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Патент USA US3075617

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`Ian. 29, 1963
A. R. ArrKEN ETAL
3,075,607
SEISMIC EXPLORATION
Filed Dec. 51, 1958
2 Shee‘lzs‘Sheeìl 1
BY
¿MM
Jan. 29, 1963
A. R. A11-KEN E-r AL
3,075,607
s ISMIC EXPLORATION
2 Sheets-Sheet 2
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INVENTORS
TTORNEYS
United States Íl; arent
ddee
îßiïäßd?
Patented dan. 29, i953
l
2
3,075,637
The l2 seismic signais produced by the geophones 5l
through 62 are applied through connecting leads 7l~ä§2 to
SEiSMifC EXPLÜRATEÜN
Alexander R. Aitken, .lohn A. E. Gerrard, and George l’.
ilarratian, Bailes, and Hal Si. iones, Houston, Tex., as
signors to Texas instruments incorporated, Dalias, Tex.,
a corporation of Delaware
>different channels of a multichannel preamplifier l5.
After being ampliiied by the preampliher l5 the analogue
seismic signals are applied through connecting leads 83
Sie to a multiplexer 16, which samples the amplitude of
cach seismic signal at regular time intervals and then
transmits the samples through connecting lead 95 in a
single channel sequentially to analogue-to~digital con
Prior to the present invention, the process of seismic
exploration has been carried «out by making seismic rec 10 verter 17.
ords in the held. These seismic records are then physically
According to Shannon’s sampling theorem, an analogue
signal containing no frequencies f cycles per second or
we shall refere to as channels l through l2, respectively.
higher may be completely represented by a sot of samples
transported back to a data processing location Where the
records are analyzed mentally, or with the aid of analyti
cal apparatus such as that disclosed in the Patent No. 15
2,794,965, issued June 4, 1957, to William l. Yost. This
procedure necessarily takes a lot of time. The iinal re
seconds apart in time. For example, an analogue signal
sults of any test are often not available until days after
containing no frequencies 250 cycles per second or higher
the test is performed.
can >be completely represented by samples taken two
20
According to the system of the present invention, the
milliseconds apart. It should be pointed out, however,
seismic signals produced by the geophones are sequen
that frequencies 250 cycles per second or above may not
tially sampled and the sequentially sampled amplitudes
be iiltered out from .an analogue signal by sampling the
are converted into digital data. The digital data is then
analogue signal at two millisecond intervals. Neverthe
transmitted over a radio link to a computer, such as dis
less, a faithful representation of an ordinary seismic sig«
closed in British 1?atent 749,836, issued June 6, 1956, at 25 nal may be made for the purposes of digital analysis by
the data processing center which processes the seismic
samples taken not impractically close to one another.
data and makes the results available after a matter of
For most seismic signals, the samplinfy at intervals of two
minutes instead of days.
milliseconds will be satisfactory.
‘Erior to the present invention there was no known
The multiplexer, since it samples the amplitudes of all
method which gave satisfactory results of operating a 30
twelve
channels, will transmit l2 sampled amplitudes for
digital computer to process seismic data. This lack was
each sampling interval to the analogue to digital con~
due to the fact that the mental process of analyzing the
verter 1'7. The analogue to digital converter ll'î converts
analog seismic records was for a large part subjective
each sampled amplitude to a binary number. The ana
and hence could not be programmed into a digital com
35 logue to digital converter also identities each group of
puter`
sampled amplitudes for each sampling interval and as
The present invention comprises a method of program
signs a binary number to each group to identify the time
ming a digital computer to process the seismic data to
of
»the sampling for that group. The binary number as
give results superior to those obtained by the subjective
signed to each group of sampled amplitudes equals the
mental or analog methods of the prior art.
interval between the time of the shot and the time
An additional object is to provide an improved method 40 time
of
sampling
of such group of sampled amplitudes. These
of seismic exploration which lends itself to an improved
time intervals are expressed in sampling intervals rather
quality, or as it is sometimes identilied, a more sophisti
than seconds to facilitate the operation of the assigning
cated data reduction procedure.
of these time intervals to each group. A simple counter
Further objects and advantages of the present inven
may be used to determine the time interval assigned to
tion can be understood when taken in conjunction with
each group of sampled intervals. If the count registere
the following drawings in which:
FIG. l is a bloeit diagram illustrating the ovenall
method and system of seismic surveying; and
in the counter is increased by one for each succeeding
group, the count registered in the counter will always
EEG. 2 is an analog representation of a typical set oi 50 be the time interval, expressed in sampling intervals, be
tween the time of the sampling and the time of the shot.
seismic signals that may be obtained in a method of seis
The binaryidata including the sampled amplitudes land
mic surveying or that may be obtained when monitoring
the
assigned time intervals may be delivered through con
the system of the present invention.
necting lead 95 to and recorded by magnetic tape recorder
ln a seismic surveying operation an explosion is set
22 to provide a record of the data in the tield. rl`he data
oil below the ground to send shock waves traveling
is also delivered through lead 97 to transmitter 18 and
through the earth. This explosion is referred to in the
then transmitted by transmitter 1S over a radio link to
art as a shot. ln FIG. l the point of the explosion is
receiver i9 in the data processing center. The data re
designated by the reference number 3i. The shock
ceived by receiver i9 is delivered through connection 99
waves travel in the direction indicated by the arrows and
to tape transport 20 and recorded in binary digital form
are reilected by the rock strata 32 and 33. After being 60 on a magnetic tape loop on tape transport itl. The data
reflected by the rocl; strata, the shock waves travel up to
is then fed from the magnetic tape loop to computer 2l
gcophones Si through 62 which are spaced laterally
through connection ltlll where it is processed. In the
across the earth’s surface. The geophones 5l through 62
computer the data is digitally filtered, corrected for time
transduce the waves into eletcrical energy to produce l2
displacement, the reilection zones determined which is
analogue electrical signals in l2 separate channels which 65 called reflection picking, and then the depth and dip in
we shall refer to as channels ll throuhg l2, respectively.
formation computed.
These signals are referred to as seismic signals. The re
If O( t) is a time function vwith :a value of Zero outside
iiected shock waves in the seismic signals are referred to
»some ñnite time interval and if X(t) is another time
as reiiection zones. A typical series of seismic signals that
function, then the function
would be obtained by monitoring such a process is shown 70
in FIG. 2. From these signals the depth and dip of
the strata 32 and 33 can be determined.
3,075,6o7
3
4
.
through @1_30 would be partially completed. Next, the
seismic signal amplitude Xt+1 would be multiplied times
constitutes a time function with certain frequencies re
duced and/or eliminated from X(t). In other words,
O1 through O32. The resulting product O1X1+1 would
<I>(1-) is what is obtained after XU) has been filtered.
The frequency transfer function Y(w) of vsuch filtering is
the frequency spectrum G00) of the function O(t). Thus,
by a proper choice of the filter operator 0(1‘) any filter
start a new summation @t+1 and resulting products O2X1+1
through O32X1+1 would be added to the partially computed
sums dit through @1_30.
This process will go on until all
of the ifs have been computed for the seismic signal.»
As is well known in the seismic surveying art, the times
by conventional L-C circuits. This kind of filtering is
of the seismic signals must be corrected for normal move
called cross-correlation (or convolution where the sign is
minus) filtering. In the case of a signal existing in gaus 10 out, and incremental shock wave velocity increases with
depth. Also, a static time correction must be added to
sian noise,> the optimum cross-correlation filter procedure
each signal. Because of the incremental average velocity
involves the cross-correlation between a representation of
increase with depth, the time correction is less for that part
the 'signal and the signal plus noise function. AlthoughA
of the seismic signal which occurs later. Thus, if t
the noise in a seismic signal is not actually gaussian, quite
favorable results can be obtained by using a typical shock 15 designates the time interval from the shot to the amplitude'y
sampling, the time correction will vary with t and mustv
wave reflection in the seismic signal as the filter operator
be determined for each t. The time correction for each t"
0(1).
is often determined from the formula AT=ATS+A in
To carry out this operation digitally, the operator O(`t)
which ATS is the known static time correction and
is sampled at 32 points at sampling intervals equal to the
sampling interval used in obtaining the digitalized seismic 20
signals. 'I‘he amplitude of the operator at each of these
32 points is converted to the binary system to give 32
binary numbers O1 through O32. Letting the binary num
In the formula for A, d equals the lateral distance between
ers equalling the sampled amplitudes of the seismic sig
the geophone producing the seismic signal and the shot,
nal for a single channel be designated by X1, X2, X3, . . . 25 V0 is the average initial velocity, and V1 is the incremental
XI1 . . . in which the subscript indicates the time of the
increase in the average velocity with depth.
sampling, the computer is programmed to solve for each
By rearranging the terms of the formula for A, the
may be simulated including many which are not realizable
sampled amplitude of the seismi-s signal the equation
equation
30
in which X(t) is any one of the sampled amplitudes of
the seismic signal. The «P’s obtained then will represent
the amplitudes of the seismic signal after it has been
filtered.
For every `<I>, an X is determined. Thus, @tris deter
mined for X(t). Together all of the «ifs for one seismic
signal comprise sampled amplitudes of the ñltered seismic
signal.
These <I>’s are spaced at Vthe same intervals or
the sampling intervals of the X’s.
l
is obtained. If an arbitrary value is assumed for A, for
example 50 sample intervals, then the expression on the
left side of the equation will have a negative value for all
35 t less than the t for which the assumed value of A is core
rect. Therefore, if the expression
21/’12t3-l-2V0V1t2-l-2V02t-íiÃ
40 is evaluated for increasing values of t with A equal to
the assumed value, the value of t at the time the expres
sion turns positive will be the t for which the assumed
operation on the seismic signals of each of the 12 channels.
value of A is correct.
This operation will produce twelve series of binary num
1 By evaluating Ythe expression for increasing t and de
bers, „one series for each channel, each of which is the
sequentially sampled amplitudes of a seismic signal of a 45 creasing the value of A by one increment each time the
expression becomes positive, the A’s for each t after the
different one of the signal channels after such seismic
t for which the arbitrarily assumed value of A is correct
signal has been filtered. These filtered seismic signals
may be determined. The computer is programmed to
of channels 1 through 12 shall be designated <I>‘1(t)
carry out these operations and thus the AT’s are deter
through <ï>12(zf), respectively. The series of binary nurn
bers which make up the sequentially sampled amplitudes 50 mined. In this yprogramming the value of A is initially
chosen large enough that the AT at which the value of
of the functions lï>(z‘) shall be designed as follows:
The computer is programmed to carry out this filtering
the expression goes positive occurs in the seismic signals
prior to the useful part of the seismic signals.
’ It is convenient to program the computer to determine
55 the time correction AT for each <I> along with the deter
In each binary number of the above series of binary
numbers, the superscript designates the channel of the
ñltered function of which such binary number is a sam#
mination of such <I>.
To carry out the operation of reiiection picking, each
one of the filtered seismic signals is operated on to form a
-function p(t) and aU) from each seismic signal. The
tween the shot .and the sampling of the filtered function 60 function p(t) is formed from a seismic signal by identify
ing the peaks and troughs of the seismic signal. The func.
to produce such binary number. The unit'of the time in
tion 1;(1?) is made to equal l at the time of each of the
tervals expressed .bythe subscripts is sampling intervals.
pled amplitude, `and the subscript is the time interval be~
peaks and made to equal zero at each of the troughs..
`In carrying out the filtering operation for one of the
Numerical representation of straight lines are then con
seismic signals it is convenient `to perform the summation
for several lIfs at once. To do this, partially completed 65 nected between the peaks and the troughs thus forming
the new function p(t). The function rr(t) is derived
summations for @1_1 through @1_31 will be stored in the
from a seismic signal by identifying the peaks and troughs
computer at sequential adresses in the computer. Then
ofthe seismic signal. The function a(t) is then made to
XU) is multiplied in sequence by the Values O1 through
equal the absolute value of the peaks and troughs at the
O32. The product X101 will be stored to start a new
summation. -The product X102 will be added to the 70 times of the respective peaks and troughs. Straight lines
are then connected between the adjacent absolute values
partially computed snmfor @1_1. Likewise, each of the
and thus the function :1(1‘) is derived from the seismic sig
products X103 through XtOgZ Vwill be added to the par
nal. The functions a‘l-(t) through a12(t) are derived from
tially completed summations @1__2 through <I>1_31, respec
the filtered seismic signals of channels 1 through 12, re
tively, to further compute these summations. The summa
tion @1_31 would then be completed and the summations @t 75 spectively. TheV functions p1(t) through P120) are
¿finil4
3,075,607'
5
derived from the ñltered seismic signals of channels 1
obtained from the formula S(9, t) :K0P(0, t)[A(0, l)
through l2, respectively.
-l-Ks] in which K0 and Ks are constants. After all of
the combined search functions Sw, t) are obtained they
From the functions a1(t) through ¿112(1‘), a plurality of
search functions A(0, t) are computed at each sampling
from the following formula:
are examined to determine whether they exceed an arbi
trary selection level L1. if one of the S(0, t)’s for -any
given time t is found to be above the arbitrary selection
value, the highest S(0, t) for that time t is selected as in
dicating the existence of a rellection Zone.
Once the existence of a reflection zone is determined,
This formula for A(0, t) perhaps may be better under 10 the criteria selection level is changed from L1 to L2,
which is slightly less than L1 for all the SU), 2)’s of that
stood graphically. If the functions a1(t) through ¿112(1?)
reflection zone. Thus, the reilection Zones are identiîicd.
were plotted on the same time coordinates with each func
The depth and dip of the rock stratum or strata causing
tion placed in order according to its superscript, then the
each reilecticn zone can then be determined.
values of the function (11(1‘) through ttl-2U) used in the
The computer is programmed to carry out this reflec
summation in the formula for computing A(0, t) will be 15
tion picking operation. Of course, the computer oper
found at the intersection of a straight line with the zero
ates on the e’s, the binary numbers which represent the
amplitude ordinate of each of the functions ¿11(t) through
sequentially sampled seismic signals after they have been
@12(1‘). The straight line is referred to as a search line.
lîltered and time corrected.
The search line will intersect the zero amplitude ordinate
To identify the peaks and troughs, the series of e’s
of ¿11(2) at time t and the zero ordinate of the function 20
representing each seismic signal are taken in time se
¿112(1) at the time t+0. The search factors A(0, t) corn
quence and each preceding e is subtracted from each
puted at each sampling interval will have different H’s rang
succeeding <î>. Whenever the sign of the result of this
ing from plus 4 to minus 4 sampling intervals.
series of subtractions changes from positive to negative,
From the functions p1(t) through p12(t) a plurality of
search functions P(9, t) are computed from the following 25 a peak is identiiied at this point'. Whenever the results
from the series of subtractions change from negative to
formula:
v-i
l n HM)
positive a trough is identified 4at this time.
To compute the function p(t) from a seismic l.signal
the computer is programmed to assign the binary nun»l
30 ber l to the time of the identified peaks and O to the
time of the identiiied troughs. At the standard sampling
intervals between the peaks zuid the troughs, the com
puter is programmed to assign values interpolated be~
In this formula P1' is a constant equal to 0.25 which is the
average coherence coeiiicient for a set of random time
functions, and S is an integer selected so that 2S is the
tween 0 and l.
Thus, a series of binary numbers are
computed assigned to times at the standard sampling
intervals. rthis series of numbers will represent sequen
approximate length of a single cycle of one of the central
tially sampled amplitudes of a p(1). The computer is
frequencies in the spectrum of a shock wave reflection.
programmed to make this computation for each filtered
seismic signal to produce a series of binary numbers for
each seismic signal. These series of binary numbers
4.0
p12(t) are plotted on the same time coordinates with their
shall be identified as follows.
Zero amplitude ordinates equally spaced and each func~
tio-n placed in sequence- accorcling to its superscript, then
The formula for P(0, t) may be better understod if
explained graphically.
if the functions p10) through
the summation
1 12
L
L~1
45
12?;1'113 (H‘ 11 9)
P12(f)=p112, @12,11312 - » ~ P1112
equals the average value of the values of the functions
n10) through [1120) at the intersection of the zero ordi 50 Here again, the superscripts designate the channel and
the subscripts designate the time t.
nates of the functions with a search line intersecting
To compute the function 0(1) for `a seismic trace the
1:1(1‘) at time t and intersecting a12(t) at time z‘-}-0. The
computer is programmed to assign the absolute value of
summation
the amplitudes of the filtered and time corrected seismic
signal to the times of the peaks and troughs. The com
puter is programmed to assign at the standard sampling
intervals between the times of the peaks and troughs, A
values interpolated between the values assigned at the
peaks and troughs. rthus, a series of binary numbers
of numbers obtained by taking the value of each func
are computed and assigned to times at the standard satu~
tion at the intersection with the said search line and sub
tracting from each value the average value of the func 60 pling interval. This series 0f numbers will represent the
sequentially sampled function @(1‘) derived from the ñl
tions at all the intersections. The average of the abso~
then equals the average of the absolute values of a series
lute values of the series of numbers is obtained as de
scribed above for each of a` series of parallel search lines
spaced at intervals of one sampling interval. If each of
these averages is subtracted from Pr and the results of
tered signal.
the subtraction added together, then the summation
The computer is programmed to make this computa
tion for each filtered seismic signal to produce a series
o-f binary numbers for each seismic signal. These series
of numbers shall be identified as follows.
will be obtained,
The subscript of the cz’s of each of these series desig
For each 0 and t a combined search factor S(6, t) is
nates the time t and the superscript designates the chan
amaca?
d»
7
and scope of the invention which is to be limited only
`as defined in the appended claims.
What is claimed is:
'1. A method of seismic exploration comprising the
5 steps of:
nel. The computer is programmed to compute A(0, t)
for each t and 6 according to the formula:
l
12
.4(0, wzïêzaœwm
N=1
in which DN equals a set of digital delays such that
D12=0, D1=O and the other DN's are chosen such that
DN
11 5
is equal to a minimum. The computer is programmed
to compute P(6, t) according to the formula
a. creating a seismic disturbance at a field test site
-where reilectionzones of interest may be present,
b. detecting the -seismic Waves resulting from said
seismic disturbance and converting the detected
Waves into a series of electrical signals from spaced
points in the vicinity of said seismic disturbance,
9 amplifying said series of electrical signals in an
analog'preampliiier and
d. Vdelivering said series to multiplexing means and
e. therein mixing and combining said series into a
l2
PtL+D+M
121751
single channel of analog signal,
f. delivering said single channel of analog signal to
an analog-to-digital converter and
‘
in which DN is determined in the same manner it is de
20
termined in the formula for determining A(0, t).
The computer is programmed to then compute S(6, t)
g. converting said single channel of analog signal into
'
a single channel of digital signal,
l. delivering said single channel of digital signal to a
zones in the following manner.
radio transmitter,
í. transmitting said -digital signal to a remotely lo
cated radio receiver,
j. delivering said received digital signal to a computer,
`and
S(0, t). The selected S(0, t) indicates the existence of
. analyzing said received signal for detecting reflec
tion zones whereby an immediate result is obtained
at said remote location while said seismic explora
tion operation is in progress.
2. A method of seismic exploration as in claim 1,
for each 6 and t according to formula
The computer is programmed to select the reflection
All of the SU?, t)’s are
compared in time sequence With L1 to determine which
S(0, t)’s are greater than L1. When one of the S(6, t)’s
is found to be greater than L1, the S(0, t) at the same
time t having the highest value is selected and recorded 30
along with the 0 and t used to compute the selected
a reflection zone.
Once the existence of a reflection zone
has been indicated, all the succeeding S(0, t)’s in the
same reilection zone are compared with L2, which is
slightly less than L1, to minimize -lluctuations at the be~
ginning and end of the reflection zone.
The computer is programmed to determine accurately
k. unscrambling said previously mixed signal, and
wherein said step Iof unscrambling said mixed signal
comprises digitally filtering and separating said signal
into a plurality of digital signals for computation pur
poses.
v'3. A method of seismic exploration as in claim 2,
wherein said step of analyzing said received signal com
prises: generating a set of first functions based on the
the times and responses from the reflection zones using
the data obtained from the operation of selecting reflec 40 absolute values of the peaks of said plurality of digital
signals; generating a set of second functions based on
tion Zones. The computer carries out this operation by
the positive and negative peaks of said digital signals;
examining the reflection zone information with increas
generating a set of third functions based on said first
ing t until a picked zone is encountered. The computer
functions; generating a set of fourth functions based on
then examines the values of <I>1(t) occurring after the
time of the start of thepicked reflection Zone to locate 45 said second functions; generating a set of ñfth functions
based on the combined third and fourth functions to pro
the first trough occurring in <ID1(t)‘ after the start of the
vide a set of search functions for indicating the existence
picked reflection zone. The computer next examines the
of a reflection zone.
value of @120) to find the nearest trough in the func
4. A method of seismic exploration as in claim 3,
tion @120) to a time occurring the time 0 after the time
of the trough determined in @10). The times of the two 50 wherein said search functions are generated in accord
ance with the formula:
located troughs then are recorded. The computer is
programmed to carry out the above operation for each
picked reflection.
i
The computer may be programmed to make these re
corded times of these troughs available to the operator, 55
or the computer may be programmed to convert this
information into dips and depths for the strata causing
the reflections.
In the above description the number of seismic signal
channels is twelve. The invention, of course, may be 60
used with a different number of channels. This and
other modifications are deemed to come Within the spirit
References Cited in the tile of this patent
UNITED STATES PATENTS
Re. 23,686
2,265,513
Heising ______________ __ July 14, 1953
Burg ________________ __ Dec. 9, 1941
’ 2,794,965
Yost ________________ __ June 4, 1957
2,836,356
Forrest et al ......... __ May 27, i958
` 2,845,597
Perkins _____________ __ July 29, 1958
2,874,356
'Peterson _____________ __ Feb. 17, 1959
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