦɚɬɪɢɰɵ ɩɪɢ ɧɚɥɢɱɢɢ ɝɚɡɨɨɛɪɚɡɧɨɣ ɮɚɡɵ ɜ ɩɨɪɨɜɨɣ ɠɢɞɤɨɫɬɢ
ɭɱɢɬɵɜɚɟɬɫɹ ɩɨɧɢɠɚɸɳɢɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ Kj ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ. Ɉɧ ɨɞɧɨɡɧɚɱɧɨ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɤɚɠɞɨɣ ɢɡ ɮɚɡ ɩɪɢ ɢɡɜɟɫɬɧɨɦ ɧɚɫɵɳɟɧɢɢ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɝɚɡɨɦ (ɋɩɪɚɜɨɱɧɢɤ ɩɨ
ɝɟɨɥɨɝɢɢ..., 1984).
6. Ɇɨɞɟɥɶ ɝɟɧɟɪɚɰɢɢ ɍȼ ɮɥɸɢɞɚ
Ɍɟɦɩ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ GG0(t) ɬɜɟɪɞɨɣ ɮɚɡɵ ɍȼ ɜ ɠɢɞɤɭɸ ɥɢɛɨ ɝɚɡɨɨɛɪɚɡɧɭɸ (ɫɦ. ɮɨɪɦɭɥɭ (5) ɢɥɢ
(5*) ɜ ɪɚɡɞɟɥɟ 3) ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧ, ɤɚɤ ɮɭɧɤɰɢɹ ɜɪɟɦɟɧɢ, ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɫɜɨɣɫɬɜ
ɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ (ɍȼ ɩɨɬɟɧɰɢɚɥɚ), ɧɚ ɨɫɧɨɜɟ ɤɢɧɟɬɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɩɟɪɜɢɱɧɨɣ ɦɢɝɪɚɰɢɢ ɧɟɮɬɢ ɢ ɝɚɡɚ,
ɜɩɟɪɜɵɟ ɩɪɟɞɥɨɠɟɧɧɵɯ Ɍɢɫɫɨ (Tissot, Welte, 1978). Ʉɥɚɫɫɢɱɟɫɤɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɷɬɨɣ ɪɟɚɤɰɢɢ
ɨɩɢɫɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ 1-ɝɨ ɩɨɪɹɞɤɚ:
dM(t) / dt = k(t) M(t),
(11)
ɤɨɬɨɪɨɟ ɪɟɤɭɪɪɟɧɬɧɨ ɫɜɹɡɵɜɚɟɬ ɦɝɧɨɜɟɧɧɵɣ ɬɟɦɩ ɤɨɧɜɟɪɫɢɢ ɮɚɡ ɫ ɨɫɬɚɸɳɟɣɫɹ ɦɚɫɫɨɣ ɬɜɟɪɞɨɝɨ ɜɟɳɟɫɬɜɚ
ɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ, ɟɳɟ ɫɩɨɫɨɛɧɨɝɨ ɤ ɤɨɧɜɟɪɫɢɢ, ɱɟɪɟɡ ɤɢɧɟɬɢɱɟɫɤɭɸ ɮɭɧɤɰɢɸ Ⱥɪɪɟɧɢɭɫɚ k(t):
k(t) = A exp[ E/ RT(t)].
(12)
Ɂɞɟɫɶ Ⱥ – ɤɨɧɫɬɚɧɬɚ Ⱥɪɪɟɧɢɭɫɚ, ɨɩɪɟɞɟɥɹɸɳɚɹ ɚɫɢɦɩɬɨɬɢɱɟɫɤɢɣ ɬɟɦɩ ɪɟɚɤɰɢɢ (ɩɪɢ ɛɟɫɤɨɧɟɱɧɨ ɜɵɫɨɤɨɣ
ɬɟɦɩɟɪɚɬɭɪɟ) [1/ɟɞ.ɜɪɟɦɟɧɢ]; ȿ – ɷɧɟɪɝɢɹ ɚɤɬɢɜɚɰɢɢ ɪɟɚɤɰɢɢ [ɤɤɚɥ/ɦɨɥɶ]; R – ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ = 1.986
 103 ɤɤɚɥ/(ɦɨɥɶqɄ); T(t) – ɬɟɦɩɟɪɚɬɭɪɚ ɩɨ Ʉɟɥɶɜɢɧɭ [qɄ], ɞɚɧɧɚɹ ɤɚɤ ɮɭɧɤɰɢɹ ɜɪɟɦɟɧɢ, ɬ.ɟ. ɜ
ɪɟɬɪɨɫɩɟɤɬɢɜɟ ɬɪɚɟɤɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ. ɉɪɢ ɥɢɧɟɣɧɨɣ ɫɜɹɡɢ ɝɥɭɛɢɧɵ ɫ
ɬɟɦɩɟɪɚɬɭɪɨɣ ɱɟɪɟɡ ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɝɪɚɞɢɟɧɬ, ɤɨɬɨɪɚɹ ɢɫɩɨɥɶɡɨɜɚɧɚ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ, ɡɚɜɢɫɢɦɨɫɬɶ
T(t) ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɦɩɨɦ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ.
ɍȼ-ɩɨɬɟɧɰɢɚɥ, ɤɚɤ ɢɡɜɟɫɬɧɨ (Ungerer, 1993; Tissot, Welte, 1978), ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɨɥɟɣ ɦɚɫɫɵ
ɬɜɟɪɞɨɣ ɮɚɡɵ – ɤɟɪɨɝɟɧɚ, ɩɨɬɟɧɰɢɚɥɶɧɨ ɫɩɨɫɨɛɧɨɣ ɤ ɩɨɥɧɨɦɭ ɩɪɟɨɛɪɚɡɨɜɚɧɢɸ ɜ ɍȼ ɮɥɸɢɞ ɜ ɯɨɞɟ
ɤɢɧɟɬɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɜ ɟɞɢɧɢɱɧɨɣ ɦɚɫɫɟ ɦɚɬɟɪɢɧɫɤɨɣ ɩɨɪɨɞɵ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ (P0, T0), ɬ.ɟ. ɜ
ɭɫɥɨɜɢɹɯ ɩɪɚɤɬɢɱɟɫɤɢ ɧɭɥɟɜɨɝɨ ɬɟɦɩɚ ɪɟɚɤɰɢɢ. ɂɫɩɨɥɶɡɭɹ ɩɪɢɧɹɬɵɟ ɜɵɲɟ ɨɛɨɡɧɚɱɟɧɢɹ ɢ ɫɨɜɦɟɳɚɹ
ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɫ ɩɨɥɨɠɟɧɢɟɦ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ ɜ ɧɚɱɚɥɟ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɵ
ɤɨɨɪɞɢɧɚɬ (0;0) Ù (0;P0,T0), ɨɩɪɟɞɟɥɢɦ ɷɬɨ ɮɭɧɞɚɦɟɧɬɚɥɶɧɨɟ ɫɜɨɣɫɬɜɨ ɥɢɬɨɬɢɩɚ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
H0 = M(0)/U0h0. Ɍɟɩɟɪɶ ɜɵɪɚɡɢɦ ɢɫɤɨɦɭɸ ɮɭɧɤɰɢɸ GG0(t) ɱɟɪɟɡ ɩɚɪɚɦɟɬɪɵ ɤɢɧɟɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɢ ɍȼɩɨɬɟɧɰɢɚɥ ɞɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ. Ⱦɥɹ ɷɬɨɝɨ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɨɩɪɟɞɟɥɟɧɢɟɦ ɝɟɧɟɪɚɰɢɨɧɧɨɝɨ ɱɥɟɧɚ,
ɩɟɪɟɩɢɲɟɦ ɩɟɪɜɨɟ ɭɪɚɜɧɟɧɢɟ ɫɢɫɬɟɦɵ (5*) ɫ ɭɱɟɬɨɦ (11). ɉɨɥɭɱɢɦ:
GG0(t) = k(t)M(t) /U0h0.
102
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɉɨɫɤɨɥɶɤɭ ɪɟɲɟɧɢɟɦ (11) ɹɜɥɹɟɬɫɹ M(t) = M(0) exp[³ k(t)dt], ɬɨ ɨɤɨɧɱɚɬɟɥɶɧɨ ɛɭɞɟɦ ɢɦɟɬɶ:
GG(t) = H0 k(t) exp [³ k(t)dt ].
(13)
ɂɫɫɥɟɞɨɜɚɧɢɹ ɩɨɫɥɟɞɧɢɯ ɥɟɬ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɞɥɹ ɛɨɥɟɟ ɚɞɟɤɜɚɬɧɨɝɨ ɨɩɢɫɚɧɢɹ ɦɨɞɟɥɶ ɍȼɝɟɧɟɪɚɰɢɢ ɬɪɟɛɭɟɬ ɨɛɴɟɞɢɧɟɧɢɹ ɧɟɫɤɨɥɶɤɢɯ ɤɢɧɟɬɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ (11) ɜ ɨɞɧɨɜɪɟɦɟɧɧɨ ɩɪɨɬɟɤɚɸɳɢɣ
ɩɚɪɚɥɥɟɥɶɧɵɣ ɩɪɨɰɟɫɫ (Akihisa, 1978; Tissot, 1987). Ʉɪɨɦɟ ɬɨɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɞɨɩɨɥɧɢɬɶ ɦɨɞɟɥɶ ɮɚɡɨɜɵɯ
ɬɪɚɧɫɮɨɪɦɚɰɢɣ ɜɬɨɪɢɱɧɵɦ ɤɪɟɤɢɧɝɨɦ ɧɟɮɬɢ ɜ ɝɚɡ, ɩɪɨɢɫɯɨɞɹɳɢɦ ɩɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɛɨɥɟɟ ɜɵɫɨɤɢɯ
ɬɟɦɩɟɪɚɬɭɪɚɯ, ɱɟɦ ɩɟɪɜɢɱɧɵɣ ɤɪɟɤɢɧɝ ɤɟɪɨɝɟɧɚ ɜ ɍȼ (Ungerer, 1993).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɦɟɫɬɨ ɜɵɪɚɠɟɧɢɹ (12), ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɬɟɦɩɚ k(t) ɩɪɚɤɬɢɱɟɫɤɢ ɢɫɩɨɥɶɡɭɟɬɫɹ
ɫɭɦɦɚ ɜɢɞɚ:
k(t) = ¦Yi Ai exp [ Ei / RT(t) ],
(14)
ɝɞɟ i – ɫɱɟɬɱɢɤ ɮɪɚɤɰɢɣ ɍȼ, ɨɛɴɟɞɢɧɟɧɧɵɯ ɩɨ ɨɛɳɟɣ ɷɧɟɪɝɢɢ ɚɤɬɢɜɚɰɢɢ; Yi – ɜɟɫɨɜɚɹ ɞɨɥɹ ɮɪɚɤɰɢɢ ɜ
ɤɟɪɨɝɟɧɟ ɧɚ ɦɨɦɟɧɬ ɧɚɱɚɥɚ ɪɟɚɤɰɢɢ.
ɇɚɛɨɪ ɩɚɪɚɦɟɬɪɨɜ (Yi, Ⱥi, ȿi) ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɬɢɩ ɤɟɪɨɝɟɧɚ ɢ ɞɨɫɬɭɩɟɧ ɢɡɭɱɟɧɢɸ ɧɚ ɨɛɪɚɡɰɚɯ ɜ
ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɥɨɜɢɹɯ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɟɫɨɜɵɯ ɞɨɥɟɣ Yi ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɷɧɟɪɝɢɣ
ɚɤɬɢɜɚɰɢɢ ȿi, ɢɡɜɟɫɬɧɵ 3 ɬɢɩɚ ɤɟɪɨɝɟɧɚ, ɨɩɢɫɚɧɧɵɟ ɜ ɥɢɬɟɪɚɬɭɪɟ (Ungerer, 1993; Tissot, Welte, 1978;
ɀɭɡɟ, 1986). ɗɬɨ ɫɨɡɞɚɟɬ ɩɪɟɞɩɨɫɵɥɤɭ ɞɥɹ ɥɨɤɚɥɢɡɚɰɢɢ ɡɨɧɵ ɩɨɢɫɤɚ, ɢɥɢ ɯɨɪɨɲɢɯ ɫɬɚɪɬɨɜɵɯ ɭɫɥɨɜɢɣ,
ɩɪɢ ɤɚɥɢɛɪɨɜɤɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ. Ɍɨɱɧɨ ɬɚɤ ɠɟ ɟɳɟ ɞɨ ɧɚɱɚɥɚ ɤɚɥɢɛɪɨɜɤɢ ɦɨɝɭɬ ɛɵɬɶ ɜɵɫɤɚɡɚɧɵ
ɚɩɪɢɨɪɧɵɟ ɫɭɠɞɟɧɢɹ ɨɛ ɍȼ-ɩɨɬɟɧɰɢɚɥɟ ɩɨɪɨɞ. Ʉɚɤ ɩɪɚɜɢɥɨ, ɧɟɮɬɟɝɚɡɨɦɚɬɟɪɢɧɫɤɢɦɢ ɹɜɥɹɸɬɫɹ ɛɨɝɚɬɵɟ
ɨɪɝɚɧɢɤɨɣ ɝɥɢɧɢɫɬɵɟ ɪɚɡɧɨɫɬɢ, ɢɡɜɟɫɬɧɵɟ ɜ ɛɚɫɫɟɣɧɟ ɡɚɪɚɧɟɟ. ȼ ɱɚɫɬɧɨɫɬɢ, ɫɬɚɧɞɚɪɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɧɟɮɬɟɝɚɡɨɦɚɬɟɪɢɧɫɤɢɯ ɩɨɪɨɞ: TOC (Total Organic Content) ɢ HI (Hydrocarbon Index), ɤɚɤ ɩɪɚɜɢɥɨ,
ɤɨɥɟɛɥɸɬɫɹ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 0.1 ɞɨ 10 % ɢ 100-600 ɦɝ ɤɨɧɜɟɪɬɢɪɭɟɦɨɣ ɮɚɡɵ/ɝ ɌɈɋ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
(Verweij, 1993). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɚɪɚɦɟɬɪ ɇ0 ɦɨɠɟɬ ɫ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɶɸ ɜɟɪɨɹɬɧɨɫɬɢ ɩɨɩɚɞɚɬɶ ɜ ɢɧɬɟɪɜɚɥ
10-4 – 610-2 ɤɝ ɍȼ/ɤɝ ɬɜ. ɮɚɡɵ ɩɨɪɨɞɵ.
ɉɪɢɦɟɪ ɦɨɞɟɥɢ ɍȼ-ɝɟɧɟɪɚɰɢɢ, ɪɚɫɩɚɪɚɥɥɟɥɟɧɧɨɣ ɩɨ ɲɟɫɬɢ ɮɪɚɤɰɢɹɦ, ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 13. Ɂɞɟɫɶ
ɬɟɦɩ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ GG0(t) ɬɜɟɪɞɨɣ ɮɚɡɵ ɜ ɍȼ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɬɟɦɩɟɪɚɬɭɪɧɨɣ ɲɤɚɥɟ ɜ ɧɨɪɦɢɪɨɜɚɧɧɨɦ ɜɢɞɟ
(ɬ.ɟ. ɞɥɹ ɟɞɢɧɢɱɧɨɝɨ ɍȼ-ɩɨɬɟɧɰɢɚɥɚ). ɉɨɫɤɨɥɶɤɭ ɮɚɡɨɜɚɹ ɞɢɚɝɪɚɦɦɚ ɞɚɧɧɨɣ ɫɦɟɫɢ ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧɚ
ɡɚɪɚɧɟɟ, ɠɢɞɤɢɟ ɤɨɦɩɨɧɟɧɬɵ ɨɛɴɟɞɢɧɟɧɵ ɜ ɧɟɮɬɹɧɵɟ ɮɪɚɤɰɢɢ, ɚ ɝɚɡɨɨɛɪɚɡɧɵɟ – ɜ ɝɚɡɨɜɵɟ. Ⱦɨɥɹ ɜɬɨɪɢɱɧɨ
ɝɟɧɟɪɢɪɭɟɦɨɝɨ ɢɡ ɧɟɮɬɢ ɝɚɡɚ ɜɤɥɸɱɟɧɚ ɜ ɝɚɡɨɜɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ ɝɟɧɟɪɚɰɢɢ ɢ ɩɨɤɚɡɚɧɚ ɨɬɞɟɥɶɧɨ. ɋɬɚɪɬɨɜɵɣ
ɫɨɫɬɚɜ ɤɟɪɨɝɟɧɚ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɞɢɚɝɪɚɦɦɟ ɷɧɟɪɝɢɣ ɚɤɬɢɜɚɰɢɢ (ɪɢɫ. 13ɛ).
Ɋɢɫ. 13. Ɇɨɞɟɥɶ ɍȼ-ɝɟɧɟɪɚɰɢɢ
ɚ ɬɟɦɩ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɬɜɟɪɞɨɣ ɮɚɡɵ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ;
ɛ ɞɢɚɝɪɚɦɦɚ ɷɧɟɪɝɢɣ ɚɤɬɢɜɚɰɢɢ ɩɨ ɢɫɯɨɞɧɵɦ ɮɪɚɤɰɢɹɦ ɤɟɪɨɝɟɧɚ
7. ɍɪɚɜɧɟɧɢɹ ɞɥɹ ɨɞɧɨɪɨɞɧɨɣ ɫɪɟɞɵ. Ⱥɧɚɥɢɡ ɭɫɥɨɜɢɣ ɪɚɡɝɪɭɡɤɢ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ
ɉɭɫɬɶ ɜɨ ɜɧɟɲɧɟɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɡɚɞɚɧɚ ɬɪɚɟɤɬɨɪɢɹ ɩɨɝɪɭɠɟɧɢɹ ɞɧɚ ɛɚɫɫɟɣɧɚ ɢ ɨɩɪɟɞɟɥɟɧ
ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɝɪɚɞɢɟɧɬ (ɪɢɫ. 2). ɍɫɥɨɜɢɟ ɨɞɧɨɪɨɞɧɨɫɬɢ ɫɪɟɞɵ ɪɟɚɥɢɡɭɟɬɫɹ ɞɨɩɭɳɟɧɢɹɦɢ ɨ
ɧɟɢɡɦɟɧɧɨɫɬɢ ɩɥɨɬɧɨɫɬɢ ɬɜɟɪɞɨɣ ɮɚɡɵ U0, ɚ ɬɚɤɠɟ ɤɨɧɫɬɚɧɬ ɭɩɥɨɬɧɟɧɢɹ (I0,K), ɩɪɨɧɢɰɚɟɦɨɫɬɢ (O) ɢ ɍȼɝɟɧɟɪɚɰɢɢ (H0, {Ai, Ei, Yi}) ɩɪɢ ɥɸɛɨɦ ɩɨɥɨɠɟɧɢɢ ɫɬɚɪɬɨɜɨɣ ɬɨɱɤɢ (0,0) ɢɫɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ
ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ ɢ ɩɪɢ ɡɚɞɚɧɧɵɯ ɡɚɤɨɧɚɯ ɭɩɥɨɬɧɟɧɢɹ I(Z) ɢ ɩɪɨɧɢɰɚɟɦɨɫɬɢ K(I) ɦɚɬɪɢɰɵ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɥɸɛɨɣ ɬɨɱɤɟ (Z, t) ɧɚ ɛɚɫɫɟɣɧɨɜɨɣ ɲɤɚɥɟ ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɨ ɞɨɫɬɢɝɧɭɬɨɟ ɝɨɪɧɨɟ
103
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɞɚɜɥɟɧɢɟ L(t,Z) ɢ ɬɟɦɩɟɪɚɬɭɪɚ T(t,Z). ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ (Mouchet, Mitchell, 1989), ɝɨɪɧɨɟ (ɥɢɬɨɫɬɚɬɢɱɟɫɤɨɟ)
ɞɚɜɥɟɧɢɟ ɧɚ ɝɥɭɛɢɧɟ Z ɪɚɜɧɨ ɜɟɫɭ ɫɬɨɥɛɚ ɩɨɪɨɞɵ, ɩɪɢɯɨɞɹɳɟɝɨɫɹ ɧɚ ɟɞɢɧɢɱɧɭɸ ɩɨɩɟɪɟɱɧɭɸ
ɩɨɜɟɪɯɧɨɫɬɶ. Ɉɧɨ ɦɨɠɟɬ ɛɵɬɶ ɬɚɤɠɟ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɜɢɞɟ ɫɭɦɦɵ ɩɨɪɨɜɨɝɨ ɞɚɜɥɟɧɢɹ Ɋ(t,Z) ɢ
ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɫɬɪɟɫɫɚ V(t,Z). Ɍ.ɟ.:
L(t,Z) = {[1 I (t)] U0 + I (t)U1}Zg = Ɋ(t,Z) + V(t,Z),
ɝɞɟ g – ɭɫɤɨɪɟɧɢɟ ɫɢɥɵ ɬɹɠɟɫɬɢ.
ɇɚɲɚ ɡɚɞɚɱɚ ɜ ɷɬɨɦ ɪɚɡɞɟɥɟ ɛɭɞɟɬ ɫɨɫɬɨɹɬɶ ɜ ɩɨɥɭɱɟɧɢɢ ɧɚ ɨɫɧɨɜɚɧɢɢ ɷɬɢɯ ɞɚɧɧɵɯ ɭɪɚɜɧɟɧɢɣ,
ɹɜɧɨ ɫɜɹɡɵɜɚɸɳɢɯ ɮɭɧɤɰɢɢ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ, ɍȼ-ɧɚɫɵɳɟɧɢɣ ɢ ɩɨɪɢɫɬɨɫɬɢ ɦɚɬɪɢɰɵ ɫ
ɩɟɪɟɱɢɫɥɟɧɧɵɦɢ ɜɵɲɟ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɦɢ ɤɨɧɫɬɚɧɬɚɦɢ ɩɨɪɨɞɵ ɞɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ. ɂɫɯɨɞɧɵɦɢ ɛɭɞɟɦ
ɫɱɢɬɚɬɶ: ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (5*) ɛɚɥɚɧɫɚ ɦɚɫɫ ɞɥɹ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ U ɢ ɭɪɚɜɧɟɧɢɹ (6-8),
ɫɜɹɡɵɜɚɸɳɢɟ ɝɥɚɞɤɨɟ ɢɡɦɟɧɟɧɢɟ ɩɥɨɬɧɨɫɬɟɣ ɩɨɪɨɞɵ ɢ ɮɥɸɢɞɚ ɫ ɬɪɚɟɤɬɨɪɢɟɣ ɩɨɝɪɭɠɟɧɢɹ U ɜɨ ɜɧɟɲɧɟɣ
ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
ɋɞɟɥɚɧɧɵɟ ɜɵɲɟ ɞɨɩɭɳɟɧɢɹ ɨ "ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɫɬɢ" ɷɥɟɦɟɧɬɚ U, ɨɞɧɨɪɨɞɧɨɫɬɢ ɫɪɟɞɵ ɢ
ɩɪɚɤɬɢɱɟɫɤɨɣ ɧɟɫɠɢɦɚɟɦɨɫɬɢ ɠɢɞɤɨɣ ɮɚɡɵ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɨɬɪɚɡɢɦ ɛɨɥɟɟ ɮɨɪɦɚɥɶɧɨ:
grad (Uj) = 0, j = 0, 1, 2
wU0 /wt = 0
1/U1 wU1/wt = E1 dT/dt
1/U2 wU2/wt = J2 dP/dt E2 dT/dt
ɪåïðåçåíòàòèâíîñòü ýëåìåíòà U, ɬ.ɟ. ɩɨɫɬɨɹɧɫɬɜɨ ɫɜɨɣɫɬɜɚ ɜɧɭɬɪɢ
ɦɚɥɨɝɨ ɨɛɴɟɦɚ;
ɫɬɚɛɢɥɶɧɨɫɬɶ ɦɢɧɟɪɚɥɶɧɨɝɨ ɫɤɟɥɟɬɚ ɦɚɬɪɢɰɵ ɜ ɩɪɨɰɟɫɫɟ
ɩɨɝɪɭɠɟɧɢɹ;
ɧɟɫɠɢɦɚɟɦɨɫɬɶ ɢ ɬɟɪɦɚɥɶɧɨɟ ɪɚɡɭɩɥɨɬɧɟɧɢɟ ɩɨɪɨɜɨɣ ɜɨɞɵ;
(15)
ɫɠɢɦɚɟɦɨɫɬɶ ɢ ɬɟɪɦɚɥɶɧɨɟ ɪɚɡɭɩɥɨɬɧɟɧɢɟ ɍȼ.
Ɉɩɪɟɞɟɥɢɦ ɬɟɦɩ (ɩɪɨɢɡɜɨɞɧɭɸ ɩɨ ɜɪɟɦɟɧɢ) ɧɚɫɵɳɟɧɢɹ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɍȼ-ɮɥɸɢɞɨɦ ɜ
ɩɪɨɰɟɫɫɟ ɭɩɥɨɬɧɟɧɢɹ ɦɚɬɪɢɰɵ, ɦɢɝɪɚɰɢɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɢ ɍȼ-ɝɟɧɟɪɚɰɢɢ. ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɜɬɨɪɵɦ
ɭɪɚɜɧɟɧɢɟɦ ɫɢɫɬɟɦɵ (5*):
dS/dt = 1/Qh0 [h0 (1-S) dQ/dt + Q (1-S) dh0/dt Qh0 (1-S) E1 dT/dt + Qh0 div q1 /I ].
ɍɱɬɟɦ ɩɟɪɜɨɟ ɢɡ ɭɪɚɜɧɟɧɢɣ ɫɢɫɬɟɦɵ (5*) ɢ ɩɨɫɥɟ ɭɩɪɨɳɟɧɢɣ ɩɨɥɭɱɢɦ:
dS/dt = (1-S) [1/Q dQ/dt - dG0/dt - E1 dT/dt + div(q1) /I ].
(16)
ɉɟɪɟɩɢɲɟɦ ɩɨɫɥɟɞɧɟɟ ɭɪɚɜɧɟɧɢɟ ɫɢɫɬɟɦɵ (5*), ɜɵɩɨɥɧɹɹ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ:
h0SU2 dQ/dt + QSU2 dh0/dt + Qh0U2 dS/dt + Qh0S dU2/dt = U0h0 dG0/dt Qh0 div q1 /I.
ȼɵɩɨɥɧɹɹ ɩɨɞɫɬɚɧɨɜɤɢ dh0/dt, dU2/dt, dS/dt ɢɡ (5*), (15), (16), ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɩɨɥɭɱɢɦ ɩɨɫɥɟ
ɝɪɭɩɩɢɪɨɜɨɤ ɢ ɭɩɪɨɳɟɧɢɣ:
(1/Q) dQ/dt – SJ2 dP/dt = [SE2 + (1-S) E1] dT/dt + [U0/(QU2) + 1] dG0/dt – (div q1 + div q2) /I.
(17)
Ɍɟɦɩ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɨɬɟɪɢ ɩɨɪɢɫɬɨɫɬɢ, ɫ ɭɱɟɬɨɦ ɧɨɪɦɚɥɶɧɨɝɨ ɬɪɟɧɞɚ ɭɩɥɨɬɧɟɧɢɹ ɢ ɝɟɧɟɪɚɰɢɢ ɍȼ
ɢɡ ɱɚɫɬɢ ɬɜɟɪɞɨɣ ɮɚɡɵ, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɟɧ ɜɵɪɚɠɟɧɢɟɦ (7). Ⱦɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɚɧɚɥɢɡɚ
ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɞɨɫɬɚɬɨɱɧɨ ɨɛɳɢɦ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɦ ɡɚɤɨɧɨɦ ɭɛɵɜɚɧɢɹ ɩɨɪɢɫɬɨɫɬɢ ɨɬ ɜɟɪɬɢɤɚɥɶɧɨɝɨ
ɫɬɪɟɫɫɚ:
I = I0 exp[WV(t,Z)].
(18)
Ɍɚɤɚɹ ɮɨɪɦɭɥɚ ɨɤɚɡɵɜɚɟɬɫɹ ɞɚɠɟ ɛɨɥɟɟ ɬɨɱɧɨɣ ɞɥɹ ɝɥɢɧɢɫɬɨɝɨ ɥɢɬɨɬɢɩɚ (Magara, 1978), ɚ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɤɨɧɫɬɚɧɬɚ ɭɩɥɨɬɧɟɧɢɹ W ɦɨɠɟɬ ɛɵɬɶ ɥɟɝɤɨ ɫɜɹɡɚɧɚ ɫ ɜɜɟɞɟɧɧɨɣ ɜɵɲɟ ɤɨɧɫɬɚɧɬɨɣ
ɭɩɥɨɬɧɟɧɢɹ K ɜ ɮɨɪɦɭɥɟ Ⱥnthy (ɪɢɫ. 9):
W = K / [(1 I) (U0 U1) g].
(19)
Ɍɨɝɞɚ ɩɟɪɟɩɢɲɟɦ (7) ɫ ɭɱɟɬɨɦ (18) ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɥɢɬɨɫɬɚɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ (ɫɦ. ɧɚɱɚɥɨ ɪɚɡɞɟɥɚ):
1/Q dQ/dt = 1/I dG0/dt – W / (1-I) d(L-P)/dt.
(7*)
ɉɨɞɫɬɚɜɥɹɹ (7*) ɜ (16) ɢ (17) ɩɨɥɭɱɢɦ ɩɨɫɥɟ ɭɩɪɨɳɟɧɢɹ:
dS/dt = (1-S) /I [(1-I) dG0/dt – WQ d(L-P)/dt – IE1 dT/dt + div q1]
(20)
I [W/(1-I)+SJ2] dP/dt = {(1-I) (U0/U2 -1) dG0/dt + IW/(1-I) dL/dt + [SE2 + (1-S)E1] dT/dt} –
(20*)
– [div (q1+q2)].
104
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɍɪɚɜɧɟɧɢɹ (20-20*) ɮɨɪɦɢɪɭɸɬ ɫɢɫɬɟɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɱɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ
ɤɨɬɨɪɨɣ ɩɨɡɜɨɥɹɟɬ ɦɨɞɟɥɢɪɨɜɚɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ ɝɥɭɛɢɧɟ ɩɨɪɢɫɬɨɫɬɢ, ɍȼ-ɧɚɫɵɳɟɧɢɹ ɢ
ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ ɞɥɹ ɜɵɛɪɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ. ɉɪɢ ɷɬɨɦ, ɨɱɟɜɢɞɧɨ, ɪɟɲɟɧɢɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ
ɧɚɫɬɨɹɳɟɦɭ ɜɪɟɦɟɧɢ ɜ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɦɨɠɟɬ ɛɵɬɶ ɫɨɩɨɫɬɚɜɢɦɨ ɫ ɧɚɛɥɸɞɟɧɧɵɦɢ
ɪɚɫɩɪɟɞɟɥɟɧɢɹɦɢ ɷɬɢɯ ɢɡɦɟɪɹɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɪɟɡɭɥɶɬɚɬ ɩɪɢ ɜɵɛɪɚɧɧɨɦ ɥɢɬɨɬɢɩɟ (ɬ.ɟ. ɡɚɮɢɤɫɢɪɨɜɚɧɧɵɯ ɡɚɤɨɧɚɯ ɭɩɥɨɬɧɟɧɢɹ ɢ
ɍȼ-ɝɟɧɟɪɚɰɢɢ) ɢ ɞɚɧɧɨɣ ɬɪɚɟɤɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ ɛɭɞɟɬ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɬɶɫɹ ɤɨɧɫɬɚɧɬɚɦɢ
ɭɩɥɨɬɧɟɧɢɹ, ɩɪɨɜɨɞɢɦɨɫɬɢ ɢ ɍȼ-ɝɟɧɟɪɚɰɢɢ, ɚ ɬɚɤɠɟ ɩɚɪɚɦɟɬɪɨɦ "ɫɬɨɤ" ɜ 1.5D ɮɨɪɦɭɥɢɪɨɜɤɟ ɡɚɤɨɧɚ
Ⱦɚɪɫɢ. Ʉɨɧɫɬɚɧɬɵ ɜɹɡɤɨɫɬɢ, ɬɟɪɦɚɥɶɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɢ ɢɡɨɬɟɪɦɢɱɟɫɤɨɝɨ ɫɠɚɬɢɹ ɞɥɹ ɤɨɦɩɨɧɟɧɬ
ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɩɪɢɧɢɦɚɸɬɫɹ ɩɪɢ ɷɬɨɦ ɧɟɢɡɦɟɧɧɵɦɢ (ɬɚɛɥ. 1).
Ɉɛɚ ɭɪɚɜɧɟɧɢɹ ɧɟ ɢɦɟɸɬ ɮɢɡɢɱɟɫɤɨɣ ɪɚɡɦɟɪɧɨɫɬɢ ɢ, ɩɨ ɫɭɬɢ, ɨɩɢɫɵɜɚɸɬ ɞɢɧɚɦɢɤɭ ɛɚɥɚɧɫɚ
ɧɚɝɪɭɡɤɢ ɢ ɪɚɡɝɪɭɡɤɢ ɷɥɟɦɟɧɬɚ ɩɨ ɫɨɞɟɪɠɚɧɢɸ ɍȼ ɜ ɩɨɪɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɢ ɝɟɨɮɥɸɢɞɚɥɶɧɵɦ
ɞɚɜɥɟɧɢɹɦ. ɉɪɨɚɧɚɥɢɡɢɪɭɟɦ, ɧɚɩɪɢɦɟɪ, ɭɪɚɜɧɟɧɢɟ (20*).
Ʉɨɷɮɮɢɰɢɟɧɬ C = I [W/(1-I) + SJ2] ɢɦɟɟɬ ɫɦɵɫɥ ɩɨɥɧɨɣ (ɦɚɬɪɢɰɵ + ɮɥɸɢɞɚ) ɫɠɢɦɚɟɦɨɫɬɢ
ɷɥɟɦɟɧɬɚ U ɢ ɢɡɦɟɪɹɟɬɫɹ ɜ [1/Pa].
Ɉɛɨɡɧɚɱɢɦ ɩɟɪɜɵɣ ɱɥɟɧ ɩɪɚɜɨɣ ɱɚɫɬɢ (20*) ɱɟɪɟɡ GU<. Ɉɧ ɨɛɴɟɞɢɧɹɟɬ ɜ ɮɢɝɭɪɧɵɯ ɫɤɨɛɤɚɯ ɜɫɟ
ɢɫɬɨɱɧɢɤɢ, ɜɵɡɵɜɚɸɳɢɟ ɦɝɧɨɜɟɧɧɵɣ ɞɟɮɢɰɢɬ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ (ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ). Ʉ ɧɢɦ
ɨɬɧɨɫɹɬɫɹ, ɜ ɱɚɫɬɧɨɫɬɢ: ɬɪɚɧɫɮɨɪɦɚɰɢɹ ɱɚɫɬɢ ɦɢɧɟɪɚɥɶɧɨɝɨ ɫɤɟɥɟɬɚ ɦɚɬɪɢɰɵ ɜ ɦɟɧɟɟ ɩɥɨɬɧɭɸ ɍȼ ɮɚɡɭ –
1; ɭɩɥɨɬɧɟɧɢɟ ɦɚɬɪɢɰɵ ɩɪɢ ɩɨɝɪɭɠɟɧɢɢ – 2 ɢ ɪɚɫɲɢɪɟɧɢɢ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɩɪɢ ɧɚɝɪɟɜɟ – 3. ɉɟɪɟɯɨɞɹ ɤ
ɤɨɧɟɱɧɵɦ ɪɚɡɧɨɫɬɹɦ (dt  Gt) ɢ ɩɪɢɧɢɦɚɹ ɲɚɝ ɩɨ ɜɪɟɦɟɧɢ Gt ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɡɚɩɢɲɟɦ ɜɵɪɚɠɟɧɢɟ
ɞɥɹ ɢɫɬɨɱɧɢɤɨɜ ɞɟɮɢɰɢɬɚ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ:
GU< = (1-I) (U0 /U2 -1)GG0 + IW/(1-I)GL + [SE2 + (1-S) E1]GT.
(21)
Ɍɪɢ ɫɥɚɝɚɟɦɵɯ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ (21) ɨɩɪɟɞɟɥɹɸɬ ɬɪɢ ɜɚɠɧɟɣɲɢɯ ɦɟɯɚɧɢɡɦɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɡɨɧ
ɚɧɨɦɚɥɶɧɨ ɜɵɫɨɤɢɯ ɩɨɪɨɜɵɯ ɢ ɩɥɚɫɬɨɜɵɯ ɞɚɜɥɟɧɢɣ (ȺȼɉȾ): 1 – ɝɚɡɨɝɟɧɟɪɚɰɢɹ; 2 – ɧɟɤɨɦɩɟɧɫɢɪɨɜɚɧɧɨɟ
ɭɩɥɨɬɧɟɧɢɟ ɦɚɬɪɢɰɵ ɩɪɢ ɜɟɪɬɢɤɚɥɶɧɨɦ ɫɬɪɟɫɫɟ ɡɚ ɫɱɟɬ ɛɵɫɬɪɨɝɨ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ; 3 – ɬɟɦɩɟɪɚɬɭɪɧɨɟ
ɪɚɫɲɢɪɟɧɢɟ ɡɚɛɥɨɤɢɪɨɜɚɧɧɨɝɨ ɜ ɩɨɪɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɮɥɸɢɞɚ (Mann, Mackenzie, 1990).
ȼɬɨɪɨɣ ɱɥɟɧ ɩɪɚɜɨɣ ɱɚɫɬɢ (20*) ɨɛɨɡɧɚɱɢɦ ɱɟɪɟɡ GU>. Ɉɧ ɨɩɪɟɞɟɥɹɟɬ ɫɭɦɦɚɪɧɵɣ (ɩɨ ɜɨɞɟ ɢ ɍȼ)
ɜɤɥɚɞ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɬɬɨɤɚ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɩɪɨɢɫɯɨɞɹɳɟɝɨ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɢ
ɥɚɬɟɪɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɹɯ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɝɪɚɞɢɟɧɬɭ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ, ɞɨɫɬɢɝɧɭɬɨɦɭ ɡɚ ɬɨɬ
ɠɟ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ.
ɋ ɭɱɟɬɨɦ ɩɟɪɟɯɨɞɚ ɤ ɤɨɧɟɱɧɵɦ ɪɚɡɧɨɫɬɹɦ ɩɟɪɟɩɢɲɟɦ (20*) ɜ ɭɩɪɨɳɟɧɧɨɦ ɜɢɞɟ:
C G Ɋ = GU< GU>.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ GU< >/C ɢɦɟɟɬ ɪɚɡɦɟɪɧɨɫɬɶ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ ɢ ɫɦɵɫɥ
ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ GɎ ɧɚɤɚɩɥɢɜɚɟɦɨɝɨ (GU</C) ɢ ɪɚɡɝɪɭɠɚɟɦɨɝɨ (GU>/C) ɫɢɫɬɟɦɨɣ ɡɚ
ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ Gt. ɍɫɥɨɜɢɟ ɩɨɥɧɨɣ ɪɚɡɝɪɭɡɤɢ ɷɥɟɦɟɧɬɚ U ɩɨ ɝɟɨɮɥɸɢɞɚɥɶɧɵɦ ɞɚɜɥɟɧɢɹɦ ɫɨɫɬɨɢɬ ɜ ɬɨɦ,
ɱɬɨ ɞɟɮɢɰɢɬ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɧɚɤɚɩɥɢɜɚɟɦɵɣ ɜ ɧɟɦ ɩɨ ɜɫɟɦ ɢɫɬɨɱɧɢɤɚɦ ɡɚ ɜɪɟɦɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ, ɧɟ
ɞɨɥɠɟɧ ɩɪɟɜɵɲɚɬɶ ɫɭɦɦɚɪɧɨɝɨ (ɩɨ ɮɚɡɚɦ ɢ ɧɚɩɪɚɜɥɟɧɢɹɦ) ɨɬɬɨɤɚ ɢɡ ɧɟɝɨ ɮɥɸɢɞɚ. ɂɧɚɱɟ, ɩɨɬɟɧɰɢɚɥ
ɧɚɝɪɭɡɤɢ GɎ< ɧɟ ɞɨɥɠɟɧ ɩɪɟɜɵɲɚɬɶ ɩɨɬɟɧɰɢɚɥɚ ɪɚɡɝɪɭɡɤɢ GɎ>. Ⱦɥɹ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɷɬɨɣ ɩɪɨɛɥɟɦɵ
ɧɟɨɛɯɨɞɢɦɨ ɡɚɞɚɬɶ ɨɞɧɨ ɧɚɱɚɥɶɧɨɟ ɢ ɞɜɚ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹ ɩɨ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ
ɧɚ ɫɟɬɤɟ, ɡɚɞɚɧɧɨɣ ɜ ɛɚɫɫɟɣɧɨɜɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ. ɋɯɟɦɚ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɢ ɪɟɡɭɥɶɬɚɬɵ ɞɥɹ ɪɟɚɥɶɧɵɯ
ɦɨɞɟɥɟɣ ɨɛɫɭɠɞɚɸɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ ɪɚɡɞɟɥɟ. Ɂɞɟɫɶ ɠɟ ɦɵ ɨɝɪɚɧɢɱɢɦɫɹ ɩɪɢɛɥɢɠɟɧɧɨɣ ɨɰɟɧɤɨɣ
ɫɨɫɬɚɜɥɹɸɳɢɯ ɞɟɮɢɰɢɬɚ ɩɨɪɢɫɬɨɫɬɢ GU< ɢ ɫɨɨɬɧɨɲɟɧɢɹ GU</GU>, ɤɚɤ ɮɭɧɤɰɢɣ ɬɟɤɭɳɟɣ ɝɥɭɛɢɧɵ Z ɷɥɟɦɟɧɬɚ
U ɞɥɹ ɢɞɟɚɥɢɡɢɪɨɜɚɧɧɨɣ ɨɞɧɨɪɨɞɧɨɣ ɫɪɟɞɵ.
ɉɪɟɠɞɟ ɜɫɟɝɨ ɨɰɟɧɢɦ ɭɞɟɥɶɧɵɣ ɜɤɥɚɞ ɤɚɠɞɨɝɨ ɢɡ ɬɪɟɯ ɷɥɟɦɟɧɬɨɜ, ɮɨɪɦɢɪɭɸɳɢɯ GU< ɜ (21) ɩɪɢ
ɫɥɟɞɭɸɳɢɯ ɞɨɩɭɳɟɧɢɹɯ:
Ⱦɟɮɢɰɢɬ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɜɵɡɵɜɚɟɦɵɣ ɧɚ ɥɸɛɨɣ ɝɥɭɛɢɧɟ Z ɫɪɟɞɧɢɦ ɡɚ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɬɟɦɩɨɦ
ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ Gh(0) [ɦ/MY], ɰɟɥɢɤɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɪɟɧɞɨɦ ɧɨɪɦɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ ɞɥɹ ɞɚɧɧɨɝɨ
ɥɢɬɨɬɢɩɚ (MY – ɦɢɥɥɢɨɧ ɥɟɬ. ɗɬɨɬ ɲɚɝ ɩɪɢɧɹɬ ɡɚ ɲɚɝ ɤɜɚɧɬɨɜɚɧɢɹ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ).
Ɍɟɪɦɚɥɶɧɨɟ ɪɚɫɲɢɪɟɧɢɟ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɞɥɹ ɫɥɭɱɚɹ ɨɞɧɨɮɚɡɧɨɝɨ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ
(E = 510-4 qɋ-1 – ɩɨɪɨɜɚɹ ɜɨɞɚ) ɢ ɝɪɚɞɢɟɧɬɧɨɣ ɦɨɞɟɥɢ ɧɚɝɪɟɜɚɧɢɹ ɫ ɝɥɭɛɢɧɨɣ T(Z+GZ) = T(Z)+GTGZ, (GT
= 0.03qɋ/ɦ).
Ⱦɟɮɢɰɢɬ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɫɜɹɡɚɧɧɵɣ ɫ ɩɟɪɜɢɱɧɨɣ ɦɢɝɪɚɰɢɟɣ ɍȼ ɜ ɭɩɥɨɬɧɟɧɧɨɣ ɦɚɬɟɪɢɧɫɤɨɣ
ɩɨɪɨɞɟ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɧɚ ɨɫɧɨɜɚɧɢɢ ɦɨɞɟɥɢ ɍȼ-ɝɟɧɟɪɚɰɢɢ ɞɚɧɧɨɣ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ (ɪɢɫ. 13).
Ʉɚɤ ɜɢɞɧɨ ɢɡ ɪɢɫ. 14, ɬɟɪɦɚɥɶɧɵɣ ɷɮɮɟɤɬ ɫɪɚɜɧɢɬɟɥɶɧɨ ɧɟɜɟɥɢɤ ɢ ɦɨɠɟɬ ɫɨɡɞɚɜɚɬɶ ɡɧɚɱɢɬɟɥɶɧɵɣ
ɩɨɬɟɧɰɢɚɥ ɧɚɝɪɭɡɤɢ ɥɢɲɶ ɩɪɢ ɧɢɡɤɨɣ (ɛɥɢɡɤɨɣ ɤ ɧɭɥɸ) ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɜɵɲɟɥɟɠɚɳɟɣ ɬɨɥɳɢ, ɱɬɨ ɜɩɨɥɧɟ
105
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɫɨɝɥɚɫɭɟɬɫɹ ɫ (Xiaorong, Vasseur, 1992). ȼɤɥɚɞ ɮɚɤɬɨɪɚ ɭɩɥɨɬɧɟɧɢɹ ɜ ɫɪɟɞɧɟɦ ɧɚ ɞɜɚ ɩɨɪɹɞɤɚ ɡɧɚɱɢɦɟɟ.
Ɉɞɧɚɤɨ ɨɧ ɦɨɠɟɬ ɭɫɬɭɩɚɬɶ ɡɧɚɱɢɦɨɫɬɢ ɮɚɤɬɨɪɚ ɍȼ-ɝɟɧɟɪɚɰɢɢ ɜ ɦɨɦɟɧɬ ɩɢɤɨɜɨɝɨ ɬɟɦɩɚ.
ɇɚ ɪɢɫ. 15 ɩɪɢɜɟɞɟɧɵ ɝɪɚɮɢɤɢ ɫɨɨɬɧɨɲɟɧɢɣ ɩɨɬɟɧɰɢɚɥɨɜ ɧɚɝɪɭɡɤɢ ɤ ɩɨɬɟɧɰɢɚɥɚɦ ɪɚɡɝɪɭɡɤɢ
(GɎ</GɎ> = GU</GU>) ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɬɟɦɩɨɜ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ ɨɞɧɨɪɨɞɧɨɣ ɫɪɟɞɵ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ
ɬɟɦɩɟɪɚɬɭɪɧɨɦ ɝɪɚɞɢɟɧɬɟ 0.03qɋ/ɦ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɢɧɬɟɪɜɚɥ ɝɥɭɛɢɧ ɞɨ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɨɣ GU</GU> ɫ
ɭɪɨɜɧɟɦ 1.0 ɛɭɞɟɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɨɛɥɚɫɬɢ ɩɨɥɧɨɣ ɪɚɡɝɪɭɡɤɢ ɫɢɫɬɟɦɵ ɩɪɢ ɞɚɧɧɵɯ ɩɚɪɚɦɟɬɪɚɯ
ɩɨɝɪɭɠɟɧɢɹ ɢ ɤɨɧɫɬɚɧɬɚɯ ɥɢɬɨɬɢɩɚ. ȼɢɞɧɨ, ɱɬɨ ɩɪɢ ɜɵɫɨɤɨɦ ɬɟɦɩɟ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ (Gh = 100 ɦ/MY)
ɫɢɫɬɟɦɚ ɧɟ ɭɫɩɟɜɚɟɬ ɪɚɡɝɪɭɠɚɬɶ ɷɥɟɦɟɧɬ U ɭɠɟ ɫ ɝɥɭɛɢɧɵ 1000 ɦ. "ȼɤɥɸɱɟɧɢɟ" ɫ ɝɥɭɛɢɧɵ ɩɪɢɦɟɪɧɨ
3100 ɦ ɝɚɡɨɝɟɧɟɪɚɰɢɢ ɨɫɬɚɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɧɟɡɚɦɟɬɧɵɦ ɮɚɤɬɨɪɨɦ. ɇɚɨɛɨɪɨɬ, ɩɪɢ ɧɢɡɤɨɦ
ɬɟɦɩɟ (Gh = 1ɦ/MY) ɝɟɧɟɪɚɰɢɹ ɝɚɡɚ ɜ ɩɨɪɨɜɨɦ
ɩɪɨɫɬɪɚɧɫɬɜɟ ɫɬɚɧɨɜɢɬɫɹ ɤɥɸɱɟɜɵɦ ɮɚɤɬɨɪɨɦ ɢ
ɦɨɠɟɬ ɧɟɦɟɞɥɟɧɧɨ ɜɵɡɜɚɬɶ ȺȼɉȾ.
Ⱦɚɧɧɵɣ ɚɧɚɥɢɡ, ɨɞɧɚɤɨ, ɧɨɫɢɬ ɫɭɝɭɛɨ
ɤɚɱɟɫɬɜɟɧɧɵɣ ɯɚɪɚɤɬɟɪ ɢ ɩɪɢɜɟɞɟɧ ɞɥɹ
ɢɥɥɸɫɬɪɚɰɢɢ ɬɟɧɞɟɧɰɢɣ. Ʉɚɤ ɛɭɞɟɬ ɩɨɤɚɡɚɧɨ
ɧɢɠɟ, ɛɨɥɟɟ ɬɨɱɧɵɣ ɪɚɫɱɟɬ, ɨɫɧɨɜɚɧɧɵɣ ɧɚ
ɝɟɧɟɪɚɬɨɪɧɨɣ ɦɨɞɟɥɢ, ɨɩɢɫɚɧɧɨɣ ɜ ɪɚɡɞɟɥɟ 6 ɢ
ɜɤɥɸɱɚɸɳɟɣ ɪɚɡɥɢɱɧɵɟ ɥɢɬɨɥɨɝɢɢ, ɫɤɨɪɨɫɬɢ
ɩɨɝɪɭɠɟɧɢɹ ɢ ɨɫɨɛɟɧɧɨɫɬɢ ɦɧɨɝɨɮɚɡɧɨɝɨ ɩɨɬɨɤɚ
ɜ ɧɟɨɞɧɨɪɨɞɧɨɣ ɫɪɟɞɟ, ɦɨɠɟɬ ɢɡɦɟɧɢɬɶ ɩɨɞɨɛɧɵɟ
ɪɚɫɫɭɠɞɟɧɢɹ
ɫɭɳɟɫɬɜɟɧɧɵɦ
ɨɛɪɚɡɨɦ.
ȿɫɬɟɫɬɜɟɧɧɨ, ɱɬɨ ɢ ɩɪɨɝɧɨɡɵ ȺȼɉȾ, ɨɫɧɨɜɚɧɧɵɟ Ɋɢɫ. 14. Ⱦɟɮɢɰɢɬ ɩɨɪɢɫɬɨɫɬɢ, ɜɵɡɜɚɧɧɵɣ ɪɚɡɥɢɱɧɵɦɢ
ɧɚ ɩɨɞɨɛɧɨɣ ɭɩɪɨɳɟɧɧɨɣ ɦɨɞɟɥɢ ɫɪɟɞɵ, ɦɨɝɭɬ ɢɫɬɨɱɧɢɤɚɦɢ, ɞɥɹ ɨɞɧɨɪɨɞɧɨɣ ɫɪɟɞɵ ɩɪɢ ɫɪɟɞɧɟɦ
ɬɟɦɩɟ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ 75 ɦ/MY
ɞɚɜɚɬɶ ɤɨɥɨɫɫɚɥɶɧɵɟ ɨɲɢɛɤɢ.
8. ɑɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ ɩɪɹɦɨɣ 1.5D ɡɚɞɚɱɢ ɞɥɹ ɦɧɨɝɨɫɥɨɣɧɨɣ ɫɪɟɞɵ
ȼ ɥɸɛɨɣ ɤɨɧɟɱɧɵɣ ɢɧɬɟɪɜɚɥ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ ɛɭɞɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɧɚɪɚɳɢɜɚɧɢɟ (ɩɪɢ
ɩɨɝɪɭɠɟɧɢɢ) ɢɥɢ ɫɨɤɪɚɳɟɧɢɟ (ɩɪɢ ɩɨɞɴɟɦɟ ɢ ɷɪɨɡɢɢ) ɜɵɫɨɬɵ ɤɨɥɨɧɧɵ ɨɫɚɞɨɱɧɵɯ ɩɨɪɨɞ, ɞɥɹ ɤɨɬɨɪɵɯ
ɜɵɩɨɥɧɹɟɬɫɹ ɦɨɞɟɥɢɪɨɜɚɧɢɟ (ɪɢɫ. 16). ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɬɟɦɩ ɢ ɥɢɬɨɥɨɝɢɱɟɫɤɢɣ ɬɢɩ ɨɫɚɞɤɨɜ ɧɟɩɪɟɪɵɜɧɨ
ɦɟɧɹɟɬɫɹ, ɚ ɩɪɨɰɟɫɫɵ ɧɚɝɪɭɡɤɢ ɢ ɪɚɡɝɪɭɡɤɢ ɫɢɫɬɟɦɵ ɩɨ ɝɟɨɮɥɸɢɞɚɥɶɧɵɦ ɞɚɜɥɟɧɢɹɦ, ɜɤɥɸɱɚɸɳɢɟ
ɦɢɝɪɚɰɢɸ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ, ɢɞɭɬ ɨɞɧɨɜɪɟɦɟɧɧɨ.
Ⱦɥɹ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ (20-20*) ɩɪɢ ɡɚɞɚɧɧɵɯ ɧɚɱɚɥɶɧɵɯ ɢ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɫɟɬɨɱɧɵɦɢ
ɦɟɬɨɞɚɦɢ ɜɨ ɜɧɟɲɧɟɣ (ɛɚɫɫɟɣɧɨɜɨɣ) ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ (Z, t) ɡɚɞɚɞɢɦ ɩɪɹɦɨɭɝɨɥɶɧɭɸ ɫɟɬɤɭ, ɧɚ ɤɨɬɨɪɨɣ
ɦɨɠɟɬ ɛɵɬɶ ɪɟɚɥɢɡɨɜɚɧɚ ɥɸɛɚɹ ɢɡ ɢɡɜɟɫɬɧɵɯ ɫɟɬɨɱɧɵɯ ɫɯɟɦ. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɜɵɛɪɚɧɚ ɱɟɬɵɪɟɯɬɨɱɟɱɧɚɹ
ɧɟɹɜɧɚɹ ɫɟɬɨɱɧɚɹ ɫɯɟɦɚ, ɨɛɥɚɞɚɸɳɚɹ ɧɟɨɛɯɨɞɢɦɵɦɢ ɫɜɨɣɫɬɜɚɦɢ ɭɫɬɨɣɱɢɜɨɫɬɢ. ɑɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ
ɧɚɱɢɧɚɟɬɫɹ ɫ ɧɭɥɟɜɨɝɨ ɜɪɟɦɟɧɧɨɝɨ ɫɥɨɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɦɨɦɟɧɬɭ ɧɚɱɚɥɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɢɫɫɥɟɞɭɟɦɨɝɨ
ɝɥɭɛɢɧɧɨɝɨ ɪɚɡɪɟɡɚ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɪɟɲɟɧɢɹ ɧɚ ɫɥɟɞɭɸɳɟɦ ɜɪɟɦɟɧɧɨɦ ɫɥɨɟ ɮɨɪɦɢɪɭɟɬɫɹ ɢ ɪɟɲɚɟɬɫɹ
ɦɟɬɨɞɨɦ ɩɪɨɝɨɧɤɢ ɬɪɟɯɞɢɚɝɨɧɚɥɶɧɚɹ ɫɢɫɬɟɦɚ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ.
ȼ ɩɪɨɰɟɫɫɟ ɪɟɚɥɢɡɚɰɢɢ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɩɪɨɰɟɞɭɪɵ ɞɥɹ ɩɨɜɵɲɟɧɢɹ ɟɟ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ
ɭɫɬɨɣɱɢɜɨɫɬɢ ɢ ɫ ɰɟɥɶɸ ɢɫɤɥɸɱɟɧɢɹ ɜɨɡɦɨɠɧɨɫɬɢ ɩɨɥɭɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢ ɧɟɨɛɨɫɧɨɜɚɧɧɵɯ
ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɭɫɥɨɜɧɨɟ ɪɚɡɞɟɥɟɧɢɟ ɩɪɨɰɟɫɫɨɜ ɧɚɝɪɭɡɤɢ ɢ ɪɚɡɝɪɭɡɤɢ.
ɉɭɫɬɶ ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ, ɜɨɡɧɢɤɚɸɳɢɣ ɡɚ n-ɣ ɲɚɝ ɧɚ ɜɪɟɦɟɧɧɨɣ ɫɟɬɤɟ – "ɬɚɤɬ
ɧɚɤɨɩɥɟɧɢɹ", ɫɨɡɞɚɟɬɫɹ ɦɝɧɨɜɟɧɧɨ ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (21), ɜ ɜɢɞɟ:
GɎ< = {(1-I) (U0 /U2 -1)GG0 + IW/(1-I)GL + [SE2 + (1-S) E1]GT}/ {I[W/(1-I)+SJ2]}.
(22)
Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɟ (20*) ɨɩɢɫɵɜɚɟɬ ɩɪɨɰɟɫɫ ɪɚɡɝɪɭɡɤɢ ɷɬɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɩɭɬɟɦ ɦɢɝɪɚɰɢɢ ɞɜɭɯɮɚɡɧɨɝɨ ɮɥɸɢɞɚ
ɫɤɜɨɡɶ n ɧɚɤɨɩɥɟɧɧɵɯ ɤ ɷɬɨɦɭ ɦɨɦɟɧɬɭ ɮɨɪɦɚɰɢɣ ɜ ɜɟɪɬɢɤɚɥɶɧɨɦ ɢ ɥɚɬɟɪɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɹɯ.
106
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
Ɋɢɫ. 15. ɋɨɨɬɧɨɲɟɧɢɟ ɩɨɬɟɧɰɢɚɥɨɜ ɧɚɝɪɭɡɤɢ ɢ ɪɚɡɝɪɭɡɤɢ
ɷɥɟɦɟɧɬɚ ɩɨ ɞɚɜɥɟɧɢɹɦ ɞɥɹ ɨɞɧɨɪɨɞɧɨɣ ɦɨɞɟɥɢ ɫɪɟɞɵ ɜ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɤɭɳɟɣ ɝɥɭɛɢɧɵ. ɑɢɫɥɚ ɧɚ ɤɪɢɜɵɯ – ɬɟɦɩ
ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ, ɦ/MY
ɫɬɪ.89-114
Ɋɢɫ. 16. ɋɯɟɦɚ ɪɚɡɛɢɜɤɢ ɬɪɚɟɤɬɨɪɢɢ
ɩɨɝɪɭɠɟɧɢɹ ɧɚ ɬɚɤɬɵ ɫ ɩɟɪɟɦɟɧɧɵɦ
ɬɟɦɩɨɦ ɢ ɫɨɫɬɚɜɨɦ ɧɚɤɚɩɥɢɜɚɟɦɵɯ
ɨɫɚɞɤɨɜ
Ɍɨɬ ɠɟ ɩɪɢɟɦ ɢɫɩɨɥɶɡɭɟɦ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɦ ɭɪɚɜɧɟɧɢɢ (20) ɞɥɹ ɧɚɫɵɳɟɧɢɣ. ȼɵɱɥɟɧɹɹ
ɞɢɜɟɪɝɟɧɰɢɸ ɩɨɬɨɤɚ ɩɨɪɨɜɨɣ ɜɨɞɵ ɜ ɤɚɱɟɫɬɜɟ ɪɚɡɝɪɭɡɤɢ ɞɚɧɧɨɝɨ ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɡɚ ɬɚɤɬ,
ɨɩɪɟɞɟɥɢɦ ɦɝɧɨɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɞɨɥɢ ɍȼ ɜ ɩɨɪɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɩɪɨɢɡɨɲɟɞɲɟɟ ɩɟɪɟɞ ɷɬɢɦ ɬɚɤɬɨɦ
ɜɫɥɟɞɫɬɜɢɟ ɍȼ-ɝɟɧɟɪɚɰɢɢ, ɭɩɥɨɬɧɟɧɢɹ ɦɚɬɪɢɰɵ ɢ ɪɚɫɲɢɪɟɧɢɹ ɩɨɪɨɜɨɣ ɜɨɞɵ ɜ ɜɢɞɟ:
GS = [(1-I)GG0 – WQGV –IE1GT] (1-S)/I.
(23)
ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɢɫɬɟɦɚ (20-20*) ɨɩɢɫɵɜɚɟɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɪɟɥɚɤɫɚɰɢɨɧɧɵɯ ɩɪɨɰɟɫɫɨɜ
ɪɚɡɝɪɭɡɤɢ ɝɟɨɮɥɸɢɞɚɥɶɧɵɯ ɩɨɬɟɧɰɢɚɥɨɜ (22) ɢ ɍȼ-ɧɚɫɵɳɟɧɢɣ (23), ɦɝɧɨɜɟɧɧɨ ɝɟɧɟɪɢɪɭɸɳɢɯɫɹ ɧɚ
ɬɪɚɟɤɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ ɷɥɟɦɟɧɬɚ U ɜ ɤɚɠɞɵɣ ɬɚɤɬ ɜɵɱɢɫɥɟɧɢɣ.
ɋɯɟɦɚ, ɩɪɟɞɫɬɚɜɥɟɧɧɚɹ ɧɚ ɪɢɫ. 16, ɩɨɹɫɧɹɟɬ ɫɤɚɡɚɧɧɨɟ. Ɂɞɟɫɶ ɜɟɫɶ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɧɨɣ ɲɤɚɥɵ ɪɚɡɛɢɬ
ɧɚ N ɬɚɤɬɨɜ ɧɚɝɪɭɡɤɢ-ɪɚɡɝɪɭɡɤɢ, ɜ ɬɟɱɟɧɢɟ ɤɚɠɞɨɝɨ ɢɡ ɤɨɬɨɪɵɯ ɩɪɨɢɫɯɨɞɢɬ ɦɝɧɨɜɟɧɧɨɟ ɩɪɢɪɚɳɟɧɢɟ ɨɛɳɟɣ
ɦɚɫɫɵ ɥɢɬɨɥɨɝɢɱɟɫɤɨɣ ɤɨɥɨɧɤɢ ɟɞɢɧɢɱɧɨɝɨ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɭ hnUn:
hnUn = h0nU0 n + h0nQ n[(1-S n)U1 n + S nU2 n],
(24)
ɝɞɟ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɧɢɠɧɢɣ ɢɧɞɟɤɫ ɭɤɚɡɵɜɚɟɬ ɧɚ ɮɚɡɭ ɜɟɳɟɫɬɜɚ, ɚ ɜɟɪɯɧɢɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɬɚɤɬɚ.
ɉɪɢ ɷɬɨɦ ɤɚɠɞɵɣ ɢɡ (n-1) ɭɠɟ ɨɬɥɨɠɢɜɲɢɯɫɹ ɷɥɟɦɟɧɬɨɜ ɪɚɡɪɟɡɚ ɩɨɝɪɭɠɚɟɬɫɹ ɫ ɭɩɥɨɬɧɟɧɢɟɦ, ɚ ɬɚɤɠɟ
ɧɚɝɪɟɜɚɟɬɫɹ ɢ ɦɝɧɨɜɟɧɧɨ ɩɨɜɵɲɚɟɬ ɫɜɨɣ ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ (22) ɢ ɍȼ ɧɚɫɵɳɟɧɢɟ (23) ɧɚ
ɜɟɥɢɱɢɧɭ GɎ< ɢ GS ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
ɉɪɚɜɚɹ ɤɨɥɨɧɤɚ ɫɯɟɦɚɬɢɱɟɫɤɢ ɨɬɨɛɪɚɠɚɟɬ ɮɚɡɨɜɵɣ ɫɨɫɬɚɜ ɩɨ ɷɥɟɦɟɧɬɚɦ ɧɚɤɨɩɥɟɧɧɨɝɨ ɡɚ N
ɲɚɝɨɜ ɪɚɡɪɟɡɚ. ɉɨɫɤɨɥɶɤɭ ɬɜɟɪɞɚɹ ɮɚɡɚ ɨɛɥɚɞɚɟɬ ɧɭɥɟɜɨɣ ɩɨɪɢɫɬɨɫɬɶɸ ɢ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ, ɜɟɪɬɢɤɚɥɶɧɚɹ
ɦɢɝɪɚɰɢɹ ɦɨɞɟɥɢɪɭɟɬɫɹ ɜɵɜɨɞɨɦ ɠɢɞɤɨɣ ɢ ɝɚɡɨɨɛɪɚɡɧɨɣ ɮɚɡ ɱɟɪɟɡ ɩɪɚɜɵɟ ɩɚɬɪɭɛɤɢ ɜ ɨɛɳɢɣ ɤɚɧɚɥ
ɜɟɪɬɢɤɚɥɶɧɨɣ ɦɢɝɪɚɰɢɢ – ɬɪɭɛɭ ɫ ɧɟɩɪɨɧɢɰɚɟɦɵɦ ɨɫɧɨɜɚɧɢɟɦ ɢ ɜɵɜɨɞɨɦ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ. Ʌɟɜɵɟ
ɩɚɬɪɭɛɤɢ ɦɨɞɟɥɢɪɭɸɬ ɨɬɜɨɞ ɩɨɪɨɜɨɝɨ ɮɥɸɢɞɚ ɜ ɥɚɬɟɪɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ɉɪɨɜɨɞɹɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ
ɩɚɬɪɭɛɤɨɜ ɦɨɞɟɥɢɪɭɟɬ ɝɟɨɮɥɸɢɞɚɥɶɧɭɸ ɩɪɨɜɨɞɢɦɨɫɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɷɥɟɦɟɧɬɨɜ ɪɚɡɪɟɡɚ. ȼɯɨɞɧɨɣ
ɤɥɚɩɚɧ ɞɥɹ ɩɚɬɪɭɛɤɨɜ, ɜɵɜɨɞɹɳɢɯ ɝɚɡ, – ɤɚɩɢɥɥɹɪɧɵɣ ɛɚɪɶɟɪ. Ɍɟɤɭɳɟɟ ɫɨɨɬɧɨɲɟɧɢɟ ɦɨɳɧɨɫɬɟɣ ɬɜɟɪɞɨɣ
ɢ ɝɟɨɮɥɸɢɞɚɥɶɧɨɣ ɮɚɡ ɨɬɪɚɠɚɟɬ ɞɨɫɬɢɝɧɭɬɵɣ ɭɪɨɜɟɧɶ ɩɨɪɢɫɬɨɫɬɢ, ɚ ɫɨɨɬɧɨɲɟɧɢɟ ɬɨɥɳɢɧɵ ɍȼ-ɩɪɨɫɥɨɹ
ɤ ɨɛɳɟɣ ɬɨɥɳɢɧɟ, ɧɟ ɡɚɧɹɬɨɣ ɬɜɟɪɞɨɣ ɮɚɡɨɣ – ɬɟɤɭɳɢɣ ɭɪɨɜɟɧɶ ɧɚɫɵɳɟɧɢɹ ɩɨɪɨɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ
ɭɝɥɟɜɨɞɨɪɨɞɚɦɢ.
ȿɫɥɢ ɩɨ ɡɚɜɟɪɲɟɧɢɢ N-ɝɨ ɬɚɤɬɚ ɨɫɚɞɤɨɧɚɤɨɩɥɟɧɢɹ ɭɫɥɨɜɢɟ ɩɨɥɧɨɣ ɪɚɡɝɪɭɡɤɢ ɫɢɫɬɟɦɵ ɜɵɩɨɥɧɟɧɨ ɞɥɹ
ɜɫɟɯ ɷɥɟɦɟɧɬɨɜ ɪɚɡɪɟɡɚ, ɬɨ, ɨɱɟɜɢɞɧɨ, ɞɚɜɥɟɧɢɟ ɜ ɜɟɪɬɢɤɚɥɶɧɨɣ ɜɵɜɨɞɹɳɟɣ ɬɪɭɛɟ ɛɭɞɟɬ ɷɤɜɢɜɚɥɟɧɬɧɨ
ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɦɭ ɧɚ ɥɸɛɨɦ ɭɪɨɜɧɟ, ɚ ɫɨɨɬɧɨɲɟɧɢɟ ɦɨɳɧɨɫɬɟɣ ɬɜɟɪɞɨɣ ɢ ɮɥɸɢɞɚɥɶɧɨɣ ɮɚɡ ɩɨ ɤɚɠɞɨɦɭ
ɷɥɟɦɟɧɬɭ ɛɭɞɟɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɡɧɚɱɟɧɢɹɦ ɩɨɪɢɫɬɨɫɬɢ ɧɚ ɬɪɟɧɞɚɯ ɧɨɪɦɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɥɢɬɨɬɢɩɨɜ. ɇɚɩɪɨɬɢɜ, ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɮɥɸɢɞɨɞɢɧɚɦɢɱɟɫɤɢɯ ɛɚɪɶɟɪɨɜ ɧɚ ɩɭɬɢ
ɜɟɪɬɢɤɚɥɶɧɨɣ ɪɚɡɝɪɭɡɤɢ ɩɪɢɜɟɞɟɬ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɫɜɟɪɯɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ, ɤɨɬɨɪɨɟ ɨɫɥɚɛɢɬ
ɫɬɪɟɫɫ. Ɏɨɪɦɚɥɶɧɨ, ɟɫɥɢ ɛɚɪɶɟɪ ɨɤɚɠɟɬɫɹ ɧɟɩɪɨɧɢɰɚɟɦɵɦ, ɬɨ ɪɚɡɝɪɭɡɤɚ ɫɢɫɬɟɦɵ ɜɨɡɦɨɠɧɚ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ
ɥɚɬɟɪɚɥɶɧɨɝɨ ɞɪɟɧɚɠɚ ɢɡ-ɩɨɞ ɩɨɤɪɵɲɤɢ. ȿɫɥɢ ɢ ɷɬɚ ɜɨɡɦɨɠɧɨɫɬɶ ɨɬɫɭɬɫɬɜɭɟɬ, ɬɨ ɝɟɨɮɥɸɢɞɚɥɶɧɵɟ ɞɚɜɥɟɧɢɹ
ɧɚ ɭɪɨɜɧɟ ɛɚɪɶɟɪɚ ɢ ɧɢɠɟ ɛɭɞɭɬ ɜɨɡɪɚɫɬɚɬɶ ɫ ɥɢɬɨɫɬɚɬɢɱɟɫɤɢɦ ɝɪɚɞɢɟɧɬɨɦ, ɚ ɩɪɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɝɟɧɟɪɚɰɢɢ
ɮɥɸɢɞɚ ɢ ɡɚ ɫɱɟɬ ɬɟɪɦɚɥɶɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɩɨɪɨɜɨɣ ɜɨɞɵ ɫɭɳɟɫɬɜɟɧɧɨ ɛɵɫɬɪɟɟ, ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ
ɞɨɫɬɢɝɧɭɬ ɩɪɟɞɟɥɚ ɬɪɟɳɢɧɨɜɚɬɨɫɬɢ ɡɚɩɢɪɚɸɳɟɣ ɞɪɟɧɚɠ ɩɨɪɨɞɵ (Mouchet, Mitchell, 1989). ɉɨɫɥɟɞɧɟɟ ɭɫɥɨɜɢɟ
107
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɜɵɫɬɭɩɚɟɬ ɜ ɤɚɱɟɫɬɜɟ ɮɢɡɢɱɟɫɤɢ ɨɛɨɫɧɨɜɚɧɧɨɝɨ ɨɝɪɚɧɢɱɟɧɢɹ ɪɨɫɬɚ ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ ɩɪɢ ɪɟɚɥɢɡɚɰɢɢ
ɪɚɡɧɨɫɬɧɨɣ ɫɯɟɦɵ.
ȼ ɯɨɞɟ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵ (20-20*) ɧɟɨɛɯɨɞɢɦɨ ɭɜɹɡɚɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ
ɩɪɨɰɟɫɫɨɜ ɧɚɝɪɭɡɤɢ-ɪɚɡɝɪɭɡɤɢ ɫɤɜɨɡɧɵɦɢ (ɬ.ɟ. ɧɟɡɚɜɢɫɢɦɵɦɢ ɨɬ ɧɨɦɟɪɚ ɬɚɤɬɚ) ɧɚɱɚɥɶɧɵɦɢ ɢ
ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨɜɢɹɦɢ ɩɨ ɞɚɜɥɟɧɢɹɦ ɢ ɧɚɫɵɳɟɧɢɹɦ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɩɨɬɟɧɰɢɚɥɨɜ (22-23)
ɥɟɝɤɨ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɧɚ ɩɪɨɢɡɜɨɥɶɧɨɣ ɝɥɭɛɢɧɟ ɩɪɢ ɡɚɞɚɧɧɵɯ ɬɪɚɟɤɬɨɪɢɢ ɩɨɝɪɭɠɟɧɢɹ, ɬɟɦɩɟɪɚɬɭɪɧɨɦ
ɝɪɚɞɢɟɧɬɟ ɢ ɥɢɬɨɬɢɩɚɯ ɨɫɚɞɤɨɜ, ɡɚɩɢɲɟɦ ɷɬɢ ɭɫɥɨɜɢɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
PN,k = 0, SN,k = 0
P0,k = P1,k
Pk,N = Pk-1,N-1 + GɎ
Sk,N = Sk-1,N-1 + GSk
ɪɚɡɝɪɭɡɤɚ ɩɨ ɞɚɜɥɟɧɢɸ ɢ ɧɚɫɵɳɟɧɢɸ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɞɥɹ ɥɸɛɨɝɨ ɬɚɤɬɚ;
ɨɬɫɭɬɫɬɜɢɟ ɩɨɬɨɤɚ ɫɤɜɨɡɶ ɧɢɠɧɸɸ ɝɪɚɧɢɰɭ, ɬ.ɟ. ɧɟɩɪɨɧɢɰɚɟɦɨɫɬɶ ɮɭɧɞɚɦɟɧɬɚ;
ɩɪɟɟɦɫɬɜɟɧɧɨɫɬɶ ɩɪɟɞɲɟɫɬɜɭɸɳɟɝɨ ɪɟɲɟɧɢɹ ɩɨ ɞɚɜɥɟɧɢɸ ɢ ɧɚɫɵɳɟɧɢɸ ɞɥɹ
ɥɸɛɨɝɨ ɷɥɟɦɟɧɬɚ ɝɥɭɛɢɧɧɨɣ ɫɟɬɤɢ;
ɝɞɟ ɩɟɪɜɵɣ ɢɧɞɟɤɫ ɨɬɧɨɫɢɬɫɹ ɤ ɲɤɚɥɟ ɝɥɭɛɢɧɵ, ɜɬɨɪɨɣ – ɤ ɲɤɚɥɟ ɜɪɟɦɟɧɢ, ɚ N – ɨɛɳɟɟ ɱɢɫɥɨ ɷɥɟɦɟɧɬɨɜ
ɪɚɡɪɟɡɚ, ɫɨɜɩɚɞɚɸɳɟɟ ɫ ɧɨɦɟɪɨɦ ɩɨɫɥɟɞɧɟɝɨ ɬɚɤɬɚ ɧɚ ɜɪɟɦɟɧɧɨɣ ɫɟɬɤɟ.
Ⱦɨɫɬɢɝɚɟɦɵɟ ɭɪɨɜɧɢ ɝɟɨɮɥɸɢɞɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɍȼ-ɧɚɫɵɳɟɧɢɹ ɜ ɤɚɠɞɨɣ ɬɨɱɤɟ ɝɥɭɛɢɧɧɨɣ ɫɟɬɤɢ
ɚɧɚɥɢɡɢɪɭɸɬɫɹ ɩɨ ɨɤɨɧɱɚɧɢɢ ɤɚɠɞɨɝɨ ɬɚɤɬɚ ɪɚɡɝɪɭɡɤɢ ɧɚ ɩɪɟɞɦɟɬ ɩɪɟɜɵɲɟɧɢɹ ɤɪɢɬɢɱɟɫɤɢɯ ɡɧɚɱɟɧɢɣ. ɗɬɨ
ɧɟɨɛɯɨɞɢɦɨ ɞɟɥɚɬɶ, ɱɬɨɛɵ ɭɞɨɜɥɟɬɜɨɪɢɬɶ ɭɫɥɨɜɢɹɦ ɩɪɢɦɟɧɢɦɨɫɬɢ ɡɚɤɨɧɚ Ⱦɚɪɫɢ ɞɥɹ ɞɜɭɯɮɚɡɧɨɝɨ ɩɨɬɨɤɚ ɜ
ɩɨɪɢɫɬɨɣ ɫɪɟɞɟ. Ɉɝɪɚɧɢɱɟɧɢɹ ɧɚɤɥɚɞɵɜɚɸɬɫɹ ɧɚ ɡɧɚɱɟɧɢɹ ɤɨɧɫɬɚɧɬ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɬɟɱɟɧɢɟ ɫɬɨɥɶɤɢɯ
ɜɪɟɦɟɧɧɵɯ ɲɚɝɨɜ, ɫɤɨɥɶɤɨ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɜɵɜɨɞɚ ɪɟɲɟɧɢɣ ɢɡ ɡɚɤɪɢɬɢɱɟɫɤɢɯ ɨɛɥɚɫɬɟɣ. ȼ ɱɚɫɬɧɨɫɬɢ,
ɫɥɟɞɭɸɳɢɟ ɨɝɪɚɧɢɱɟɧɢɹ ɜɜɨɞɹɬɫɹ ɩɨ ɩɪɨɜɨɞɢɦɨɫɬɢ ɍȼ-ɮɚɡɵ K2k,n:
Sk,n d Skcr o K2k,n = 0 ɞîïðåäåëüíîå íàñûùåíèå ãàçîâîé ôàçû â æèäêîì ïîðîâîì ôëþèäå;
P +gz (U1-U2n) d CAP2k o K2k,n=0 ɝɚɡɨɞɢɧɚɦɢɱɟɫɤɢɣ ɩɨɬɟɧɰɢɚɥ ɧɟ ɩɪɟɜɵɲɚɟɬ ɤɚɩɢɥɥɹɪɧɨɝɨ ɛɚɪɶɟɪɚ,
k,n
n
ɝɞɟ Scr – ɤɪɢɬɢɱɟɫɤɨɟ ɧɚɫɵɳɟɧɢɟ ɩɨɪɨɜɨɣ ɠɢɞɤɨɫɬɢ ɝɚɡɨɦ, CAP2 – ɤɚɩɢɥɥɹɪɧɵɣ ɛɚɪɶɟɪ ɩɨ ɝɚɡɭ.
108
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
-132
-172
-92
-52
-12 0
T [MY]
7
Z, [km]
1.0
1.5
2.0
Pn,7
1.0
12
ɫɬɪ.89-114
2.5
3.0
3.5
2.5
3.0
3.5
Pn,6 + Ɏn,7
1.5
2.0
Pn,12
Snɤɪɢɬ.
Pn,11 + Ɏn,12
Sn,12
1.0
1.5
2.0
2.5
3.0
3.5
0
Ⱦɚɜɥɟɧɢɟ [g/cm3]
1
1
2
3
4
5
2
4
5
13
12
11
10
9
8
7
6
5
4
2
1
I nNORM I
6
7
n
8
9
10
Sn
Pn
Ɂɨɧɚ ɫɜɨɛɨɞɧɨɝɨ ɝɚɡɚ
11
12
0.1
0.2
0.3
ɉɨɪɢɫɬɨɫɬɶ
13
0
10
-1
-2
10
10
ɍȼ ɇɚɫɵɳɟɧɢɟ
0.4
0.5
10
-3
-4
10
Ɋɢɫ. 17. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɵɟ ɷɬɚɩɵ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ 1.5D ɡɚɞɚɱɢ ɞɥɹ ɢɫɬɨɪɢɢ ɭɩɥɨɬɧɟɧɢɹ
– ɦɢɝɪɚɰɢɢ – ɍȼ-ɝɟɧɟɪɚɰɢɢ, ɩɨɞɪɚɡɞɟɥɟɧɧɨɣ ɧɚ 13 ɬɚɤɬɨɜ (ɧɨɦɟɪɚ ɜ ɪɚɦɨɱɤɚɯ). Ɋɟɚɥɶɧɵɣ ɩɪɢɦɟɪ
ɩɨ ɐɟɧɬɪɚɥɶɧɨɦɭ ɝɪɚɛɟɧɭ ɋɟɜɟɪɧɨɝɨ ɦɨɪɹ.
ɚ – ɪɚɡɝɪɭɡɤɚ ɧɚ ɩɪɨɦɟɠɭɬɨɱɧɨɦ ɬɚɤɬɟ 7 (ɫɥɟɜɚ ɫɯɟɦɚ ɩɨɝɪɭɠɟɧɢɹ, ɫɩɪɚɜɚ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɪɟɲɟɧɢɟ);
ɛ – ɪɚɡɝɪɭɡɤɚ ɧɚ ɩɪɨɦɟɠɭɬɨɱɧɨɦ ɬɚɤɬɟ 12 (ɫɥɟɜɚ ɫɯɟɦɚ ɩɨɝɪɭɠɟɧɢɹ, ɫɩɪɚɜɚ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɪɟɲɟɧɢɟ);
ɜ – ɪɚɡɝɪɭɡɤɚ ɧɚ ɩɨɫɥɟɞɧɟɦ ɬɚɤɬɟ (ɫɥɟɜɚ ɫɯɟɦɚ ɩɨɝɪɭɠɟɧɢɹ, ɫɩɪɚɜɚ ɪɟɲɟɧɢɹ, ɨɬɜɟɱɚɸɳɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɸ
ɝɟɨɮɥɸɢɞɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɩɨɪɢɫɬɨɫɬɢ ɢ ɧɚɫɵɳɟɧɢɹ ɩɨ ɝɥɭɛɢɧɟ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ).
Ɉɛɨɡɧɚɱɟɧɢɹ ɢ ɢɧɞɟɤɫɵ ɫɨɜɩɚɞɚɸɬ ɫ ɜɜɟɞɟɧɧɵɦɢ ɜ ɬɟɤɫɬɟ ɞɥɹ ɮɨɪɦɭɥ (22-24). Ⱦɨɩɨɥɧɢɬɟɥɶɧɨ:
InNORM – ɤɪɢɜɚɹ ɧɨɪɦɚɥɶɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ ɤɨɦɛɢɧɢɪɨɜɚɧɧɚɹ ɩɨ ɪɚɡɥɢɱɧɵɦ ɥɢɬɨɬɢɩɚɦ;
Snɤɪɢɬ. – ɬɟɤɭɳɢɣ ɩɪɟɞɟɥ ɪɚɫɬɜɨɪɢɦɨɫɬɢ ɝɚɡɚ ɜ ɠɢɞɤɨɦ ɩɨɪɨɜɨɦ ɮɥɸɢɞɟ.
ɉɨ ɩɪɨɜɨɞɢɦɨɫɬɢ ɦɚɬɪɢɰɵ K1k,n ɜ ɫɥɭɱɚɟ ɩɪɟɜɵɲɟɧɢɹ ɩɪɟɞɟɥɚ ɬɪɟɳɢɧɨɜɚɬɨɫɬɢ ɩɨɪɨɞɵ FR
ɜɜɨɞɢɬɫɹ ɫɥɟɞɭɸɳɚɹ ɩɨɞɫɬɚɧɨɜɤɚ:
Pk,n + gzn(U1 U2n) t FRk o K1k,n = KFRk >> K1k,m,
ɝɞɟ m – ɧɨɦɟɪ ɬɚɤɬɚ, ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɢɡɨɲɟɥ "ɩɪɨɛɨɣ" ɩɨɪɨɞɵ.
109
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɜɪɟɦɟɧɧɨɣ ɲɚɝ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɬɚɤɬɨɜ ɧɚɝɪɭɡɤɢ-ɪɚɡɝɪɭɡɤɢ ɩɨ ɨɫɢ ɜɪɟɦɟɧɢ ɧɟ
ɨɞɢɧɚɤɨɜ, ɩɨɫɤɨɥɶɤɭ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɥɢɬɟɥɶɧɨɫɬɶɸ ɨɬɥɨɠɟɧɢɹ ɞɚɧɧɨɝɨ ɥɢɬɨɬɢɩɚ. ɑɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ
(20-20*) ɜ ɩɪɟɞɟɥɚɯ ɤɚɠɞɨɝɨ ɬɚɤɬɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɫɟɬɤɟ (Z, t) ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɲɚɝɨɦ
ɩɨ ɜɪɟɦɟɧɢ ɩɪɢ ɫɨɛɥɸɞɟɧɢɢ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɝɪɚɧɢɱɧɵɯ ɢ ɧɚɱɚɥɶɧɵɯ (ɩɨ ɤɚɠɞɨɦɭ ɬɚɤɬɭ) ɭɫɥɨɜɢɣ.
ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɞɥɹ ɦɧɨɝɨɫɥɨɣɧɨɣ ɫɪɟɞɵ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 17.
9. Ɉɛɪɚɬɧɚɹ ɡɚɞɚɱɚ (ɡɚɞɚɱɚ ɨ ɤɚɥɢɛɪɨɜɤɟ)
ȼ ɞɚɧɧɨɦ ɪɚɡɞɟɥɟ ɩɪɢɜɨɞɢɬɫɹ ɮɨɪɦɚɥɶɧɨɟ ɨɩɢɫɚɧɢɟ ɩɨɫɬɚɧɨɜɤɢ ɢ ɩɨɞɯɨɞɨɜ ɤ ɪɟɲɟɧɢɸ
ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɞɟɤɥɚɪɢɪɨɜɚɧɧɵɦɢ ɜɵɲɟ (ɫɦ. ȼɜɟɞɟɧɢɟ) ɨɛɳɢɦɢ ɢɞɟɹɦɢ, ɫɜɹɡɚɧɧɵɦɢ
ɫ ɟɟ ɩɨɫɬɚɧɨɜɤɨɣ, ɢ ɫ ɭɱɟɬɨɦ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɜ ɩɪɟɞɵɞɭɳɢɯ ɪɚɡɞɟɥɚɯ ɩɨɫɬɚɧɨɜɨɤ ɢ ɦɟɬɨɞɨɜ ɪɟɲɟɧɢɹ
ɩɪɹɦɨɣ ɡɚɞɚɱɢ. ȼ ɫɨɜɨɤɭɩɧɨɫɬɢ ɜɵɱɢɫɥɢɬɟɥɶɧɵɟ ɩɪɨɰɟɞɭɪɵ ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ ɢ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱ,
ɫɨɝɥɚɫɨɜɚɧɧɵɟ ɩɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɢ ɜɪɟɦɟɧɧɵɦ ɤɨɨɪɞɢɧɚɬɚɦ, ɩɨɥɨɠɟɧɵ ɜ ɨɫɧɨɜɭ ɪɚɡɪɚɛɨɬɚɧɧɨɣ
ɚɜɬɨɪɚɦɢ ɢ ɭɫɩɟɲɧɨ ɢɫɩɨɥɶɡɨɜɚɜɲɟɣɫɹ ɧɚ ɩɪɚɤɬɢɤɟ ɤɨɦɩɶɸɬɟɪɧɨɣ ɬɟɯɧɨɥɨɝɢɢ ɩɪɨɝɧɨɡɚ ɩɨɪɨɜɵɯ
ɞɚɜɥɟɧɢɣ.
9.1. Ɉɛɳɢɟ ɩɨɥɨɠɟɧɢɹ
ɉɭɫɬɶ ɩɪɹɦɚɹ ɡɚɞɚɱɚ ɦɨɠɟɬ ɛɵɬɶ ɪɟɲɟɧɚ ɞɥɹ ɧɟɤɨɬɨɪɨɝɨ ɝɥɭɛɢɧɧɨɝɨ ɪɚɡɪɟɡɚ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ
ɢɦɟɟɬɫɹ ɢɧɮɨɪɦɚɰɢɹ, ɞɨɫɬɚɬɨɱɧɚɹ, ɱɬɨɛɵ ɚɩɪɢɨɪɧɨ ɡɚɞɚɬɶ ɜɟɤɬɨɪ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ F0 = (F10, F20, ..., Fr0)T,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɫɜɨɣɫɬɜɚ ɩɨɪɨɞ ɢ ɮɥɸɢɞɚ, ɢ ɩɨɡɜɨɥɹɸɳɢɯ ɪɚɫɫɱɢɬɚɬɶ (ɧɚ ɨɫɧɨɜɚɧɢɢ ɩɪɢɧɹɬɵɯ ɦɨɞɟɥɶɧɵɯ
ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɨ ɝɟɨɥɨɝɢɱɟɫɤɢɯ, ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɚɯ – ɫɦ. ɩɪɟɞɵɞɭɳɢɟ ɪɚɡɞɟɥɵ)
ɦɨɞɟɥɶɧɨɟ (ɫɢɧɬɟɬɢɱɟɫɤɨɟ) ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɰɟɥɟɜɨɝɨ ɮɚɤɬɨɪɚ (ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ, ɩɨɪɢɫɬɨɫɬɟɣ ɢ ɬ.ɩ.) ɜ ɭɡɥɚɯ
ɬɨɣ ɠɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɫɟɬɤɢ, ɜ ɤɨɬɨɪɨɣ ɩɪɟɞɫɬɚɜɥɟɧɨ "ɪɟɚɥɶɧɨɟ" ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɭɤɚɡɚɧɧɨɝɨ ɮɚɤɬɨɪɚ,
ɩɨɥɭɱɚɟɦɨɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɹɦɵɯ ɢɥɢ ɨɩɨɫɪɟɞɨɜɚɧɧɵɯ ɢɡɦɟɪɟɧɢɣ.
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɫɢɧɬɟɬɢɱɟɫɤɨɟ ɢ "ɪɟɚɥɶɧɨɟ" ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɛɭɞɭɬ ɪɚɡɥɢɱɚɬɶɫɹ. ɑɟɦ ɛɨɥɶɲɢɦ ɛɭɞɟɬ
ɬɚɤɨɟ ɪɚɡɥɢɱɢɟ, ɬɟɦ ɛɨɥɶɲɟ ɜɟɪɨɹɬɧɨɫɬɶ, ɱɬɨ ɚɩɪɢɨɪɧɵɟ ɞɚɧɧɵɟ ɢɥɢ ɦɨɞɟɥɶɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ, ɩɨɥɨɠɟɧɧɵɟ
ɜ ɨɫɧɨɜɭ ɩɨɫɬɚɧɨɜɤɢ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɨɲɢɛɨɱɧɵ ɢ ɬɪɟɛɭɸɬ ɭɬɨɱɧɟɧɢɹ (ɫɦ. ȼɜɟɞɟɧɢɟ).
Ȼɭɞɟɦ ɧɚɡɵɜɚɬɶ ɷɮɮɟɤɬɢɜɧɵɦɢ ɜ ɫɦɵɫɥɟ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɬɚɤɢɟ ɡɧɚɱɟɧɢɹ ɟɟ ɩɚɪɚɦɟɬɪɨɜ, ɤɨɬɨɪɵɟ
ɩɪɢ ɡɚɞɚɧɧɵɯ ɦɨɞɟɥɶɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɹɯ ɩɨɡɜɨɥɹɸɬ ɩɨɥɭɱɢɬɶ ɫɢɧɬɟɬɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɰɟɥɟɜɨɝɨ
ɮɚɤɬɨɪɚ, ɨɬɥɢɱɚɸɳɟɟɫɹ ɨɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ "ɪɟɚɥɶɧɨɝɨ" ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜ ɩɪɟɞɟɥɚɯ ɦɚɤɫɢɦɚɥɶɧɨɣ
ɜɨɡɦɨɠɧɨɣ ɨɲɢɛɤɢ ɨɩɪɟɞɟɥɟɧɢɹ ɡɧɚɱɟɧɢɣ ɩɨɫɥɟɞɧɟɝɨ.
Ɉɛɪɚɬɧɨɣ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɡɚɞɚɱɭ ɨɩɪɟɞɟɥɟɧɢɹ ɷɮɮɟɤɬɢɜɧɵɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ ɩɪɹɦɨɣ ɡɚɞɚɱɢ
ɞɥɹ ɡɚɞɚɧɧɨɝɨ "ɪɟɚɥɶɧɨɝɨ" ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɰɟɥɟɜɨɝɨ ɮɚɤɬɨɪɚ, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɨɝɨ ɹɜɥɹɸɬɫɹ, ɬɚɤɢɦ
ɨɛɪɚɡɨɦ, ɢɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ ɞɥɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ.
Ɋɟɲɟɧɢɟ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɹɜɥɹɟɬɫɹ, ɩɨ ɫɭɳɟɫɬɜɭ, ɷɮɮɟɤɬɢɜɧɨɣ ɧɚɫɬɪɨɣɤɨɣ (ɤɚɥɢɛɪɨɜɤɨɣ)
ɦɨɞɟɥɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɝɥɭɛɢɧɧɨɝɨ ɪɚɡɪɟɡɚ (ɩɪɹɦɨɣ ɡɚɞɚɱɢ) ɧɚ ɢɫɫɥɟɞɭɟɦɵɣ ɝɥɭɛɢɧɧɵɣ ɪɚɡɪɟɡ. Ɍɚɤɚɹ
ɧɚɫɬɪɨɣɤɚ ɦɨɠɟɬ ɫɩɨɫɨɛɫɬɜɨɜɚɬɶ ɡɚɬɟɦ ɷɮɮɟɤɬɢɜɧɨɦɭ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɩɪɹɦɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɥɹ
ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɞɚɜɥɟɧɢɣ ɜ ɞɚɧɧɨɦ ɢ ɜ ɞɪɭɝɢɯ ɛɚɫɫɟɣɧɚɯ ɫ ɚɧɚɥɨɝɢɱɧɵɦɢ ɝɟɨɥɨɝɢɱɟɫɤɢɦɢ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ.
ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɮɨɪɦɚɥɶɧɨɣ ɩɨɫɬɚɧɨɜɤɢ ɢ ɦɟɬɨɞɚ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɛɭɞɟɦ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɬɟɪɦɢɧɵ ɢ ɨɛɨɡɧɚɱɟɧɢɹ:
Ɋ* = (Ɋ*1, Ɋ*2, ..., Ɋ*L)Ɍ – ɡɚɞɚɧɧɨɟ ("ɪɟɚɥɶɧɨɟ") ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɰɟɥɟɜɨɝɨ ɮɚɤɬɨɪɚ ɩɨ ɝɥɭɛɢɧɟ
ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ, L – ɤɨɥɢɱɟɫɬɜɨ ɬɨɱɟɤ ɩɨ ɝɥɭɛɢɧɟ ɪɚɡɪɟɡɚ, ɜ ɤɨɬɨɪɵɯ ɩɪɨɢɡɜɨɞɢɥɢɫɶ
ɢɡɦɟɪɟɧɢɹ ɡɧɚɱɟɧɢɣ "ɩɨɥɟɜɵɯ" ɞɚɧɧɵɯ. ɂɡɜɟɫɬɧɵ ɬɚɤɠɟ ɝɥɭɛɢɧɵ ɡɚɥɟɝɚɧɢɹ ɷɬɢɯ ɬɨɱɟɤ.
P*P0, ɝɞɟ ɨɛɥɚɫɬɶ P0FEL (EL – L-ɦɟɪɧɨɟ ɟɜɤɥɢɞɨɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɱɧɨɫɬɶɸ ɡɧɚɱɟɧɢɣ
"ɪɟɚɥɶɧɨɝɨ" ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɰɟɥɟɜɨɝɨ ɮɚɤɬɨɪɚ, F – ɨɛɥɚɫɬɶ ɫɨɩɨɫɬɚɜɥɟɧɢɹ.
F = (F1, F2, ..., Fr)Ɍ – ɜɟɤɬɨɪ ɡɧɚɱɟɧɢɣ ɛɟɡɪɚɡɦɟɪɧɵɯ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɹɦɨɣ ɡɚɞɚɱɢ, r – ɨɛɳɟɟ
ɤɨɥɢɱɟɫɬɜɨ ɬɚɤɢɯ ɩɚɪɚɦɟɬɪɨɜ.
F X0, ɝɞɟ X0Er (Er – r-ɦɟɪɧɨɟ ɟɜɤɥɢɞɨɜɨ ɩɪɨɫɬɪɚɧɫɬɜɨ) – ɨɛɥɚɫɬɶ ɚɩɪɢɨɪɧɨ ɞɨɩɭɫɬɢɦɵɯ ɡɧɚɱɟɧɢɣ
ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ.
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɟɞɩɨɥɨɠɟɧɢɟɦ ɨ ɜɨɡɦɨɠɧɨɫɬɢ ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ ɡɚɞɚɱɢ, ɞɥɹ ɥɸɛɨɝɨ ɧɚɛɨɪɚ
ɞɨɩɭɫɬɢɦɵɯ ɡɧɚɱɟɧɢɣ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ, ɡɚɞɚɜɚɟɦɵɯ ɜɟɤɬɨɪɨɦ F X0, ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɨ (ɜ
ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ ɡɚɞɚɱɢ) ɫɢɧɬɟɬɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ P(F)F – ɰɟɥɟɜɨɝɨ ɮɚɤɬɨɪɚ ɩɨ ɝɥɭɛɢɧɟ
ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ ɤɚɤ ɮɭɧɤɰɢɹ F:
P(F) = G(F),
(25)
ɝɞɟ G(F) – ɫɟɬɨɱɧɵɣ ɨɩɟɪɚɬɨɪ ɩɪɹɦɨɣ ɡɚɞɚɱɢ, ɨɫɭɳɟɫɬɜɥɹɸɳɢɣ ɨɬɨɛɪɚɠɟɧɢɟ ɬɨɱɟɤ ɢɡ ɩɪɨɫɬɪɚɧɫɬɜɚ X0 ɜ
ɬɨɱɤɢ ɢɡ ɨɛɥɚɫɬɢ ɫɨɩɨɫɬɚɜɥɟɧɢɹ F. ȼɨɩɪɨɫɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ, ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɤɨɧɟɱɧɨ110
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ɪɚɡɧɨɫɬɧɵɦ ɩɪɟɞɫɬɚɜɥɟɧɢɟɦ ɩɪɨɢɡɜɨɞɧɵɯ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɞɥɹ ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɫɟɬɨɱɧɵɯ
ɦɟɬɨɞɨɜ, ɜ ɤɨɧɬɟɤɫɬɟ ɞɚɧɧɨɣ ɪɚɛɨɬɵ ɧɟ ɹɜɥɹɸɬɫɹ ɤɪɢɬɢɱɟɫɤɢɦɢ. Ɉɧɢ ɞɨɫɬɚɬɨɱɧɨ ɩɨɞɪɨɛɧɨ ɨɛɫɭɠɞɚɸɬɫɹ
ɜ ɥɢɬɟɪɚɬɭɪɟ ɩɨ ɱɢɫɥɟɧɧɵɦ ɦɟɬɨɞɚɦ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɪɟɤɨɦɟɧɞɚɰɢɢ ɭɱɬɟɧɵ ɚɜɬɨɪɚɦɢ ɩɪɢ ɪɚɡɪɚɛɨɬɤɟ
ɤɨɧɤɪɟɬɧɵɯ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɚɥɝɨɪɢɬɦɨɜ.
Ɉɩɟɪɚɬɨɪ G(F) ɹɜɥɹɟɬɫɹ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɟɥɢɧɟɣɧɵɦ, ɢ ɟɝɨ ɫɜɨɣɫɬɜɚ ɫɭɳɟɫɬɜɟɧɧɵɦ ɨɛɪɚɡɨɦ
ɡɚɜɢɫɹɬ ɨɬ ɩɪɢɧɹɬɵɯ ɩɪɢ ɪɟɲɟɧɢɢ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɦɨɞɟɥɶɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɫɟɬɨɱɧɨɝɨ
ɦɟɬɨɞɚ ɢ ɡɧɚɱɟɧɢɣ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ F – ɨɬɨɛɪɚɠɚɟɦɨɣ ɬɨɱɤɢ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ.
ȼɜɟɞɟɦ ɜ ɪɚɫɫɦɨɬɪɟɧɢɟ ɜɟɤɬɨɪɧɭɸ ɮɭɧɤɰɢɸ R(F):
R(F) = :(P(F) P*)/ ||P*||,
(26)
ɝɞɟ: : ɞɢɚɝɨɧɚɥɶɧɚɹ LuL ɦɚɬɪɢɰɚ ɡɚɞɚɧɧɵɯ ɜɟɫɨɜɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɥɹ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ
(P(F) P*); ||P*|| ɟɜɤɥɢɞɨɜɚ ɧɨɪɦɚ ɜɟɤɬɨɪɚ P*. ɗɥɟɦɟɧɬɵ ɦɚɬɪɢɰɵ : ɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ
ɫɬɟɩɟɧɢ "ɞɨɜɟɪɢɹ" ɡɧɚɱɟɧɢɹɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ (P(F) P*) ɢ ɦɨɝɭɬ, ɜɨɨɛɳɟ ɝɨɜɨɪɹ,
ɦɟɧɹɬɶɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ F.
Ɍɨɝɞɚ ɨɛɪɚɬɧɭɸ ɡɚɞɚɱɭ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
ɉɭɫɬɶ ɩɨ ɝɥɭɛɢɧɟ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ ɡɚɞɚɧɨ "ɪɟɚɥɶɧɨɟ" ɪɚɫɩɪɟɞɟɥɟɧɢɟ P*P0.
Ɍɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɜ ɪɚɦɤɚɯ ɡɚɞɚɧɧɵɯ ɦɨɞɟɥɶɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɬɚɤɢɟ ɡɧɚɱɟɧɢɹ ɜɚɪɶɢɪɭɟɦɵɯ
ɩɚɪɚɦɟɬɪɨɜ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ F*X0, ɤɨɬɨɪɵɟ ɞɨɫɬɚɜɥɹɸɬ ɦɢɧɢɦɭɦ <(F) ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɫɢɧɬɟɬɢɱɟɫɤɨɝɨ ɢ "ɪɟɚɥɶɧɨɝɨ" ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɰɟɥɟɜɨɝɨ ɮɚɤɬɨɪɚ ɩɨ
ɝɥɭɛɢɧɟ ɞɚɧɧɨɝɨ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ:
(27)
min <(F) = ||R(F)||2
FX0
Ɂɚɞɚɱɚ (27) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ, ɩɨ ɫɭɳɟɫɬɜɭ, ɧɟɥɢɧɟɣɧɭɸ ɡɚɞɚɱɭ ɨ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɚɯ.
ɉɪɨɜɟɫɬɢ ɫɬɪɨɝɢɣ ɚɧɚɥɢɡ ɫɜɨɣɫɬɜ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɜɨɡɦɨɠɧɨ ɜ ɫɜɹɡɢ ɫ
ɩɪɢɧɰɢɩɢɚɥɶɧɨɣ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶɸ ɫɜɨɣɫɬɜ ɨɩɟɪɚɬɨɪɚ ɩɪɹɦɨɣ ɡɚɞɚɱɢ G(F). Ɉɞɧɚɤɨ ɢɡ ɨɛɳɢɯ
ɫɨɨɛɪɚɠɟɧɢɣ ɦɨɠɧɨ ɫ ɭɜɟɪɟɧɧɨɫɬɶɸ ɩɪɟɞɩɨɥɚɝɚɬɶ, ɱɬɨ ɷɬɚ ɮɭɧɤɰɢɹ ɹɜɥɹɟɬɫɹ ɧɟɥɢɧɟɣɧɨɣ ɢ
ɦɧɨɝɨɷɤɫɬɪɟɦɚɥɶɧɨɣ ɜ ɨɛɥɚɫɬɢ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ X0, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ
ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɧɟɟɞɢɧɫɬɜɟɧɧɨɫɬɢ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ. ɉɨɫɥɟɞɧɹɹ ɦɨɠɟɬ ɢɦɟɬɶ ɟɞɢɧɫɬɜɟɧɧɨɟ
ɪɟɲɟɧɢɟ ɥɢɲɶ ɜ ɫɥɭɱɚɟ ɞɨɫɬɚɬɨɱɧɨ "ɦɚɥɨɣ" ɨɛɥɚɫɬɢ X0, ɱɬɨ ɨɬɜɟɱɚɟɬ ɦɚɥɵɦ ɢɧɬɟɪɜɚɥɚɦ ɜɨɡɦɨɠɧɵɯ
ɡɧɚɱɟɧɢɣ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ. Ɍɚɤɚɹ ɫɢɬɭɚɰɢɹ, ɤɚɤ ɩɪɚɜɢɥɨ, ɯɚɪɚɤɬɟɪɧɚ ɞɥɹ ɯɨɪɨɲɨ ɢɡɭɱɟɧɧɵɯ
ɨɞɧɨɪɨɞɧɵɯ ɫ ɝɟɨɥɨɝɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɪɟɝɢɨɧɨɜ.
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɩɨɢɫɤ ɬɨɱɧɨɝɨ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ (27) ɜɪɹɞ ɥɢ ɹɜɥɹɟɬɫɹ ɫ ɩɪɚɤɬɢɱɟɫɤɨɣ
ɬɨɱɤɢ ɡɪɟɧɢɹ ɰɟɥɟɫɨɨɛɪɚɡɧɵɦ, ɬɚɤ ɤɚɤ ɨɛɵɱɧɨ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɢ ɩɨɝɪɟɲɧɨɫɬɢ ɢɫɯɨɞɧɵɯ "ɪɟɚɥɶɧɵɯ"
ɪɚɫɩɪɟɞɟɥɟɧɢɣ, ɢ ɞɨɫɬɚɬɨɱɧɨ ɧɟɬɨɱɧɵɦɢ ɹɜɥɹɸɬɫɹ ɦɧɨɝɢɟ ɦɨɞɟɥɶɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ, ɩɪɢɧɹɬɵɟ ɜ ɧɚɫɬɨɹɳɟɟ
ɜɪɟɦɹ ɞɥɹ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɮɨɪɦɢɪɨɜɚɧɢɹ ɝɟɨɥɨɝɢɱɟɫɤɢɯ ɪɚɡɪɟɡɨɜ.
Ɍɟɦ ɧɟ ɦɟɧɟɟ ɩɨɞɛɨɪ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ "ɷɮɮɟɤɬɢɜɧɵɯ" ɡɧɚɱɟɧɢɣ ɜɚɪɶɢɪɭɟɦɵɯ
ɩɚɪɚɦɟɬɪɨɜ, ɩɨɡɜɨɥɹɸɳɢɯ ɩɨɥɭɱɢɬɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ (ɪɟɲɟɧɢɹ ɩɪɹɦɨɣ ɡɚɞɚɱɢ) ɫɢɧɬɟɬɢɱɟɫɤɨɟ
ɪɚɫɩɪɟɞɟɥɟɧɢɟ P(F)P0, ɧɟɫɨɦɧɟɧɧɨ ɢɦɟɟɬ ɜɚɠɧɨɟ ɩɪɚɤɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɷɬɢɯ
ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɜ ɩɪɟɞɟɥɚɯ ɪɟɝɢɨɧɚ, ɜ ɤɨɬɨɪɨɦ ɨɫɭɳɟɫɬɜɥɹɥɚɫɶ ɤɚɥɢɛɪɨɜɤɚ ɦɨɞɟɥɢ.
9.2. Ɇɟɬɨɞɵ ɪɟɲɟɧɢɹ
Ⱦɥɹ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (27) ɜɨɡɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɪɚɡɥɢɱɧɵɯ ɢɬɟɪɚɰɢɨɧɧɵɯ
ɚɥɝɨɪɢɬɦɨɜ. ȼ ɫɚɦɨɦ ɨɛɳɟɦ ɜɢɞɟ ɷɬɢ ɚɥɝɨɪɢɬɦɵ ɦɨɝɭɬ ɛɵɬɶ ɡɚɞɚɧɵ ɪɟɤɭɪɪɟɧɬɧɨɣ ɮɨɪɦɭɥɨɣ:
Fk+1 = Fk + qkSk, k = 0,1,2,.... .
(28)
Ɍɨ ɟɫɬɶ, ɧɚɱɢɧɚɹ ɫ ɧɟɤɨɬɨɪɨɝɨ ɧɚɱɚɥɶɧɨɝɨ (ɫɬɚɪɬɨɜɨɝɨ) ɜɟɤɬɨɪɚ F0X0, ɨɧɢ ɛɭɞɭɬ ɫɬɪɨɢɬɶ ɜ
ɨɛɥɚɫɬɢ X0 ɩɨ ɪɟɤɭɪɪɟɧɬɧɨɣ ɮɨɪɦɭɥɟ (28) ɛɟɫɤɨɧɟɱɧɭɸ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɟɤɬɨɪɨɜ F0,
F1, ..., Fk ..., ɫɯɨɞɹɳɭɸɫɹ ɤ ɧɟɤɨɬɨɪɨɦɭ F*X0 – ɬɨɱɤɟ ɥɨɤɚɥɶɧɨɝɨ ɦɢɧɢɦɭɦɚ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ
<(F). ȼɟɤɬɨɪ Sk ɜ ɮɨɪɦɭɥɟ (28) ɡɚɞɚɟɬ ɧɚɩɪɚɜɥɟɧɢɟ ɞɜɢɠɟɧɢɹ ɢɡ ɬɨɱɤɢ Fk ɜ ɬɨɱɤɭ Fk+1, ɚ ɱɢɫɥɨ qk
ɨɩɪɟɞɟɥɹɟɬ ɞɥɢɧɭ ɲɚɝɚ ɜ ɜɵɛɪɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ.
ɋɜɨɣɫɬɜɚ ɪɟɲɟɧɢɣ, ɩɨɥɭɱɚɟɦɵɯ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɛɨɬɵ ɦɟɬɨɞɨɜ ɬɢɩɚ (28), ɛɭɞɭɬ ɫɭɳɟɫɬɜɟɧɧɨ
ɡɚɜɢɫɟɬɶ, ɫɪɟɞɢ ɩɪɨɱɟɝɨ, ɨɬ ɚɞɟɤɜɚɬɧɨɫɬɢ ɦɨɞɟɥɶɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ, ɩɨɥɨɠɟɧɧɵɯ ɜ ɨɫɧɨɜɭ ɩɪɹɦɨɣ
ɡɚɞɚɱɢ, ɨɬ ɬɨɱɧɨɫɬɢ ɩɨɥɟɜɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ (ɨɛɥɚɫɬɶ P0) ɢ ɚɩɪɢɨɪɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɨ ɜɨɡɦɨɠɧɵɯ
ɡɧɚɱɟɧɢɹɯ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɡɚɞɚɱɢ (ɨɛɥɚɫɬɶ X0). ȿɫɥɢ ɩɨɥɭɱɟɧɧɨɟ ɪɟɲɟɧɢɟ ɩɨ ɬɟɦ ɢɥɢ ɢɧɵɦ
ɩɪɢɱɢɧɚɦ ɧɟɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨ, ɢɥɢ ɬɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɢ ɞɪɭɝɢɟ ɥɨɤɚɥɶɧɵɟ ɦɢɧɢɦɭɦɵ ɮɭɧɤɰɢɢ
ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ, ɬɨ ɞɪɭɝɨɟ ɪɟɲɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ, ɜ ɩɪɢɧɰɢɩɟ, ɧɚɣɞɟɧɨ ɟɫɥɢ ɧɚɱɚɬɶ ɫ ɞɪɭɝɨɝɨ ɧɚɱɚɥɶɧɨɝɨ
111
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɩɪɢɛɥɢɠɟɧɢɹ F0X0. ȼ ɰɟɥɨɦ ɫɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ, ɜ ɫɜɹɡɢ ɫ ɧɟɞɨɫɬɚɬɨɱɧɵɦ ɡɧɚɧɢɟɦ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ
ɫɜɨɣɫɬɜ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ <(F), ɪɟɚɥɢɡɚɰɢɹ ɥɸɛɨɣ ɫɬɪɚɬɟɝɢɢ ɞɜɢɠɟɧɢɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ
ɩɚɪɚɦɟɬɪɨɜ ɧɟ ɞɨɥɠɧɚ ɢɫɤɥɸɱɚɬɶ ɭɱɚɫɬɢɟ ɷɤɫɩɟɪɬɚ.
Ƚɥɚɜɧɨɟ ɨɬɥɢɱɢɟ ɨɞɧɨɝɨ ɦɟɬɨɞɚ ɜɢɞɚ (28) ɨɬ ɞɪɭɝɨɝɨ ɛɭɞɟɬ ɡɚɤɥɸɱɚɬɶɫɹ ɜ ɫɩɨɫɨɛɟ ɜɵɛɨɪɚ
ɜɟɤɬɨɪɚ Sk ɢ ɱɢɫɥɚ qk ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɢɬɟɪɚɰɢɨɧɧɨɝɨ ɩɪɨɰɟɫɫɚ (28). ȼɚɠɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ
ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (27) ɦɟɬɨɞɚ ɹɜɥɹɟɬɫɹ ɬɚɤɠɟ ɤɪɢɬɟɪɢɣ ɨɤɨɧɱɚɧɢɹ ɟɝɨ ɪɚɛɨɬɵ. Ȼɭɞɟɦ
ɫɱɢɬɚɬɶ ɩɪɢɟɦɥɟɦɵɦ ɫ ɩɪɚɤɬɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɤɪɢɬɟɪɢɟɦ ɩɨɩɚɞɚɧɢɟ ɦɨɞɟɥɶɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ P(F)
ɜ ɨɛɥɚɫɬɶ P0.
Ɉɞɧɢɦ ɢɡ ɩɪɨɫɬɟɣɲɢɯ ɩɨɞɯɨɞɨɜ ɤ ɱɢɫɥɟɧɧɨɦɭ ɪɟɲɟɧɢɸ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ (27) ɹɜɥɹɟɬɫɹ
ɝɪɚɞɢɟɧɬɧɵɣ ɦɟɬɨɞ ɧɚɢɫɤɨɪɟɣɲɟɝɨ ɫɩɭɫɤɚ. ɉɪɢ ɪɟɚɥɢɡɚɰɢɢ ɷɬɨɝɨ ɦɟɬɨɞɚ ɜ ɤɚɱɟɫɬɜɟ ɜɟɤɬɨɪɚ Sk ɧɚ
ɤɚɠɞɨɦ ɲɚɝɟ ɢɬɟɪɚɰɢɨɧɧɨɝɨ ɩɪɨɰɟɫɫɚ (28) ɜɵɛɢɪɚɟɬɫɹ ɜɟɤɬɨɪ ɚɧɬɢɝɪɚɞɢɟɧɬɚ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ
<(F), ɜɵɱɢɫɥɟɧɧɵɣ ɜ ɬɨɱɤɟ Fk, ɚ ɱɢɫɥɨ qk ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɫɪɟɞɫɬɜɨɦ ɪɟɲɟɧɢɹ ɨɞɧɨɦɟɪɧɨɣ ɡɚɞɚɱɢ
ɦɢɧɢɦɢɡɚɰɢɢ:
<(Fk+qkSk) = min <(F k+qSk)
(29)
q>0
ȼ ɩɪɨɰɟɫɫɟ ɪɟɚɥɢɡɚɰɢɢ ɦɟɬɨɞɚ ɧɚɢɫɤɨɪɟɣɲɟɝɨ ɫɩɭɫɤɚ ɡɧɚɱɟɧɢɹ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ
ɚɧɬɢɝɪɚɞɢɟɧɬɚ – ɱɚɫɬɧɵɯ ɩɪɨɢɡɜɨɞɧɵɯ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ <(F) – ɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɤɨɧɟɱɧɨɪɚɡɧɨɫɬɧɨɦ ɜɢɞɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɩɪɨɰɟɫɫɚ ɩɨɬɪɟɛɭɟɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɪɟɲɟɧɢɟ r
ɩɪɹɦɵɯ ɡɚɞɚɱ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɡɧɚɱɟɧɢɣ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ Sk. Ɋɟɲɟɧɢɟ ɨɞɧɨɦɟɪɧɨɣ ɡɚɞɚɱɢ
ɨɩɬɢɦɢɡɚɰɢɢ (29) ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɨɩɬɢɦɚɥɶɧɨɣ ɞɥɢɧɵ ɲɚɝɚ ɬɚɤɠɟ ɩɨɬɪɟɛɭɟɬ ɪɟɲɟɧɢɹ ɧɟɤɨɬɨɪɨɝɨ
ɤɨɧɟɱɧɨɝɨ ɱɢɫɥɚ ɩɪɹɦɵɯ ɡɚɞɚɱ ɩɪɢ ɥɸɛɨɦ ɜɵɛɨɪɟ ɨɩɬɢɦɢɡɚɰɢɨɧɧɨɝɨ ɚɥɝɨɪɢɬɦɚ.
ɇɟɞɨɫɬɚɬɤɢ ɦɟɬɨɞɚ ɧɚɢɫɤɨɪɟɣɲɟɝɨ ɫɩɭɫɤɚ ɨɛɳɟɢɡɜɟɫɬɧɵ. Ɍɟɦ ɧɟ ɦɟɧɟɟ, ɨɧ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ
ɩɨɥɟɡɧɵɦ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɛɥɢɡɤɨɣ ɤ ɪɟɲɟɧɢɸ ɬɨɱɤɢ F0X0 – ɫɬɚɪɬɨɜɨɣ ɞɥɹ ɛɨɥɟɟ
ɷɮɮɟɤɬɢɜɧɨɝɨ ɚɥɝɨɪɢɬɦɚ, ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɞɥɹ ɭɬɨɱɧɟɧɢɹ ɪɟɲɟɧɢɹ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ
ɦɟɬɨɞ, ɤɨɬɨɪɵɣ ɦɨɠɟɬ ɛɵɬɶ ɨɬɧɟɫɟɧ (Dennis, Scnabel, 1983) ɤ ɦɟɬɨɞɚɦ ɬɢɩɚ ɦɟɬɨɞɚ Ƚɚɭɫɫɚ – ɇɶɸɬɨɧɚ ɞɥɹ
ɪɟɲɟɧɢɹ ɧɟɥɢɧɟɣɧɨɣ ɡɚɞɚɱɢ ɨ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɚɯ (27).
ɉɟɪɟɮɨɪɦɭɥɢɪɭɟɦ ɨɛɪɚɬɧɭɸ ɡɚɞɚɱɭ (27) ɤɚɤ ɡɚɞɚɱɭ ɩɨɢɫɤɚ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵ ɧɟɥɢɧɟɣɧɵɯ
ɭɪɚɜɧɟɧɢɣ:
ɉɭɫɬɶ ɞɥɹ ɧɟɤɨɬɨɪɨɝɨ ɝɥɭɛɢɧɧɨɝɨ ɪɚɡɪɟɡɚ ɡɚɞɚɧɨ "ɪɟɚɥɶɧɨɟ" ɪɚɫɩɪɟɞɟɥɟɧɢɟ P*P0.
Ɍɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɜ ɪɚɦɤɚɯ ɡɚɞɚɧɧɵɯ ɦɨɞɟɥɶɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɬɚɤɢɟ ɡɧɚɱɟɧɢɹ ɜɚɪɶɢɪɭɟɦɵɯ
ɩɚɪɚɦɟɬɪɨɜ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ F*X0, ɱɬɨ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ:
Rk(F*) = 0, k=1, 2, ..., L,
*
(30)
*
ɝɞɟ Rk(F ), k = 1, 2, ..., L ɤɨɦɩɨɧɟɧɬɵ ɜɟɤɬɨɪɚ R(F ), ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɫɨɝɥɚɫɧɨ (26).
Ɉɱɟɜɢɞɧɨ, ɟɫɥɢ ɫɭɳɟɫɬɜɭɟɬ ɬɨɱɧɨɟ ɪɟɲɟɧɢɟ ɧɟɥɢɧɟɣɧɨɣ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ (30), ɬɨ ɨɧɨ
ɨɬɜɟɱɚɟɬ ɧɭɥɟɜɨɦɭ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ <(F).
ɇɚɱɢɧɚɟɦ ɫ ɧɟɤɨɬɨɪɨɝɨ ɧɚɱɚɥɶɧɨɝɨ ɜɟɤɬɨɪɚ ɚɩɪɢɨɪɧɵɯ ɞɚɧɧɵɯ, F0 = (F01, F02, ..., F0r)Ɍ, F0X0.
ɋɬɪɨɢɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɬɨɱɟɤ F0, F1, ..., Fk ..., ɩɪɢɧɚɞɥɟɠɚɳɢɯ X0, ɩɨ ɫɥɟɞɭɸɳɟɦɭ ɩɪɚɜɢɥɭ:
J(Fk) Sk = R(Fk),
Fk+1 = Fk+ qkSk, k = 0,1,2,...,
(31)
(32)
ɝɞɟ: Sk = (Sk1, Sk2, ..., Skr)T ɩɨ-ɩɪɟɠɧɟɦɭ ɜɟɤɬɨɪ ɩɨɩɪɚɜɨɤ ɤ ɜɟɤɬɨɪɭ Fk, ɚ ɱɢɫɥɨ qk ɡɚɞɚɟɬ ɞɥɢɧɭ ɲɚɝɚ ɜ
ɜɵɛɪɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ; J(Fk) – ɦɚɬɪɢɰɚ ɜɵɱɢɫɥɟɧɧɵɯ ɜ ɬɨɱɤɟ Fk ɱɚɫɬɧɵɯ ɩɪɨɢɡɜɨɞɧɵɯ ɤɨɦɩɨɧɟɧɬ
ɜɟɤɬɨɪɧɨɣ ɮɭɧɤɰɢɢ R(Fk) ɩɨ ɤɨɦɩɨɧɟɧɬɚɦ ɜɟɤɬɨɪɚ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɡɚɞɚɱɢ (30). Ʉɚɤ ɢ ɜ ɦɟɬɨɞɟ
ɧɚɢɫɤɨɪɟɣɲɟɝɨ ɫɩɭɫɤɚ, ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɧɚɯɨɞɹɬɫɹ ɜ ɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɨɦ ɜɢɞɟ, ɢ ɞɥɹ ɢɯ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚ
ɤɚɠɞɨɦ ɲɚɝɟ ɩɪɨɰɟɫɫɚ ɬɪɟɛɭɟɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɪɟɲɟɧɢɟ r ɩɪɹɦɵɯ ɡɚɞɚɱ.
Ɋɟɚɥɢɡɚɰɢɹ ɦɟɬɨɞɚ (31-32) ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (30) ɩɪɟɞɩɨɥɚɝɚɟɬ ɩɪɚɤɬɢɱɟɫɤɨɟ ɪɚɡɪɟɲɟɧɢɟ ɪɹɞɚ
ɞɨɫɬɚɬɨɱɧɨ ɢɡɜɟɫɬɧɵɯ ɢ ɜ ɬɨɠɟ ɜɪɟɦɹ ɧɟɩɪɨɫɬɵɯ ɩɪɨɛɥɟɦ ɤɚɤ ɜɵɱɢɫɥɢɬɟɥɶɧɨɝɨ, ɬɚɤ ɢ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ
ɯɚɪɚɤɬɟɪɚ, ɫɜɹɡɚɧɧɵɯ ɫ ɪɟɲɟɧɢɟɦ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ (31) ɢ ɨɩɪɟɞɟɥɟɧɢɟɦ ɡɧɚɱɟɧɢɹ qk ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ
ɩɪɨɰɟɫɫɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɧɚɩɪɚɜɥɟɧɢɟ ɞɜɢɠɟɧɢɹ ɢɡ ɬɨɱɤɢ Fk, ɡɚɞɚɜɚɟɦɨɟ
ɜɟɤɬɨɪɨɦ Sk, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɦɨɠɟɬ ɧɟ ɛɵɬɶ ɧɚɩɪɚɜɥɟɧɢɟɦ ɫɩɭɫɤɚ ɞɥɹ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ <(F),
ɬ.ɟ. ɧɟ ɛɭɞɟɬ ɩɪɢɜɨɞɢɬɶ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɤ ɭɦɟɧɶɲɟɧɢɸ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɜ ɬɨɱɤɟ Fk+1 ɩɨ
ɫɪɚɜɧɟɧɢɸ ɫ ɟɟ ɡɧɚɱɟɧɢɟɦ ɜ ɬɨɱɤɟ Fk. Ⱦɟɬɚɥɶɧɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɷɬɢɯ ɩɪɨɛɥɟɦ ɧɟ ɹɜɥɹɟɬɫɹ ɰɟɥɶɸ
ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ, ɩɨɷɬɨɦɭ ɨɝɪɚɧɢɱɢɦɫɹ ɧɢɠɟ ɥɢɲɶ ɤɪɚɬɤɢɦ ɤɨɦɦɟɧɬɚɪɢɟɦ ɩɨ ɩɨɜɨɞɭ ɨɫɧɨɜɧɵɯ ɢɡ ɧɢɯ.
112
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 3, ʋ1, 2000 ɝ.
ɫɬɪ.89-114
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɦɚɬɪɢɰɚ J(Fk) ɩɪɹɦɨɭɝɨɥɶɧɚɹ Lur, ɫ ɱɢɫɥɨɦ ɫɬɪɨɤ, ɛɨɥɶɲɢɦ, ɱɟɦ ɱɢɫɥɨ ɫɬɨɥɛɰɨɜ
(L>r). Ɍɨ ɟɫɬɶ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɚɜɥɟɧɢɹ Sk = (Sk1, Sk2, ..., Skr)T ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɦɟɬɨɞɚ (31-32) ɪɟɲɚɟɬɫɹ, ɜ
ɨɛɳɟɦ ɫɥɭɱɚɟ, ɩɟɪɟɨɩɪɟɞɟɥɟɧɧɚɹ ɫɢɫɬɟɦɚ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ (31). Ⱦɥɹ ɬɚɤɢɯ ɫɢɫɬɟɦ, ɤɚɤ ɩɪɚɜɢɥɨ, ɢɳɟɬɫɹ
ɨɛɨɛɳɟɧɧɨɟ ɪɟɲɟɧɢɟ, ɤɨɬɨɪɨɟ ɨɬɜɟɱɚɟɬ ɪɟɲɟɧɢɸ ɜ ɫɦɵɫɥɟ ɦɟɬɨɞɚ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ. ɉɪɢ ɷɬɨɦ, ɟɫɥɢ
ɭɤɚɡɚɧɧɨɟ ɪɟɲɟɧɢɟ ɧɟ ɟɞɢɧɫɬɜɟɧɧɨ, ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɜɵɛɨɪ ɪɟɲɟɧɢɹ ɫ ɦɢɧɢɦɚɥɶɧɨɣ ɧɨɪɦɨɣ min ||Sk||. Ɍɚɤɨɣ
ɜɵɛɨɪ ɰɟɥɟɫɨɨɛɪɚɡɟɧ, ɬɚɤ ɤɚɤ ɩɪɢ ɥɢɧɟɚɪɢɡɚɰɢɢ ɧɟɥɢɧɟɣɧɨɣ ɡɚɞɚɱɢ, ɱɬɨ ɢɦɟɟɬ ɦɟɫɬɨ ɧɚ ɤɚɠɞɨɣ ɢɬɟɪɚɰɢɢ
ɦɟɬɨɞɚ (31-32), ɟɫɬɟɫɬɜɟɧɧɨ ɫɬɪɟɦɥɟɧɢɟ ɤ ɦɚɥɵɦ ɩɪɢɪɚɳɟɧɢɹɦ ɡɧɚɱɟɧɢɣ ɤɨɦɩɨɧɟɧɬ ɜɟɤɬɨɪɚ ɪɟɲɟɧɢɹ. ȼ
ɪɟɚɥɢɡɨɜɚɧɧɨɣ ɚɜɬɨɪɚɦɢ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɩɪɨɰɟɞɭɪɟ ɨɛɨɛɳɟɧɧɨɟ ɪɟɲɟɧɢɟ ɫɢɫɬɟɦɵ (31) ɢɳɟɬɫɹ ɫ
ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɢɧɝɭɥɹɪɧɨɝɨ ɪɚɡɥɨɠɟɧɢɹ ɦɚɬɪɢɰɵ J(Fk).
ȿɫɥɢ J(Fk) ɦɚɬɪɢɰɚ ɫɢɫɬɟɦɵ (31) – ɩɥɨɯɨ ɨɛɭɫɥɨɜɥɟɧɚ, ɬɨ ɩɪɢ ɪɟɲɟɧɢɢ ɷɬɨɣ ɫɢɫɬɟɦɵ
ɜɨɡɧɢɤɚɸɬ ɩɪɢɧɰɢɩɢɚɥɶɧɵɟ ɩɪɨɛɥɟɦɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɟɞɥɚɝɚɟɬɫɹ ɩɪɨɜɨɞɢɬɶ ɬɳɚɬɟɥɶɧɵɣ ɫɢɧɝɭɥɹɪɧɵɣ
ɚɧɚɥɢɡ ɫ ɰɟɥɶɸ ɜɵɹɜɥɟɧɢɹ ɧɟɭɫɬɨɣɱɢɜɨɣ ɱɚɫɬɢ ɪɟɲɟɧɢɹ. Ɍɟɯɧɢɤɚ ɩɪɨɜɟɞɟɧɢɹ ɫɢɧɝɭɥɹɪɧɨɝɨ ɚɧɚɥɢɡɚ
ɞɨɫɬɚɬɨɱɧɨ ɯɨɪɨɲɨ ɢɡɭɱɟɧɚ (Lawson, Hanson, 1974). ȿɝɨ ɩɪɚɤɬɢɱɟɫɤɚɹ ɪɟɚɥɢɡɚɰɢɹ ɜ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɜ
ɰɟɥɨɦ ɨɫɧɨɜɚɧɚ ɧɚ ɨɛɳɟɢɡɜɟɫɬɧɵɯ ɪɟɤɨɦɟɧɞɚɰɢɹɯ.
ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɫɢɧɝɭɥɹɪɧɨɝɨ ɪɚɡɥɨɠɟɧɢɹ ɦɚɬɪɢɰɵ J(Fk) ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɨɛɨɛɳɟɧɧɨɝɨ ɪɟɲɟɧɢɹ
ɩɟɪɟɨɩɪɟɞɟɥɟɧɧɨɣ ɫɢɫɬɟɦɵ (31) ɨɤɚɡɵɜɚɟɬɫɹ ɭɞɨɛɧɨɣ ɩɪɢ ɪɟɲɟɧɢɢ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ (30) ɟɳɟ ɢ ɩɨɬɨɦɭ, ɱɬɨ
ɫɢɧɝɭɥɹɪɧɨɟ ɪɚɡɥɨɠɟɧɢɟ ɢ ɟɝɨ ɚɧɚɥɢɡ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɚɬɶ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɦɟɬɨɞɚ (31-32) ɩɨɥɟɡɧɭɸ
ɢɧɮɨɪɦɚɰɢɸ ɨ ɫɢɫɬɟɦɟ (31) ɜ ɰɟɥɨɦ. ɗɬɚ ɢɧɮɨɪɦɚɰɢɹ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɞɭɤɬɢɜɧɨ ɢɫɩɨɥɶɡɨɜɚɧɚ ɞɥɹ ɢɡɭɱɟɧɢɹ ɢ
ɭɥɭɱɲɟɧɢɹ ɫɜɨɣɫɬɜ ɦɟɬɨɞɚ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ, ɜ ɬɨɦ ɱɢɫɥɟ, ɞɥɹ ɚɧɚɥɢɡɚ ɩɪɨɛɥɟɦ, ɫɜɹɡɚɧɧɵɯ ɫ
ɨɰɟɧɤɚɦɢ ɩɨɝɪɟɲɧɨɫɬɟɣ ɢ ɨɪɝɚɧɢɡɚɰɢɢ ɪɚɡɥɢɱɧɵɯ ɮɢɡɢɱɟɫɤɢ ɨɛɨɫɧɨɜɚɧɧɵɯ ɩɪɨɰɟɞɭɪ ɪɟɝɭɥɹɪɢɡɚɰɢɢ. Ɍɚɤ,
ɧɚɩɪɢɦɟɪ, ɧɚɥɢɱɢɟ ɛɥɢɡɤɢɯ ɤ ɧɭɥɸ ɫɢɧɝɭɥɹɪɧɵɯ ɱɢɫɟɥ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɩɨɱɬɢ ɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ
ɦɟɠɞɭ ɫɬɨɥɛɰɚɦɢ ɦɚɬɪɢɰɵ J(Fk), ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɨ ɡɚɜɢɫɢɦɨɫɬɢ ɦɟɠɞɭ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɤɨɦɩɨɧɟɧɬɚɦɢ
ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵ ɜ (31). Ʉɨɷɮɮɢɰɢɟɧɬɵ ɷɬɨɣ ɩɨɱɬɢ ɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɦɨɝɭɬ ɛɵɬɶ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɨ
ɩɨɥɭɱɟɧɵ ɢ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɧɵ ɩɪɢ ɢɡɜɟɫɬɧɨɦ ɫɢɧɝɭɥɹɪɧɨɦ ɪɚɡɥɨɠɟɧɢɢ. ɗɬɚ ɢɧɮɨɪɦɚɰɢɹ ɦɨɠɟɬ ɛɵɬɶ
ɱɪɟɡɜɵɱɚɣɧɨ ɩɨɥɟɡɧɚ ɷɤɫɩɟɪɬɭ ɩɪɢ ɩɪɢɧɹɬɢɢ ɪɟɲɟɧɢɹ ɨ ɤɨɪɪɟɤɬɢɪɨɜɤɟ ɚɩɪɢɨɪɧɵɯ ɞɚɧɧɵɯ. ȼ ɱɚɫɬɧɨɫɬɢ, ɜ
ɷɬɨɦ ɫɥɭɱɚɟ ɢɡɜɟɫɬɧɵ ɛɚɡɢɫɧɵɟ ɜɟɤɬɨɪɵ ɧɭɥɶ-ɦɧɨɝɨɨɛɪɚɡɢɹ ɦɚɬɪɢɰɵ J(Fk), ɱɬɨ ɜ ɩɪɢɧɰɢɩɟ ɩɨɡɜɨɥɹɟɬ
ɩɪɨɜɨɞɢɬɶ ɚɧɚɥɢɡ ɷɬɨɝɨ ɦɧɨɠɟɫɬɜɚ ɪɟɲɟɧɢɣ ɫɢɫɬɟɦɵ (31), ɚ ɬɚɤɠɟ ɨɪɝɚɧɢɡɨɜɵɜɚɬɶ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ
ɤɨɪɪɟɤɬɢɪɨɜɤɭ ɪɟɲɟɧɢɣ ɫɢɫɬɟɦɵ (31) ɛɟɡ ɭɯɭɞɲɟɧɢɹ ɤɚɱɟɫɬɜɚ ɷɬɢɯ ɪɟɲɟɧɢɣ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɫɭɦɦɵ ɤɜɚɞɪɚɬɨɜ
ɧɟɜɹɡɨɤ.
Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɹ ɭɥɭɱɲɟɧɢɹ ɫɜɨɣɫɬɜ ɩɥɨɯɨ ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɫɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ (31) ɟɳɟ ɞɨ
ɟɟ ɪɟɲɟɧɢɹ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɫɭɳɟɫɬɜɥɟɧɢɟ ɪɹɞɚ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɯ ɨɩɟɪɚɰɢɣ. Ʉ ɢɯ ɱɢɫɥɭ ɨɬɧɨɫɹɬɫɹ:
ɦɚɫɲɬɚɛɢɪɨɜɚɧɢɟ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɡɚɞɚɱɢ;
ɜɡɜɟɲɢɜɚɧɢɟ ɭɪɚɜɧɟɧɢɣ ɫɢɫɬɟɦɵ (31);
ɩɪɢɫɜɨɟɧɢɟ ɨɬɞɟɥɶɧɵɦ ɜɚɪɶɢɪɭɟɦɵɦ ɩɚɪɚɦɟɬɪɚɦ ɮɢɤɫɢɪɨɜɚɧɧɵɯ ɡɧɚɱɟɧɢɣ.
Ƚɥɚɜɧɨɣ ɰɟɥɶɸ ɬɚɤɢɯ ɨɩɟɪɚɰɢɣ ɹɜɥɹɟɬɫɹ ɫɬɪɟɦɥɟɧɢɟ ɤ ɩɨɜɵɲɟɧɢɸ ɭɫɬɨɣɱɢɜɨɫɬɢ ɪɟɲɟɧɢɣ ɢ
ɫɧɢɠɟɧɢɸ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɞɨ ɭɪɨɜɧɹ ɫɨɢɡɦɟɪɢɦɨɝɨ (ɢɥɢ ɦɟɧɶɲɟɝɨ), ɱɟɦ
ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɜ ɪɟɲɟɧɢɢ, ɜɵɡɜɚɧɧɵɟ ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ. Ɉɛɨɫɧɨɜɚɧɢɟ ɢ ɫɩɨɫɨɛɵ
ɨɪɝɚɧɢɡɚɰɢɢ ɭɤɚɡɚɧɧɵɯ ɨɩɟɪɚɰɢɣ ɬɚɤɠɟ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɵ (Lawson, Hanson, 1974). ɋɯɟɦɚ ɪɟɚɥɢɡɚɰɢɢ
ɡɚɜɢɫɢɬ ɨɬ ɨɫɨɛɟɧɧɨɫɬɟɣ ɤɨɧɤɪɟɬɧɨɣ ɡɚɞɚɱɢ ɢ ɦɨɠɟɬ ɜɚɪɶɢɪɨɜɚɬɶɫɹ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɦɟɬɨɞɚ (31-32),
ɢɫɯɨɞɹ ɢɡ ɚɧɚɥɢɡɚ ɫɜɨɣɫɬɜ ɫɢɫɬɟɦɵ (31) ɧɚ ɞɚɧɧɨɦ ɲɚɝɟ.
ɇɚɤɨɧɟɰ, ɧɚɯɨɠɞɟɧɢɟ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɦɟɬɨɞɚ (31-32) ɡɧɚɱɟɧɢɹ qk, ɨɩɪɟɞɟɥɹɸɳɟɝɨ ɞɥɢɧɭ ɲɚɝɚ ɜ
ɜɵɛɪɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ Sk, ɫɥɟɞɭɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶ, ɢɫɯɨɞɹ ɢɡ ɬɪɟɛɨɜɚɧɢɣ, ɩɪɟɞɴɹɜɥɹɟɦɵɯ ɤ ɞɥɢɧɟ ɲɚɝɚ ɜ
ɦɟɬɨɞɚɯ ɧɶɸɬɨɧɨɜɫɤɨɝɨ ɬɢɩɚ, ɭɱɢɬɵɜɚɹ ɩɪɢ ɷɬɨɦ ɧɚɥɢɱɢɟ ɨɝɪɚɧɢɱɟɧɢɣ ɧɚ ɢɡɦɟɧɟɧɢɟ ɡɧɚɱɟɧɢɣ
ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɡɚɞɚɱɢ. ɉɨɫɥɟɞɧɟɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɹɜɥɹɟɬɫɹ ɩɪɢɧɰɢɩɢɚɥɶɧɵɦ, ɩɨɫɤɨɥɶɤɭ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɦɟɬɨɞɵ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɜ ɤɥɚɫɫɢɱɟɫɤɨɦ ɜɚɪɢɚɧɬɟ ɧɟ ɨɪɢɟɧɬɢɪɨɜɚɧɵ ɧɚ
ɧɚɥɢɱɢɟ ɨɝɪɚɧɢɱɟɧɢɣ ɧɚ ɢɡɦɟɧɟɧɢɟ ɡɧɚɱɟɧɢɣ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɢ ɨɬɧɨɫɹɬɫɹ ɤ ɬɚɤ ɧɚɡɵɜɚɟɦɵɦ
ɛɟɡɭɫɥɨɜɧɵɦ ɦɟɬɨɞɚɦ. Ɉɛɥɚɫɬɶ X0, ɡɚɞɚɸɳɚɹ ɢɧɬɟɪɜɚɥɵ ɜɨɡɦɨɠɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɷɬɢɯ ɩɚɪɚɦɟɬɪɨɜ, ɤɚɤ
ɩɪɚɜɢɥɨ, ɫɭɳɟɫɬɜɟɧɧɨ ɨɝɪɚɧɢɱɟɧɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɱɬɨ ɨɬɪɚɠɚɟɬ ɟɫɬɟɫɬɜɟɧɧɨɟ ɫɬɪɟɦɥɟɧɢɟ ɤ
ɨɛɨɫɧɨɜɚɧɧɨɦɭ ɡɚɞɚɧɢɸ ɢɧɬɟɪɜɚɥɨɜ ɤɚɤ ɦɨɠɧɨ ɦɟɧɶɲɟɣ ɞɥɢɧɵ. ɗɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɛɨɥɶɲɟɣ ɚɩɪɢɨɪɧɨɣ
ɢɧɮɨɪɦɢɪɨɜɚɧɧɨɫɬɢ ɨ ɫɜɨɣɫɬɜɚɯ ɢɡɭɱɚɟɦɨɝɨ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɪɚɡɪɟɡɚ ɢ ɨɛɴɟɤɬɢɜɧɨ ɞɨɥɠɧɨ
ɫɩɨɫɨɛɫɬɜɨɜɚɬɶ ɩɨɥɭɱɟɧɢɸ ɛɨɥɟɟ ɤɚɱɟɫɬɜɟɧɧɵɯ ɪɟɲɟɧɢɣ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ, ɧɨ ɨɫɥɨɠɧɹɟɬ ɩɪɨɰɟɫɫ
ɧɚɯɨɠɞɟɧɢɹ ɷɬɢɯ ɪɟɲɟɧɢɣ.
ȼ ɪɚɦɤɚɯ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɜɵɲɟ ɦɟɬɨɞɨɜ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɨɝɪɚɧɢɱɟɧɧɨɫɬɶ ɨɛɥɚɫɬɢ X0
ɩɪɢɜɨɞɢɬ ɤ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɹ Fk+1X0 ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɢɬɟɪɚɰɢɨɧɧɨɝɨ ɩɪɨɰɟɫɫɚ. ȼ ɬɟɯ
ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɬɨɱɤɚ FkX0 ɧɚɯɨɞɢɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɛɥɢɡɤɨ ɨɬ ɝɪɚɧɢɰɵ ɨɛɥɚɫɬɢ X0, ɭɤɚɡɚɧɧɨɟ ɭɫɥɨɜɢɟ
ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɚɪɭɲɟɧɧɵɦ, ɢ ɩɨɬɪɟɛɭɟɬɫɹ ɜɵɩɨɥɧɟɧɢɟ ɤɨɪɪɟɤɬɧɨɣ ɩɪɨɰɟɞɭɪɵ ɤɨɪɪɟɤɬɢɪɨɜɤɢ
113
Ɇɚɞɚɬɨɜ Ⱥ.Ƚ. ɢ ɋɟɪɟɞɚ Ⱥ.-ȼ.ɂ. ɉɪɹɦɚɹ ɢ ɨɛɪɚɬɧɚɹ ɡɚɞɚɱɢ ɝɟɨɮɥɸɢɞɨɞɢɧɚɦɢɤɢ...
ɧɚɩɪɚɜɥɟɧɢɹ Sk ɢ ɡɧɚɱɟɧɢɹ qk. ȼ ɪɟɡɭɥɶɬɚɬɟ ɮɚɤɬɢɱɟɫɤɢ ɪɟɱɶ ɢɞɟɬ ɨ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɢ
ɪɟɚɥɢɡɚɰɢɢ ɧɟɤɨɬɨɪɵɯ ɦɨɞɢɮɢɤɚɰɢɣ ɫɬɪɚɬɟɝɢɣ ɛɟɡɭɫɥɨɜɧɨɝɨ ɩɨɢɫɤɚ ɫ ɭɱɟɬɨɦ ɨɝɪɚɧɢɱɟɧɧɨɣ ɞɨɩɭɫɬɢɦɨɣ
ɨɛɥɚɫɬɢ ɢɡɦɟɧɟɧɢɹ ɡɧɚɱɟɧɢɣ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɡɚɞɚɱɢ.
9.3. Ɉɫɨɛɟɧɧɨɫɬɢ ɩɪɨɝɪɚɦɦɧɨɣ ɪɟɚɥɢɡɚɰɢɢ
ɇɚ ɨɫɧɨɜɟ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɩɨɥɨɠɟɧɢɣ ɛɵɥɚ ɪɚɡɪɚɛɨɬɚɧɚ ɢ ɩɪɨɝɪɚɦɦɧɨ ɪɟɚɥɢɡɨɜɚɧɚ
ɩɪɨɰɟɞɭɪɚ ɮɨɪɦɢɪɨɜɚɧɢɹ ɢ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ. ɉɪɨɰɟɞɭɪɚ ɨɮɨɪɦɥɟɧɚ ɜ ɜɢɞɟ ɩɪɨɝɪɚɦɦɧɨɝɨ
ɦɨɞɭɥɹ ɢ ɩɨɡɜɨɥɹɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶ ɪɟɲɟɧɢɟ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɤɚɤ ɦɟɬɨɞɨɦ ɧɚɢɫɤɨɪɟɣɲɟɝɨ ɫɩɭɫɤɚ, ɬɚɤ ɢ
ɦɟɬɨɞɨɦ ɬɢɩɚ Ƚɚɭɫɫɚ – ɇɶɸɬɨɧɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɢɧɝɭɥɹɪɧɨɝɨ ɪɚɡɥɨɠɟɧɢɹ ɩɪɢ ɪɟɲɟɧɢɢ ɫɢɫɬɟɦɵ (31).
Ɇɨɠɧɨ ɨɬɦɟɬɢɬɶ ɫɥɟɞɭɸɳɢɟ ɯɚɪɚɤɬɟɪɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɪɟɚɥɢɡɨɜɚɧɧɵɯ ɩɪɨɰɟɞɭɪ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ
ɡɚɞɚɱɢ:
Ɉɛɚ ɭɤɚɡɚɧɧɵɯ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɧɨɝɨ ɦɨɞɭɥɹ ɩɪɟɞɩɨɥɚɝɚɸɬ ɪɟɲɟɧɢɟ ɨɞɧɨɦɟɪɧɨɣ
ɨɩɬɢɦɢɡɚɰɢɨɧɧɨɣ ɡɚɞɚɱɢ (29) ɦɟɬɨɞɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɞɪɨɛɥɟɧɢɹ ɲɚɝɚ ɫ ɤɭɛɢɱɟɫɤɨɣ
ɚɩɩɪɨɤɫɢɦɚɰɢɟɣ ɦɢɧɢɦɢɡɢɪɭɟɦɨɣ ɮɭɧɤɰɢɢ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɟɤɭɳɟɝɨ ɡɧɚɱɟɧɢɹ ɞɥɢɧɵ ɲɚɝɚ. ɉɪɢ ɷɬɨɦ
ɛɥɨɤɢɪɭɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɜɵɛɨɪɚ ɱɪɟɡɦɟɪɧɨ ɦɚɥɨɣ ɢɥɢ ɱɪɟɡɦɟɪɧɨ ɛɨɥɶɲɨɣ ɞɥɢɧɵ ɲɚɝɚ (Dennis,
Scnabel, 1983). ɉɪɢ ɪɟɚɥɢɡɚɰɢɢ ɦɟɬɨɞɚ ɬɢɩɚ Ƚɚɭɫɫɚ – ɇɶɸɬɨɧɚ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ, ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ,
ɩɨɥɧɵɣ ɧɶɸɬɨɧɨɜɫɤɢɣ ɲɚɝ.
ȼ ɩɪɨɰɟɫɫɟ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɧɨɝɨ ɦɨɞɭɥɹ ɢɫɤɥɸɱɚɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɫɬɪɨɟɧɢɹ ɨɱɟɪɟɞɧɨɝɨ
ɩɪɢɛɥɢɠɟɧɢɹ Fk+1X0. ȼ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɤɨɪɪɟɤɬɢɪɨɜɤɚ ɜɵɛɪɚɧɧɨɝɨ ɧɚ
k-ɦ ɲɚɝɟ ɩɪɨɰɟɫɫɚ ɧɚɩɪɚɜɥɟɧɢɹ Sk. ɉɨɥɭɱɟɧɧɨɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɪɪɟɤɬɢɪɨɜɤɢ ɧɚɩɪɚɜɥɟɧɢɟ
ɝɚɪɚɧɬɢɪɨɜɚɧɧɨ ɨɫɬɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧɢɟɦ ɫɩɭɫɤɚ ɞɥɹ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ.
ɉɪɢ ɪɟɲɟɧɢɢ ɩɥɨɯɨ ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɫɢɫɬɟɦɵ (31) ɪɟɚɥɢɡɨɜɚɧɵ ɨɩɪɟɞɟɥɟɧɧɵɟ ɚɥɝɨɪɢɬɦɢɱɟɫɤɢɟ ɩɪɢɟɦɵ,
ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɭɥɭɱɲɟɧɢɟ ɨɛɭɫɥɨɜɥɟɧɧɨɫɬɢ ɦɚɬɪɢɰɵ ɫɢɫɬɟɦɵ ɜɫɥɟɞɫɬɜɢɟ ɪɟɝɭɥɹɪɢɡɚɰɢɢ ɡɚɞɚɱɢ.
ȼ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɧɚ ɬɟɤɭɳɟɦ ɲɚɝɟ ɩɪɨɰɟɫɫɚ ɧɟ ɭɞɚɟɬɫɹ ɩɨɫɬɪɨɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɫɩɭɫɤɚ ɢɡ ɬɨɱɤɢ FkX0, ɷɬɚ ɬɨɱɤɚ
ɫɱɢɬɚɟɬɫɹ ɥɨɤɚɥɶɧɵɦ ɦɢɧɢɦɭɦɨɦ, ɢ ɩɪɟɞɭɫɦɨɬɪɟɧɚ ɜɨɡɦɨɠɧɨɫɬɶ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɢɡ ɷɬɨɣ ɬɨɱɤɢ ɲɚɝɚ
ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɢɧɵ ɜ ɡɚɞɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɫ ɰɟɥɶɸ ɜɵɯɨɞɚ ɢɡ "ɡɨɧɵ ɩɪɢɬɹɠɟɧɢɹ" ɞɚɧɧɨɝɨ ɥɨɤɚɥɶɧɨɝɨ
ɦɢɧɢɦɭɦɚ. Ɍɚɤɨɣ ɩɪɢɟɦ ɨɪɢɟɧɬɢɪɨɜɚɧ ɧɚ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɥɭɱɟɧɢɹ ɜ ɩɪɨɰɟɫɫɟ ɪɟɲɟɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ
ɧɟɫɤɨɥɶɤɢɯ ɥɨɤɚɥɶɧɵɯ ɦɢɧɢɦɭɦɨɜ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ.
ȼ ɤɚɱɟɫɬɜɟ ɤɪɢɬɟɪɢɹ ɨɫɬɚɧɨɜɤɢ ɪɚɛɨɬɵ ɩɪɨɰɟɞɭɪɵ ɩɪɢɧɹɬɨ ɩɨɥɭɱɟɧɢɟ ɜ ɯɨɞɟ ɪɟɲɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ
ɦɚɥɨɝɨ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɨɰɟɞɭɪɚ ɩɪɟɤɪɚɳɚɟɬ ɫɜɨɸ ɪɚɛɨɬɭ ɩɨɫɥɟ
ɩɨɫɬɪɨɟɧɢɹ ɡɚɞɚɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɧɟɭɞɚɱɧɵɯ ɲɚɝɨɜ ɢɥɢ ɡɚɞɚɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɥɨɤɚɥɶɧɵɯ ɦɢɧɢɦɭɦɨɜ
ɮɭɧɤɰɢɢ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ.
ɉɪɚɤɬɢɱɟɫɤɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɪɟɚɥɢɡɨɜɚɧɧɨɣ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɫɯɟɦɵ ɤɚɥɢɛɪɨɜɤɢ ɩɚɪɚɦɟɬɪɨɜ
ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɨɫɭɳɟɫɬɜɥɹɥɨɫɶ ɧɚ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ ɢ ɩɨɤɚɡɚɥɨ ɞɨɫɬɚɬɨɱɧɭɸ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɢ
ɧɚɞɟɠɧɨɫɬɶ ɪɚɛɨɬɵ ɩɪɨɝɪɚɦɦɧɨɝɨ ɦɨɞɭɥɹ. Ʉɚɤ ɩɪɚɜɢɥɨ, ɬɪɟɛɨɜɚɥɨɫɶ ɧɟ ɛɨɥɟɟ
20-25 ɢɬɟɪɚɰɢɣ ɦɟɬɨɞɚ (31-32) ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɛɥɢɡɤɢɯ ɤ ɧɭɥɸ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɢ
ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ. ɉɪɢ ɷɬɨɦ ɤɚɱɟɫɬɜɨ ɤɚɥɢɛɪɨɜɤɢ ɩɚɪɚɦɟɬɪɨɜ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɨɤɚɡɵɜɚɥɨɫɶ ɞɨɫɬɚɬɨɱɧɵɦ
ɞɥɹ ɧɚɞɟɠɧɨɝɨ ɩɪɨɝɧɨɡɚ ɩɨɪɨɜɵɯ ɞɚɜɥɟɧɢɣ ɜ ɫɯɨɞɧɵɯ ɭɫɥɨɜɢɹɯ.
10. Ɂɚɤɥɸɱɟɧɢɟ
Ʉɚɥɢɛɪɨɜɤɚ ɛɚɫɫɟɣɧɨɜɨɣ ɦɨɞɟɥɢ ɧɚ ɨɫɧɨɜɟ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɫɢɧɬɟɬɢɱɟɫɤɢɯ ɢ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ
ɫɜɨɞɢɬɫɹ ɤ ɪɟɲɟɧɢɸ ɨɛɪɚɬɧɨɣ ɡɚɞɚɱɢ ɮɥɸɢɞɨɞɢɧɚɦɢɤɢ, ɡɚɩɢɫɚɧɧɨɣ ɞɥɹ ɲɤɚɥɵ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɜɪɟɦɟɧɢ. Ⱦɥɹ
ɭɫɩɟɲɧɨɝɨ ɟɟ ɜɵɩɨɥɧɟɧɢɹ ɪɚɡɪɟɡ ɨɫɚɞɨɱɧɨɣ ɬɨɥɳɢ ɩɨɞɪɚɡɞɟɥɹɟɬɫɹ ɧɚ ɪɹɞ ɮɨɪɦɚɰɢɣ, ɨɬɥɢɱɚɸɳɢɯɫɹ
ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɦɢ ɥɢɬɨɥɨɝɢɱɟɫɤɢɦɢ ɤɨɧɫɬɚɧɬɚɦɢ: ɭɩɥɨɬɧɟɧɢɹ, ɮɥɸɢɞɨɩɪɨɜɨɞɢɦɨɫɬɢ, ɍȼ-ɝɟɧɟɪɚɰɢɢ. ɋɭɬɶ
ɩɪɨɝɧɨɡɚ ɬɚɤɢɯ ɹɜɥɟɧɢɣ, ɤɚɤ ȺȼɉȾ, ɥɢɛɨ ɭɪɨɜɧɟɣ ɧɟɮɬɟɝɚɡɨɧɨɫɧɨɫɬɢ ɫɜɨɞɢɬɫɹ ɤ ɜɨɫɫɬɚɧɨɜɥɟɧɢɸ ɜ ɤɚɠɞɨɣ
ɮɨɪɦɚɰɢɢ ɷɬɢɯ ɤɨɧɫɬɚɧɬ ɜ ɥɸɛɨɣ ɬɨɱɤɟ (ɨɛɥɚɫɬɢ) ɜɧɭɬɪɢ ɩɨɥɢɝɨɧɚ, ɨɝɪɚɧɢɱɢɜɚɸɳɟɝɨ ɪɚɣɨɧ ɤɚɥɢɛɪɨɜɤɢ, ɢ
ɪɟɲɟɧɢɸ ɩɪɹɦɨɣ ɡɚɞɚɱɢ ɮɥɸɢ```
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