Method for determining seismic velocities

The present invention relates generally to a method for determining seismic velocities and more particularly to a method and system for objectively determining seismic velocities from samples of the earth's subterranean formation. Additionally, the present invention provides a method for obtaining a measure of the variation of seismic velocities of propagation with pressure.

The present invention relates generally to a method for determining seismic 
velocities of propagation and, more particularly, to a method for 
objectively determining seismic velocities of propagation in samples of 
the earth's subterranean formations. 
Measurement of velocities of propagation using the pulse transmission 
technique is well established for a variety of materials. However, such 
technique can be time consuming and requires the subjective analysis of 
skilled operators to obtain estimates of the velocities of propagation. In 
fact, the use of the pulse transmission technique on samples of the earth 
is particularly difficult because of the variety of rock types and their 
complex microstructures. Consequently, an imparted energy pulse can be 
greatly attenuated as it propagates through the earth sample making 
velocity determinations difficult. In order to minimize errors in velocity 
determination resulting from the subjective analysis by the operator, 
investigators have employed higher frequency energy pulses to determine 
the velocities of propagation in both metals and ceramics. Unfortunately, 
these higher frequency techniques cannot be employed on samples of the 
earth due to scattering losses and higher intrinsic attenuation of the 
imparted energy pulse. 
Determining the effect of varying pressures on seismic velocities of 
propagation through the earth is another important aspect in the 
determination of seismic velocities of propagation. However, decreasing 
the pressures to which samples of the earth are subjected while employing 
the pulse transmission technique can result in very poor quality signals. 
Such poor quality signals substantially deteriorate the precision of the 
pulse transmission technique and can require even more subjective analysis 
by highly skilled operators. Conversely, subjecting samples of the earth 
to the highest possible pressures can have the undesirable result of 
irreversibly altering the samples if the pressures applied are greater 
than their corresponding in-situ effective pressure. 
In view of the foregoing, the present invention provides a novel method for 
determining seismic velocities of propagation from samples of the earth 
and the effect thereon of varying pressures, in addition to overcoming the 
limitations of existing pulse transmission techniques. 
SUMMARY OF THE INVENTION 
The present invention provides a novel method for determining velocities of 
propagation of seismic energy in the earth. In order to overcome the 
limitations of existing subjective methods for determining seismic 
velocities of propagation, the present invention provides an objective 
method for determining the velocity of propagation of seismic waves in the 
earth from samples of the earth. 
More particularly, the present invention comprises obtaining a time series 
signal representative of the traveltimes for an energy pulse to propagate 
through samples of the earth. A first estimate of the seismic velocity of 
propagation can be obtained from an envelope signal computed from the time 
series signal. A second estimate of the seismic velocity of propagation 
can be obtained from the time series signal directly. Selected 
characteristics of the time series signal and energy pulse can be obtained 
and compared, whereby a best estimate of the seismic velocity of 
propagation in the earth can be obtained from the first and second 
estimates of seismic velocity. 
By collecting a plurality of time series signals over a selected range of 
pressures acting on the sample of the earth, a measure of the variation of 
seismic velocities as a function of pressure can be determined. The 
pressures range from atmospheric to the in-situ effective pressure acting 
on the sample of the earth. More particularly, a master trace signal is 
obtained from the time series signal obtained at the highest pressure 
acting on the sample of the earth. The master trace signal commences at a 
traveltime corresponding to the estimated seismic velocity of propagation 
and extends for a period of time related to the spectral content of time 
series signal. The master trace can then be cross-correlated with each of 
the time series signals obtained at lesser pressures to obtain semblance 
functions. Traveltimes for peaks in the resulting semblance functions are 
located for each pressure point, and the largest peaks for each pressure 
point are curve fitted to a pressure function to obtain measures of the 
seismic velocities at selected pressure points as well as to obtain a 
measure of the variation of seismic velocity with pressure

DETAILED DESCRIPTION OF THE INVENTION 
The present invention relates generally to a method for determining 
velocities of propagation of seismic energy in the earth. 
In order to better understand the present invention, the following 
introductory discussion is provided. The velocities of propagation of 
seismic energy in the earth's formations can be estimated using the pulse 
transmission technique whereby the elapsed time for an energy pulse to 
travel through a sample of the earth's formation is determined. A system 
for implementing this technique is represented schematically in FIG. 1 
wherein an energy pulse I developed by pulse generator 10 is imparted into 
one end of sample S by a source transducer 20, and a time series signal R 
is received at an opposite end of the sample S by a receiver transducer 30 
and displayed on oscilloscope 40. Since the travel distance L of the 
imparted energy pulse through the sample S can be measured quite 
accurately, all that is required to determine the velocity of propagation 
is the traveltime for the energy pulse to traverse the distance L. 
Typically, traveltimes are determined by clocking the time of a first 
arrival of the energy pulse I by starting a clock in oscilloscope 40 with 
a trigger pulse 50 from the pulse generator 10 at a time coinciding with 
the time of imparting the energy pulse I into the sample S. 
When it is desired to determine the velocity of propagation for 
compressional waves (P) through a sample, one simply obtains signals 
generated by a P-wave source transducer and received by a P-wave receiver 
transducer. However, when it is desired to determine the velocity of 
propagation for shear waves (Sh or SV) through a sample of the earth, 
those skilled in the art will recognize that it is necessary to collect a 
dyad of signals .phi..sub.ij and process the dyad of signals .phi..sub.ij 
by rotation so as to ameliorate the effects of shear wave splitting which 
can be caused by anisotropic rock. The dyad of signals .phi..sub.ij 
comprises signals .phi..sub.11, .phi..sub.12, .phi..sub.21, and 
.phi..sub.22 wherein the subscript i indicates the polarization of the 
shear wave source transducer (Sh or SV) and the subscripting j indicates 
the polarization of the shear wave receiver transducer (Sh or SV). In 
general, a plurality of signals representative of each source-receiver 
combination (i.e., P--P, Sh--Sh, Sh--SV, SV--Sh and SV--SV) are recorded 
at each selected pressure point within the range of pressures. To simplify 
the following discussion, only signals obtained by one source-receiver 
combination will be discussed and if anisotropy corrections are required, 
they will have already been applied. 
FIG. 2 is a time series signal representative of signals typically recorded 
for rock samples using the pulse transmission technique at pressures less 
than their corresponding in-situ effective pressures. The term "effective 
pressure" is understood to be the difference between the in-situ 
overburden vertical stress acting on the sample and its pore fluid 
pressure. As can be seen in FIG. 2, determination of arrival times of the 
energy pulse, and hence seismic velocities of propagation, is not always 
as simple as suggested. Rather, inhomogeneities of the earth's formations 
comprising the sample can result in complicated time series signals. The 
time series signal of FIG. 2 exemplifies the difficulties in determining 
arrival times, and hence seismic velocities of propagation, of the 
imparted energy pulse, especially at pressures less than the in-situ 
effective pressure. Shear wave velocity determinations can be even more 
difficult than compressional wave velocity determinations because of shear 
wave splitting and the earlier arrival of compressional waves. 
Consequently, determination of arrival times (and hence seismic 
velocities) in samples of the earth oftentimes requires the subjective 
analysis of highly skilled operators and can be fraught with undetected 
errors. 
It is well established that velocities of propagation and attenuation of 
seismic energy imparted into the earth exhibit very pronounced dependence 
on the pressure. As such, the variations of seismic velocities with 
pressure are of particular concern to explorationists but difficult to 
ascertain. The pressure dependence of seismic velocities is also important 
for understanding the microstructure of rocks. Unfortunately, it is 
impractical to subject samples of the earth to the highest possible 
pressure and then measure velocities of propagation as pressure decreases 
because the samples can be irreversibly altered. Moreover, as the 
pressures decrease below the in-situ effective pressure, the quality of 
time series signals representative of the propagation of seismic energy 
can be substantially degraded, thus making velocity estimates difficult. 
Looking now to FIG. 3, a generalized flow diagram of the present invention 
is provided. At step 100, a set of time series signals are recorded which 
are representative of the traveltimes for an energy pulse to propagate 
through a sample of the earth at a plurality of pressure points within a 
selected range of pressures. Typically, the pressure points are varied 
from atmospheric to one corresponding to the in-situ effective pressure 
acting on the sample. Preferably, five time series signals are recorded 
for each source-receiver combination at each selected pressure point. The 
signals recorded for each source-receiver combination at each pressure 
point can then be summed or stacked to produce a summed signal for each 
pressure point. By controlling the amplitude and frequency spectra and 
rise time of the energy pulse imparted into the sample of the earth, the 
summed signals from step 100 can be bandpass-filtered at 110 if necessary 
to suppress noise outside the frequency spectra of the imparted energy 
pulse to form filtered signals. The filtered signal F obtained at the 
highest pressure point is depicted in FIG. 4a. 
At step 120, the filtered signal F obtained at the highest pressure point 
(e.g., the in-situ effective pressure) is normalized and an envelope 
signal E is computed therefrom, as shown in FIG. 4b. By determining the 
envelope signal E, polarity reversals in the time series signals and 
filtered signals can be compensated for. At step 130, the traveltime for 
the maximum in the envelope signal E is located at time t.sub.m. At step 
140, the envelope signal E is subdivided into two time windows 
(.DELTA.t.sub.1 and .DELTA.t.sub.2) as shown in FIG. 4b. The first time 
window .DELTA.t.sub.1 encompasses a selected time interval before the 
amplitude of the envelope signal E exceeds a predetermined threshold at 
traveltime t.sub.h. The second time window .DELTA.t.sub.2 extends from the 
point at which the amplitude of envelope signal E exceeds the 
predetermined threshold at traveltime t.sub.h to the traveltime t.sub.m of 
the maximum of the envelope signal E determined at step 130. 
Those skilled in the art will appreciate that by digitizing both the 
filtered and the envelope signals, a series of data points can be 
obtained. Data points within the first and second time windows 
(.DELTA.t.sub.1 and .DELTA.t.sub.2) of the envelope signal E are curve 
fitted to separate functions at step 150. Preferably, the functions are 
polynomials of degree 1 or 2. The best-fit functions for each time window 
are then extrapolated beyond their respective time windows and can then be 
solved simultaneously to determine their point of mutual intersection at 
step 160. The point of intersection will hereafter be referred to as the 
envelope arrival time t.sub.env and comprises a first estimate of the 
seismic velocity of propagation at the highest pressure point. 
The original filtered signal F obtained at the highest pressure point 
(e.g., the in-situ effective pressure) is next subjected to similar 
processing. In particular, at step 170, the filtered signal F is 
subdivided into time windows .DELTA.t.sub.1 and .DELTA.t.sub.2 as shown in 
FIG. 4a. The time windows (.DELTA.t.sub.1 and .DELTA.t.sub.2) can have 
generally the same temporal extent and temporal location as those for the 
envelope signal E. However, the second time window .DELTA.t.sub.2 for the 
time series preferable extends from the traveltime t.sub.h up to the 
traveltime associated with the first peak in the time series signal, 
irrespective of whether the first peak is either positive or negative. 
Data points within the time windows .DELTA.t.sub.1 and .DELTA.t.sub.2 for 
the filtered signal F are curve fitted to separate functions at step 180. 
Preferably, the functions are polynomials of degree 1 or 2. The best-fit 
functions for each time window are then extrapolated beyond their 
respective time windows and can then be solved simultaneously to determine 
their point of mutual intersection at step 190. The point of intersection 
will hereinafter be referred to as the time series arrival time t.sub.t 
and comprises a second estimate of the seismic velocity of propagation at 
the highest pressure point. 
At step 194, the original filtered signal F is evaluated at the arrival 
time t.sub.t and selected characteristics of the filtered signal F can be 
obtained, including: spectral content, spectral amplitude, and rise time 
(i.e., slope). The spectral content of the filtered signal F obtained for 
the highest pressure point at time t.sub.t can be used to determine a 
cross-correlation length .lambda.. In particular, the cross-correlation 
length .lambda. can be obtained by Fourier synthesis of the spectral 
content of the filtered signal F at time t.sub.t at step 198. 
At step 200, the arrival times t.sub.t and t.sub.env (obtained from steps 
160 and 190, respectively) are compared and if t=t.sub.env, the arrival 
time will hereafter simply be designated t.sub.a at 210. The arrival time 
t.sub.a can be employed to provide a measure of the seismic velocity of 
propagation. If however, the arrival times t.sub.env .noteq.t.sub.t, the 
characteristics obtained for the filtered signal F at step 194 are 
compared to like characteristics of the imparted energy pulse at step 220. 
If the spectral content, spectral amplitude and rise time of the filtered 
signal F do not agree, within selected limits, with the same 
characteristics for the imparted energy pulse, the arrival time t.sub.a is 
defined to be t.sub.a =t.sub.env at step 230. Alternatively, if the 
characteristics agree, within selected limits, the arrival time t.sub.a is 
defined to be t.sub.a =t.sub.t at step 240. Steps 120-240 can be repeated 
for filtered signals obtained at lesser pressures; however, it has been 
found that the time series signal quality deteriorates as pressure 
decreases and that the envelope arrival times t.sub.env for filtered 
signals obtained at lesser pressures can generally provide better 
estimates of the arrival time t.sub.a, and hence seismic velocity than the 
time series arrival time t.sub.t. 
An adaptive cross-correlation technique will now be described for 
determining arrival times, t.sub.a and hence seismic velocities of 
propagation, in filtered signals obtained at lesser pressures (e.g., less 
than the in-situ effective pressure). Additionally, a measure of the 
variation of seismic velocities of propagation with pressure can be 
obtained. 
Looking now to FIG. 5, the steps of such cross-correlation technique will 
be described. Specifically, at step 250, a segment of the filtered signal 
F obtained at the highest pressure point (e.g., in-situ effective 
pressure) is defined as a master trace for use in cross-correlating with 
the filtered signals obtained at lesser pressure points. The spectral 
content of the filtered signal F can be used to define the extent of the 
master trace. In particular, the cross-correlation length .lambda. 
obtained at step 195 can be employed to define the temporal extent of the 
master trace. The master trace starts at a time corresponding to the 
arrival time t.sub.a previously determined at steps 210, 230 or 240, and 
extends to longer transit times as determined by the cross-correlation 
length .lambda.. 
At step 260, the master trace is cross correlated with each of the filtered 
signals obtained at lesser pressures to form a series of cross-correlation 
functions for each pressure point. Since seismic velocities of propagation 
are expected to be greatest at the highest pressure, the cross correlation 
of the master trace with the filtered signals obtained at lesser pressures 
can be constrained to starting at, traveltime t.sub.a determined at the 
highest pressure point. Each cross-correlation function can then be 
searched to locate the traveltimes of the five strongest semblance peaks 
at step 270. The five strongest semblance peaks for each correlation 
function and their associated traveltimes are stored in descending order 
of semblance peak magnitude. 
At step 280, the traveltimes associated with the strongest semblance peaks 
for each pressure point are curved fitted to a pressure function to obtain 
a measure of seismic velocity of propagation at each pressure point and 
hence a measure of the variation of seismic velocity with pressure. Prior 
experience indicates that not all rocks behave similarly but generally 
exhibit a pressure dependence of seismic velocity characterized by a 
polynomial or exponential function. After fitting the traveltimes 
associated with the strongest semblance peaks to the pressure function, 
the goodness of fit of the traveltimes to the pressure function is 
evaluated at 290. In particular, the traveltimes exhibiting deviations are 
replaced by the traveltime associated with the next strongest semblance 
peak for that pressure point. The process of evaluating the goodness of 
fit of the traveltimes to the pressure function is carried out iteratively 
until a specified level of deviation has been achieved, resulting in a 
more consistent determination of seismic velocities of propagation as well 
as their variations with pressure. This curve fitting approach is 
important to avoid using a traveltime not associated with the arrival of 
the energy pulse. Having achieved the optimized fitting of the 
traveltimes, one can obtain estimates of the seismic velocities at each 
pressure point and hence a measure of the variation of seismic velocity 
with pressure at step 300. 
It has also been recognized that rather than simply employ a master trace 
developed from the signal recorded at the highest pressure point; a new 
master trace can also be developed from the signal recorded at the next 
lower pressure after an estimate of velocity (i.e., arrival time t.sub.a) 
has been obtained for the next highest pressure point by returning to 
steps 250 to 290. 
While the present invention has been described with respect to a specific 
embodiment for employing the pulse transmission method on samples of the 
earth, those skilled in the art will appreciate that the present method 
can also be applied to conventionally acquired seismic data including 
sonic logging and vertical seismic profiling data. While variations in 
pressure have been used to evaluate variations in seismic velocities, 
those skilled in the art will appreciate that variations in seismic 
velocities as a result of varying other extrinsic variables, (e.g., 
temperature, fluid saturation, deviating stress, magnetic field, 
frequency, etc.) are also comprehended within the present invention. The 
present invention is to be limited only by the appended claims.