CA1251550A - Response waveform characterization of geophysical data - Google Patents
Response waveform characterization of geophysical dataInfo
- Publication number
- CA1251550A CA1251550A CA000494631A CA494631A CA1251550A CA 1251550 A CA1251550 A CA 1251550A CA 000494631 A CA000494631 A CA 000494631A CA 494631 A CA494631 A CA 494631A CA 1251550 A CA1251550 A CA 1251550A
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- CA
- Canada
- Prior art keywords
- instantaneous
- attribute
- measure
- seismic signal
- response
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
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Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/34—Displaying seismic recordings or visualisation of seismic data or attributes
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/60—Analysis
- G01V2210/67—Wave propagation modeling
Abstract
ABSTRACT OF THE DISCLOSURE
A method of processing geophysical seismic data so as to enhance its evaluation and interpretation. A
plurality of response waveform characteristics are devel-oped from a seismic signal. The response waveform charac-teristics can provide empirical basis for correlating a seismic signal to formation geology and lithology. In accordance with the present invention, the response wave-form characteristics are chromatically quantified and the intensity of which can be modulated so as to enhance the signal-to-noise ratio of the displayed response waveform characteristics.
A method of processing geophysical seismic data so as to enhance its evaluation and interpretation. A
plurality of response waveform characteristics are devel-oped from a seismic signal. The response waveform charac-teristics can provide empirical basis for correlating a seismic signal to formation geology and lithology. In accordance with the present invention, the response wave-form characteristics are chromatically quantified and the intensity of which can be modulated so as to enhance the signal-to-noise ratio of the displayed response waveform characteristics.
Description
~;25~5~
RESPONSE WAVEFORM CHARACTERIZATION OF
GEOPHYSICAL DATA
BACKGROUND OF INVENTION
The present invention relates generally to the field of processing geophysical data so as to enhance its 15 evaluation and interpretation in the quest for subterra-nean hydrocarbons. Specifically, a plurality of response waveform characteristics are generated from seismic data which can provide empirical bases for correlating the seismic data with formation geology and lithology.
In the continuing search for hydrocarbons in the earth, geophysicists have sought out new techniques to determine the effect of geology or lithology on seismic data in order to relate such effects to the occurrence of hydrocarbons. For example, Savit U.S. Patent No.
25 3,662,325 discloses a method for displaying both extrinsic and intrinsic properties of subterranean formation which are generated from the seismic data. Using such displays, the geophysicists can infer the geological character of the formation and hence the probability of locating hydro-30 carbons. Similarly, Rice U.S. Patent No. 4,467,461 disc-loses an interactive technique for color displaying selected combinations of instantaneous attributes of a seismic signal, including: amplitude, frequency, envelope, phase and velocity, in combination so as to 35 allow an interpreter to more easily comprehend simulta-neous variations of several of the instantaneous attri-butes and to relate these effects to geophysical occur-rences of interest.
~2~
SUMMARY OF THE INVENTION
The present invention relates generally to an improved method for processing geophysical seismic data so as to enhance the evaluation and interpretation of the 5 seismic data. The present invention processes a seismic signal to generate response waveform characteristics, The response waveform characteristics of the present inven-tion, unlike the instantaneous attributes of Rice and Savit, uniquely describe the mean or dominant character of 10 the seismic signal. Response waveform characteristics of the seismic signal are chromatically quantified and the intensity of which can be modulated to enhance the appa-rent signal-to-noise ratio of displayed response waveform characteristics. Selected response waveform characteris-15 tics generated from the seismic signal can be displayed singularly or in combination so as to assist the inter-preter in detecting subtle changes in the seismic signal waveform which can provide empirical bases for correlation with formation geology and lithology.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a graphical representation of the real and quadrature components of a complex seismic signal having varying phase as well as selected instantaneous attributes of the complex signal;
Figure 2 is an expanded view of the ~ero phase seismic signal of Figure 1;
Figure 3 is a graphical representation of the real and quadrature components of a complex seismic signal having varying phase as well as selected response waveform 30 characteristics of the complex seismic signal;
Figure 4 is a graphical representation of real and quadrature components of a complex seismic signal having both varying phase as well as selected response waveform characteristics of the complex seismic signal;
Figure 5 is a graphical representation of the real and quadrature components of a complex seismic signal having varying phase and frequency content as well as response waveform characteristics of the complex seismic signal;
Figures 6a-c are a series of bandpass wavelets and their derived response waveforrn characteristics com-pared to Figure 6d, a Ricker wavelet and its response waveform characteristics;
Figures 7 b&d are a series of bandpass wavelets and their derived response waveform characteristics com-pared to Figure 7c, a Ricker wavelet and its response waveform attributes;
Figures 8a-b are block diagrams of the process 10 of the present invention;
Figure 9 is a color plot of a seismic section with seismic signals overlayed thereon;
Figure 10 is a color plot of seismic signal envelope with the seismic signals overlayed thereon; and Figures 11-13 are color plots of response wave-form characteristics with the seismic signals overlayed thereon.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
As a prelude to a description of the present 20 invention, the following discussion of complex seismic signal analysis is provided as an aid in understanding the present invention. A more comprehensive discussion of the application of complex signal analysis to seismic data is provided by M. T. Taner, F. Koehler, and R. E. Sheriff, in 25 "Complex Seismic I'race Analysis" Geophysics, Volume 44, No. 6, Pages 1041-1063 (1979).
Complex signal analysis treats a seismic signal f(t) as the real portion of a complex signal s(t). The complex seismic signal s(t) is thus composed of a real 30 signal f(t) and its corresponding Hilbert transform F(t), .eO ~
s(t) = f(t) ~ i F(t) where i = ~-1 (1) 35 The Hilbert transform F(t~ is hereafter referred to as the quadrature of the real signal f(t).
The seismic signal f(t) can be expressed in terms of a time dependent amplitude A(t) and a time depen-dent phase ~(t) as:
~s~
f(t~ = A(t) cos~t) (2) The quadrature F(t) can be expressed as:
5 F(t) = A(t) sinO(t) (3) The complex signal s(t) is then:
s(t) = A(t) (cos~(t) + i sin~(t)) = A(t)ei~(t) (~) The time derivative of the instantaneous phase O(t) is referred to as the instantaneous frequency v(t) and A(t) is hereinafter referred to as amplitude envelope.
Looking now to Figure 1, segments of a simulated 15 seismic signal f(t) having varying progressive phase shifts from 0 to 180 and its corresponding quadratures F(t) are represented. Additionally, the instantaneous attributes of phase ~(t) and frequency ~(t), as well as the amplitude envelope A(t) are represented. It can be 20 seen that the amplitude envelope A(t) waveform remains unchanged regardless of the phase of the seismic signal f(t). The instantaneous phase ~(t) associated with each of the predominant amplitude envelope A(t) lobe peaks, as indicated by the dashed vertical lines in Figure 1, 25 closely corresponds to the phase of each seismic signal f(t). Moreover, the instantaneous frequency ~(t) associ-ated with each of the predominant amplitude envelope A(t) lobe peaks closely correspond to the mean frequency fm f the seismic signal f(t) amplitude spectrum.
Next, looking to Figure 2, an expanded zero phase seismic signal f(t) of Figure 1 and its corre-sponding quadrature F(t) as well as its instantaneous attributes are shown. Here, a clear indication of the cosine-sine relationship between the seismic signal f(t) 35 and its quadrature F(t) can be seen. Moreover, it can be seen that the instantaneous frequency v(t) (approximately 42 Hz) remains generally unchanged, indicating linear phase variation within the amplitude envelope A(t) and s~
that the spikes in the instantaneous frequency v(t) occur at minima in the amplitude envelope A(t~ as indicated by the vertical lines. For both Figures 1 and 2, a bandpass wavelet (10, 15, 70, 75 Hz) has been employed to simulate 5 the seismic signal f(t). It can be seen in both Figures 1 and 2 that the instantaneous phase ~(t) at the peak or maximum of the dominant amplitude envelope A(t) lobe is in agreement with the phase of the seismic signal f(t). This is a repeatable and stable observation related to the com-10 plex energy distribution of the seismic signal f(t) whichcan be explained by mathematical theory.
In simple terms, the most significant contribu-tion to signal energy are found in the vicinity of the predominant amplitude envelope A(t) lobe peaks or sta-15 tionary points. Thus, with a degree of uncertainty depen-dent upon the seismic signal f(t) bandwidth and time dura-tion, one can measure the mean or dominant properties of the seismic signal f(t) waveform within the predominant amplitude envelope A(t) lobe using the instantaneous 20 attributes in the vicinity of the position of peak energy.
The instantaneous phase ~(t) tends to become linear about the predominant amplitude envelope A(t) peak (i.e., the stationary point) and the instantaneous frequency ~(t~
tend towards the mean frequency fm of the spectral energy 25 distribution. With selective extraction of the instanta-neous attributes at the predominant amplitude envelope A(t) lobe peaks, one can characterize the seismic signal f(t) waveform for each amplitude envelope A(t) lobe and group arrival. Thus, means for quickly and accurately 30 quantifying the seismic signal f(t) waveform as a function of time are provided.
Hereafter, the instantaneous phase ~(t) and fre-quency v(t) at each amplitude envelope A(t) lobe peak are designated the response phase ~ and response frequency 35 v, respectively.
Looking to Figure 3, the seismic signals f(t) from Figure l are represented along with their associated response phase 0, response frequency v, and amplitude envelope A(t). In particular, the response phase ~ and response frequency ~ are represented as having a constant value from trough-to-trough about each amplitude envelope A(t) lobe peak. This trough-to-trough measure about an 5 amplitude envelope A(t) lobe peak is referred to as the width of the envelope.
~ ecall that in Figures 1-3 a bandpass wavelet (lO, 15, 70, 75 Hz) was used to simulate the seismic signal f(t). Looking now to Figure 4, a bandpass wavelet lO (lO, 15, 20, 75 Hz) having an amplitude spectrum tapered on the high end of the frequency band is employed. The main difference between Figure l and Figure 4 is the low frequency side lobes of the latter seismic signal f(t) and the smoother appearance of its amplitude envelope A(t).
lS Also shown in Figure 4 are the response phase H and response frequency ~ for a series of seismic signals f(t), each having an incremental phase shift from 0 to 180. In Figure 4, the amplitude envelope A(t) waveform is identical for each seismic signal f(t) regardless of 20 its phase. The response phase ~ closely tracks the phase change from seismic signal to seismic signal and the response frequency ~ accurately measures the mean fre-quency fm of the seismic signal f(t), i.e., approximately 32 Hz. Even though the instantaneous frequency v(t) is no 25 longer constant, but is peaked in the vicinity of the pre-dominant amplitude envelope A(t) lobe peak, the response frequency ~ remains relatively constant and still closely approximates the mean frequency fm f the amplitude spectrum of the seismic signal f(t). This results since 30 the response frequency ~ is determined only at the point of the amplitude envelope A(t) lobe peak or maxima.
In Figure 5 not only does the phase of each seismic signal f(t) vary, but its frequency content as well. Each seismic signal f(t) is shown with its upper 35 bandpass frequency f and its mean frequency fm. Here it is seen that response frequency ~ closely tracks the change in the mean frequency fm from wavelet-to-wavelet even though the instantaneous frequency v(t) has signifi-cant variability in amplitude and periodicity.
In order that one may more clearly understand the relationship of instantaneous frequency v(t) to the bandpass OL the seismic signal f(t), Figures 6a-c are pro-vided with a series of bandpass wavelets differing in the 5 degree of taper on the upper part of the frequency band and its associated amplitude envelope A(t), instantaneous frequency v(t) and response frequency v. The bandpass wavelets of Figure 6a-c are compared to a 35 Hz Ricker wavelet in Figure 6d. It should be noted that the instan-lO taneous frequency v(t) is nearly flat for the bandpasswavelet in Figure 6a, but tends to develop some shaping as a tapering of the high frequency content increases in Fig-ures 6b and 6c. It is also noted that as the tapering increases, the side lobes of the amplitude envelope A(t) 15 diminish approaching the smoothness of the Ricker wavelet in Figure 6d. The bandpass wavelet with greatest tapering, Figure 6c, has relatively low frequency side lobes. This is consistent with the variations of the instantaneous frequency v(t) which measures the mean fre-20 quency fm as a function of time.
Next, looking at Figures 7a-c, the effect of varying the low frequency end of a bandpass wavelet is shown. Here, the inverse effects appear to those dis-played in Figures 6a-c. Spikes in the instantaneous fre-25 quency v(t) are associated with local minima in the ampli-tude envelope A(t) while the high frequency side lobes of the wavelet are consistent with the elevated instantaneous frequency v(t) values in those zones.
Having examined the effectiveness of the 30 response phase ~ and response frequency u to charac-terize both a smooth wavelet and tapered bandpass wave-lets, we now return to the original full bandpass wavelet of Fi~ure 3 with all of its side lobes. Recall that one first determines both the local maxima and minima in the 35 amplitude envelope A(t) and then determines the value of each instantaneous attribute associated with the local maxima to define response waveform characteristics. Each response waveform characteristics can then be displayed as a constant across the respective envelope width, i.e., trough-to-trough about the amplitude envelope A(t) maxima.
Thus, looking at Figure 3, the response phase ~ is quite broken and choppy while the response frequency v is quite 5 segmented in appearance. However, at the position of the predominant amplitude envelope A(t) lobe peak or maxima, the response phase ~ accurately measures the phase of the seismic signal f(t). The bandpass is constant for all wavelets so that response frequency ~ measures only one 10 constant mean frequency fm while in Figure 5, the response frequency v accurately tracks changes in the mean frequency fm of the seismic signal f(t).
Since it is the value of the response waveform characteristics at the predominant amplitude envelope A(t) 15 lobe peak which effectively characterize the mean or domi-nant properties of the seismic signal f(t) waveform, it is desirable to emphasize the response phase ~ and response frequency ~ measurements at the highest signal-to-noise portions of the seismic f(t), i.e., the high or predomi-2G nant amplitude envelope lobes at the expense of the loweramplitude envelope side lobes. A preferred method to achieve this result is to chromatically quantify the response waveform characteristics, i.e., employ a spectrum of colors to represent gradations in magnitude of the 25 response waveform characteristics and thereafter to modu-late the color intensity or area according to the seismic signal f(t) amplitude.
Looking now to Figure 8a, a block diagram of the process of the present invention is depicted. Seismic 30 data, including a plurality of seismic signals f(t) are collected on a magnetic tape 10 or the like. Hilbert transforms F(t) of the seismic signals f(t) are generated at 20. A complex seismic signal s(t) is formed at 30 from the seismic signals f(t) and the Hilbert transform F(t).
35 An amplitude envelope A(t) of the complex signal s(t) is generated at 40 and the instantaneous frequency ~(t) and the instantaneous phase ~(t) of the complex signal s(t) are generated at 50 and 60, respectively. At 70, local ~S~5~;~
_9_ maxima or peaks and local minima in the amplitude envelope A(t) are identified and the instantaneous frequency v(t) and instantaneous phase ~(t) associated with such local maxima or peak in the amplitude envelope A(t) are deter-5 mined at 80 and 100, respectively, and hereinafter desig-nated as response waveform characteristics of the seismic signal, i.e., response frequency v and response phase ~.
A measure of the amplitude envelope A(t) at each maxima or peak is designated the response amplitude A and 10 is obtained at 90 and is also included within the defini-tion of a response waveform characteristic. A measure of the response phase ~, response frequency v and response amplitude A so determined for each local maxima can be displayed as constants across the amplitude width i.e., 15 trough-to-trough about local peaks of the amplitude envelope A(t) as seen in Figures 1-5. Thereafter, the response waYeform characteristics can be displayed either singularly or in combination at 110. It is also advanta-geous to overlay the seismic signal f(t) wiggle trace over 20 the response waveform characteristics.
As an aid in displaying the response frequency v, response phase ~, and response amplitude A, each are chromatically quantified. That is, looking to Figure 8b, colors are assigned corresponding to a selected band of 25 frequencies (e.g., 0 to 90 Hz) at 210, a band of phase angles (e.g., -180 to +180) at 220, and normalized amplitudes at 230. Alternatively, separate colors can be assigned to each response waveform characteristic having a prescribed minimum or maximum value. Thus, when displayed 30 in combination, chromatic vector addition can indicate various combinations of the response waveform characteris-tics concurrently. The response waveform characteristics can be displayed either singularly or in combination with an overlayed seismic signal f(t) variable area wiggle 35 trace from 200 in one of three seismic section formats.
Specifically, a variable density deflection VDD
with a full intensity colored background and a black wiggle overlay is produced at 250 as shown later in Figures 11-13. A variable area deflection VAD with a white background and ~ull intensity color within the seismic signal f(t) wiggle lobe areas is produced at 260 as shown later in Figure 10. Additionally, a variable 5 intensity deflection VID with a variable intensity color background and black wiggle overlay is produced at 270.
The color intensity of the response waveform character-istic is modulated at 2~0 using the amplitude of the cor-responding seismic signal f(t). By modulating the color 10 intensity in the VID or the amount of color in the VAD
techniques, a higher apparent signal-to-noise ratio can be achieved by suppressing the response frequency v, response phase ~, and response amplitude A associated with low amplitude envelope events, i.e., with other than 15 the predominant lobe of the amplitude envelope A(t), which could be comprised primarily of noise.
Looking first to Figure 9, a colored seismic section across a high amplitude reflection is shown.
Blue, green, yellow and red are positive amplitudes while 20 brown, gray, and orange are negative values of seismic signal f(t) amplitudes. Two reflectors, B-1 and B-2 are indicated by the arrows, and both are relatively shallow events which are clearly defined as high amplitude events.
Moreover, in this section, only every third wiggle trace 25 of the seismic signal f(t) has been superimposed on the section.
The amplitude envelope A(t) derived from the seismic signals of Figure 9 is shown in Figure 10. The reflectors B-l and B-2 are clearly seen in this section.
30 The envelope section highlights regions of high reflection strength.
The response phase ~ derived from the seismic signals of Figure 9 is shown in Figure 11. The color scale ranges from purple (-180) through blue (-120), 35 green (-60), to yellow (0), then through orange (+60), red (+120), and again to purple (+180). There are sev-eral important features to note in this section. First, while all response phase ~ estimates have equal color 5C~
intensity in this plot, one can clearly see the uniform continuity of the phase reflected from reflector B-2. It measures approximately -100. The reflector B-l response phase it somewhat more variable, partly due to faulting in 5 these horizons, but in general, is of opposite polarity, approximately 70-90 . In areas of low signal-to-noise ratio of the seismic signal, the colors appear more mosaic-like or less coherent.
The nonproductive reflector B-2 in Figure 11 is 10 noticeably different from the productive reflector B-l.
Upon closer inspection of the seismic signal waveforms of the two reflectors, one can see that they are different, but the contrast is not readily apparent before seeing the color displays. One end of the nonproductive reflector 15 B-2 does not contrast as much, but is still significantly different having approximately a -20 response phase ~
compared to 60-90 response phase ~ at the other end. It is also noted that as response phase ~ undergoes a slight shift for reflector B-2 of about 45, that isl from blue 20 green to yellow green, this shift can be associated with effects of gas in a chalk formation.
Besides absorptive effects in which high fre-quencies are preferentially attenuated, a large absorption coefficient can produce a phase shift in seismic reflec-25 tion and transmitted waves. Most clear cut at present,however, is the discrimination between productive and non-productive reflectors. Looking next to Figure 12, the response phase H which has been modulated by the seismic signal f(t) amplitudes. This is done by coloring the 30 variable area lobe of the seismic trace with the color of the respective response phase ~.
Next looking at Figure 13, the response fre-quency v in Figure 12, the color scales range from white at 0 Hz through red, orange, yellow, green, blue, up to 35 90 Hz. The mean frequency for this bandpass is approxi-mately 30 Hz. It is noted that the reflector B-l response frequency v is a relatively low frequency event with respect to the nonproductive reflector B-2 and most of the other major reflectors. The productive reflector B-l is also associated with an underlying low response frequency anomaly. This is consistent with empirical resuits reported in the literature for analysis of gas zones using 5 instantaneous attributes.
It ls important to note the response phase ~
and response frequency ~ require excellent preprocessing to minimize noise effects and stabilize the stack trace waveform. The ability to quantify response waveform char-10 acteristics from seismic data is the main advantage ofusing complex seismic signal analysis. This is a prin-ciple upon which pattern recognition technology depends and which may be extended to more complicated computerized applications. With several elemental characteristics of a 15 signal, for example, phase frequency, pulse direction, amplitude, etc., one can uniquely characterize segments of seismic data and subject them to statistical analysis and correlation.
The foregoing describes a novel method for der-20 iving waveform characteristics for waveform analysis ofgeophysical data. The analysis technique provides a method whereby an operator can obtain quantitative meas-ures of the seismic signal and derive empirical relations between the seismic signal and the subterranean formation 25 to assist in determination of the formation geology and lithology. Changes may be made in combination and arrangement of the steps heretofore set forth in the spe-cification and shown in the drawing; it being understood that changes may be made without departing from the spirit 30 and scope of the invention as defined in the following claims.
RESPONSE WAVEFORM CHARACTERIZATION OF
GEOPHYSICAL DATA
BACKGROUND OF INVENTION
The present invention relates generally to the field of processing geophysical data so as to enhance its 15 evaluation and interpretation in the quest for subterra-nean hydrocarbons. Specifically, a plurality of response waveform characteristics are generated from seismic data which can provide empirical bases for correlating the seismic data with formation geology and lithology.
In the continuing search for hydrocarbons in the earth, geophysicists have sought out new techniques to determine the effect of geology or lithology on seismic data in order to relate such effects to the occurrence of hydrocarbons. For example, Savit U.S. Patent No.
25 3,662,325 discloses a method for displaying both extrinsic and intrinsic properties of subterranean formation which are generated from the seismic data. Using such displays, the geophysicists can infer the geological character of the formation and hence the probability of locating hydro-30 carbons. Similarly, Rice U.S. Patent No. 4,467,461 disc-loses an interactive technique for color displaying selected combinations of instantaneous attributes of a seismic signal, including: amplitude, frequency, envelope, phase and velocity, in combination so as to 35 allow an interpreter to more easily comprehend simulta-neous variations of several of the instantaneous attri-butes and to relate these effects to geophysical occur-rences of interest.
~2~
SUMMARY OF THE INVENTION
The present invention relates generally to an improved method for processing geophysical seismic data so as to enhance the evaluation and interpretation of the 5 seismic data. The present invention processes a seismic signal to generate response waveform characteristics, The response waveform characteristics of the present inven-tion, unlike the instantaneous attributes of Rice and Savit, uniquely describe the mean or dominant character of 10 the seismic signal. Response waveform characteristics of the seismic signal are chromatically quantified and the intensity of which can be modulated to enhance the appa-rent signal-to-noise ratio of displayed response waveform characteristics. Selected response waveform characteris-15 tics generated from the seismic signal can be displayed singularly or in combination so as to assist the inter-preter in detecting subtle changes in the seismic signal waveform which can provide empirical bases for correlation with formation geology and lithology.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a graphical representation of the real and quadrature components of a complex seismic signal having varying phase as well as selected instantaneous attributes of the complex signal;
Figure 2 is an expanded view of the ~ero phase seismic signal of Figure 1;
Figure 3 is a graphical representation of the real and quadrature components of a complex seismic signal having varying phase as well as selected response waveform 30 characteristics of the complex seismic signal;
Figure 4 is a graphical representation of real and quadrature components of a complex seismic signal having both varying phase as well as selected response waveform characteristics of the complex seismic signal;
Figure 5 is a graphical representation of the real and quadrature components of a complex seismic signal having varying phase and frequency content as well as response waveform characteristics of the complex seismic signal;
Figures 6a-c are a series of bandpass wavelets and their derived response waveforrn characteristics com-pared to Figure 6d, a Ricker wavelet and its response waveform characteristics;
Figures 7 b&d are a series of bandpass wavelets and their derived response waveform characteristics com-pared to Figure 7c, a Ricker wavelet and its response waveform attributes;
Figures 8a-b are block diagrams of the process 10 of the present invention;
Figure 9 is a color plot of a seismic section with seismic signals overlayed thereon;
Figure 10 is a color plot of seismic signal envelope with the seismic signals overlayed thereon; and Figures 11-13 are color plots of response wave-form characteristics with the seismic signals overlayed thereon.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
As a prelude to a description of the present 20 invention, the following discussion of complex seismic signal analysis is provided as an aid in understanding the present invention. A more comprehensive discussion of the application of complex signal analysis to seismic data is provided by M. T. Taner, F. Koehler, and R. E. Sheriff, in 25 "Complex Seismic I'race Analysis" Geophysics, Volume 44, No. 6, Pages 1041-1063 (1979).
Complex signal analysis treats a seismic signal f(t) as the real portion of a complex signal s(t). The complex seismic signal s(t) is thus composed of a real 30 signal f(t) and its corresponding Hilbert transform F(t), .eO ~
s(t) = f(t) ~ i F(t) where i = ~-1 (1) 35 The Hilbert transform F(t~ is hereafter referred to as the quadrature of the real signal f(t).
The seismic signal f(t) can be expressed in terms of a time dependent amplitude A(t) and a time depen-dent phase ~(t) as:
~s~
f(t~ = A(t) cos~t) (2) The quadrature F(t) can be expressed as:
5 F(t) = A(t) sinO(t) (3) The complex signal s(t) is then:
s(t) = A(t) (cos~(t) + i sin~(t)) = A(t)ei~(t) (~) The time derivative of the instantaneous phase O(t) is referred to as the instantaneous frequency v(t) and A(t) is hereinafter referred to as amplitude envelope.
Looking now to Figure 1, segments of a simulated 15 seismic signal f(t) having varying progressive phase shifts from 0 to 180 and its corresponding quadratures F(t) are represented. Additionally, the instantaneous attributes of phase ~(t) and frequency ~(t), as well as the amplitude envelope A(t) are represented. It can be 20 seen that the amplitude envelope A(t) waveform remains unchanged regardless of the phase of the seismic signal f(t). The instantaneous phase ~(t) associated with each of the predominant amplitude envelope A(t) lobe peaks, as indicated by the dashed vertical lines in Figure 1, 25 closely corresponds to the phase of each seismic signal f(t). Moreover, the instantaneous frequency ~(t) associ-ated with each of the predominant amplitude envelope A(t) lobe peaks closely correspond to the mean frequency fm f the seismic signal f(t) amplitude spectrum.
Next, looking to Figure 2, an expanded zero phase seismic signal f(t) of Figure 1 and its corre-sponding quadrature F(t) as well as its instantaneous attributes are shown. Here, a clear indication of the cosine-sine relationship between the seismic signal f(t) 35 and its quadrature F(t) can be seen. Moreover, it can be seen that the instantaneous frequency v(t) (approximately 42 Hz) remains generally unchanged, indicating linear phase variation within the amplitude envelope A(t) and s~
that the spikes in the instantaneous frequency v(t) occur at minima in the amplitude envelope A(t~ as indicated by the vertical lines. For both Figures 1 and 2, a bandpass wavelet (10, 15, 70, 75 Hz) has been employed to simulate 5 the seismic signal f(t). It can be seen in both Figures 1 and 2 that the instantaneous phase ~(t) at the peak or maximum of the dominant amplitude envelope A(t) lobe is in agreement with the phase of the seismic signal f(t). This is a repeatable and stable observation related to the com-10 plex energy distribution of the seismic signal f(t) whichcan be explained by mathematical theory.
In simple terms, the most significant contribu-tion to signal energy are found in the vicinity of the predominant amplitude envelope A(t) lobe peaks or sta-15 tionary points. Thus, with a degree of uncertainty depen-dent upon the seismic signal f(t) bandwidth and time dura-tion, one can measure the mean or dominant properties of the seismic signal f(t) waveform within the predominant amplitude envelope A(t) lobe using the instantaneous 20 attributes in the vicinity of the position of peak energy.
The instantaneous phase ~(t) tends to become linear about the predominant amplitude envelope A(t) peak (i.e., the stationary point) and the instantaneous frequency ~(t~
tend towards the mean frequency fm of the spectral energy 25 distribution. With selective extraction of the instanta-neous attributes at the predominant amplitude envelope A(t) lobe peaks, one can characterize the seismic signal f(t) waveform for each amplitude envelope A(t) lobe and group arrival. Thus, means for quickly and accurately 30 quantifying the seismic signal f(t) waveform as a function of time are provided.
Hereafter, the instantaneous phase ~(t) and fre-quency v(t) at each amplitude envelope A(t) lobe peak are designated the response phase ~ and response frequency 35 v, respectively.
Looking to Figure 3, the seismic signals f(t) from Figure l are represented along with their associated response phase 0, response frequency v, and amplitude envelope A(t). In particular, the response phase ~ and response frequency ~ are represented as having a constant value from trough-to-trough about each amplitude envelope A(t) lobe peak. This trough-to-trough measure about an 5 amplitude envelope A(t) lobe peak is referred to as the width of the envelope.
~ ecall that in Figures 1-3 a bandpass wavelet (lO, 15, 70, 75 Hz) was used to simulate the seismic signal f(t). Looking now to Figure 4, a bandpass wavelet lO (lO, 15, 20, 75 Hz) having an amplitude spectrum tapered on the high end of the frequency band is employed. The main difference between Figure l and Figure 4 is the low frequency side lobes of the latter seismic signal f(t) and the smoother appearance of its amplitude envelope A(t).
lS Also shown in Figure 4 are the response phase H and response frequency ~ for a series of seismic signals f(t), each having an incremental phase shift from 0 to 180. In Figure 4, the amplitude envelope A(t) waveform is identical for each seismic signal f(t) regardless of 20 its phase. The response phase ~ closely tracks the phase change from seismic signal to seismic signal and the response frequency ~ accurately measures the mean fre-quency fm of the seismic signal f(t), i.e., approximately 32 Hz. Even though the instantaneous frequency v(t) is no 25 longer constant, but is peaked in the vicinity of the pre-dominant amplitude envelope A(t) lobe peak, the response frequency ~ remains relatively constant and still closely approximates the mean frequency fm f the amplitude spectrum of the seismic signal f(t). This results since 30 the response frequency ~ is determined only at the point of the amplitude envelope A(t) lobe peak or maxima.
In Figure 5 not only does the phase of each seismic signal f(t) vary, but its frequency content as well. Each seismic signal f(t) is shown with its upper 35 bandpass frequency f and its mean frequency fm. Here it is seen that response frequency ~ closely tracks the change in the mean frequency fm from wavelet-to-wavelet even though the instantaneous frequency v(t) has signifi-cant variability in amplitude and periodicity.
In order that one may more clearly understand the relationship of instantaneous frequency v(t) to the bandpass OL the seismic signal f(t), Figures 6a-c are pro-vided with a series of bandpass wavelets differing in the 5 degree of taper on the upper part of the frequency band and its associated amplitude envelope A(t), instantaneous frequency v(t) and response frequency v. The bandpass wavelets of Figure 6a-c are compared to a 35 Hz Ricker wavelet in Figure 6d. It should be noted that the instan-lO taneous frequency v(t) is nearly flat for the bandpasswavelet in Figure 6a, but tends to develop some shaping as a tapering of the high frequency content increases in Fig-ures 6b and 6c. It is also noted that as the tapering increases, the side lobes of the amplitude envelope A(t) 15 diminish approaching the smoothness of the Ricker wavelet in Figure 6d. The bandpass wavelet with greatest tapering, Figure 6c, has relatively low frequency side lobes. This is consistent with the variations of the instantaneous frequency v(t) which measures the mean fre-20 quency fm as a function of time.
Next, looking at Figures 7a-c, the effect of varying the low frequency end of a bandpass wavelet is shown. Here, the inverse effects appear to those dis-played in Figures 6a-c. Spikes in the instantaneous fre-25 quency v(t) are associated with local minima in the ampli-tude envelope A(t) while the high frequency side lobes of the wavelet are consistent with the elevated instantaneous frequency v(t) values in those zones.
Having examined the effectiveness of the 30 response phase ~ and response frequency u to charac-terize both a smooth wavelet and tapered bandpass wave-lets, we now return to the original full bandpass wavelet of Fi~ure 3 with all of its side lobes. Recall that one first determines both the local maxima and minima in the 35 amplitude envelope A(t) and then determines the value of each instantaneous attribute associated with the local maxima to define response waveform characteristics. Each response waveform characteristics can then be displayed as a constant across the respective envelope width, i.e., trough-to-trough about the amplitude envelope A(t) maxima.
Thus, looking at Figure 3, the response phase ~ is quite broken and choppy while the response frequency v is quite 5 segmented in appearance. However, at the position of the predominant amplitude envelope A(t) lobe peak or maxima, the response phase ~ accurately measures the phase of the seismic signal f(t). The bandpass is constant for all wavelets so that response frequency ~ measures only one 10 constant mean frequency fm while in Figure 5, the response frequency v accurately tracks changes in the mean frequency fm of the seismic signal f(t).
Since it is the value of the response waveform characteristics at the predominant amplitude envelope A(t) 15 lobe peak which effectively characterize the mean or domi-nant properties of the seismic signal f(t) waveform, it is desirable to emphasize the response phase ~ and response frequency ~ measurements at the highest signal-to-noise portions of the seismic f(t), i.e., the high or predomi-2G nant amplitude envelope lobes at the expense of the loweramplitude envelope side lobes. A preferred method to achieve this result is to chromatically quantify the response waveform characteristics, i.e., employ a spectrum of colors to represent gradations in magnitude of the 25 response waveform characteristics and thereafter to modu-late the color intensity or area according to the seismic signal f(t) amplitude.
Looking now to Figure 8a, a block diagram of the process of the present invention is depicted. Seismic 30 data, including a plurality of seismic signals f(t) are collected on a magnetic tape 10 or the like. Hilbert transforms F(t) of the seismic signals f(t) are generated at 20. A complex seismic signal s(t) is formed at 30 from the seismic signals f(t) and the Hilbert transform F(t).
35 An amplitude envelope A(t) of the complex signal s(t) is generated at 40 and the instantaneous frequency ~(t) and the instantaneous phase ~(t) of the complex signal s(t) are generated at 50 and 60, respectively. At 70, local ~S~5~;~
_9_ maxima or peaks and local minima in the amplitude envelope A(t) are identified and the instantaneous frequency v(t) and instantaneous phase ~(t) associated with such local maxima or peak in the amplitude envelope A(t) are deter-5 mined at 80 and 100, respectively, and hereinafter desig-nated as response waveform characteristics of the seismic signal, i.e., response frequency v and response phase ~.
A measure of the amplitude envelope A(t) at each maxima or peak is designated the response amplitude A and 10 is obtained at 90 and is also included within the defini-tion of a response waveform characteristic. A measure of the response phase ~, response frequency v and response amplitude A so determined for each local maxima can be displayed as constants across the amplitude width i.e., 15 trough-to-trough about local peaks of the amplitude envelope A(t) as seen in Figures 1-5. Thereafter, the response waYeform characteristics can be displayed either singularly or in combination at 110. It is also advanta-geous to overlay the seismic signal f(t) wiggle trace over 20 the response waveform characteristics.
As an aid in displaying the response frequency v, response phase ~, and response amplitude A, each are chromatically quantified. That is, looking to Figure 8b, colors are assigned corresponding to a selected band of 25 frequencies (e.g., 0 to 90 Hz) at 210, a band of phase angles (e.g., -180 to +180) at 220, and normalized amplitudes at 230. Alternatively, separate colors can be assigned to each response waveform characteristic having a prescribed minimum or maximum value. Thus, when displayed 30 in combination, chromatic vector addition can indicate various combinations of the response waveform characteris-tics concurrently. The response waveform characteristics can be displayed either singularly or in combination with an overlayed seismic signal f(t) variable area wiggle 35 trace from 200 in one of three seismic section formats.
Specifically, a variable density deflection VDD
with a full intensity colored background and a black wiggle overlay is produced at 250 as shown later in Figures 11-13. A variable area deflection VAD with a white background and ~ull intensity color within the seismic signal f(t) wiggle lobe areas is produced at 260 as shown later in Figure 10. Additionally, a variable 5 intensity deflection VID with a variable intensity color background and black wiggle overlay is produced at 270.
The color intensity of the response waveform character-istic is modulated at 2~0 using the amplitude of the cor-responding seismic signal f(t). By modulating the color 10 intensity in the VID or the amount of color in the VAD
techniques, a higher apparent signal-to-noise ratio can be achieved by suppressing the response frequency v, response phase ~, and response amplitude A associated with low amplitude envelope events, i.e., with other than 15 the predominant lobe of the amplitude envelope A(t), which could be comprised primarily of noise.
Looking first to Figure 9, a colored seismic section across a high amplitude reflection is shown.
Blue, green, yellow and red are positive amplitudes while 20 brown, gray, and orange are negative values of seismic signal f(t) amplitudes. Two reflectors, B-1 and B-2 are indicated by the arrows, and both are relatively shallow events which are clearly defined as high amplitude events.
Moreover, in this section, only every third wiggle trace 25 of the seismic signal f(t) has been superimposed on the section.
The amplitude envelope A(t) derived from the seismic signals of Figure 9 is shown in Figure 10. The reflectors B-l and B-2 are clearly seen in this section.
30 The envelope section highlights regions of high reflection strength.
The response phase ~ derived from the seismic signals of Figure 9 is shown in Figure 11. The color scale ranges from purple (-180) through blue (-120), 35 green (-60), to yellow (0), then through orange (+60), red (+120), and again to purple (+180). There are sev-eral important features to note in this section. First, while all response phase ~ estimates have equal color 5C~
intensity in this plot, one can clearly see the uniform continuity of the phase reflected from reflector B-2. It measures approximately -100. The reflector B-l response phase it somewhat more variable, partly due to faulting in 5 these horizons, but in general, is of opposite polarity, approximately 70-90 . In areas of low signal-to-noise ratio of the seismic signal, the colors appear more mosaic-like or less coherent.
The nonproductive reflector B-2 in Figure 11 is 10 noticeably different from the productive reflector B-l.
Upon closer inspection of the seismic signal waveforms of the two reflectors, one can see that they are different, but the contrast is not readily apparent before seeing the color displays. One end of the nonproductive reflector 15 B-2 does not contrast as much, but is still significantly different having approximately a -20 response phase ~
compared to 60-90 response phase ~ at the other end. It is also noted that as response phase ~ undergoes a slight shift for reflector B-2 of about 45, that isl from blue 20 green to yellow green, this shift can be associated with effects of gas in a chalk formation.
Besides absorptive effects in which high fre-quencies are preferentially attenuated, a large absorption coefficient can produce a phase shift in seismic reflec-25 tion and transmitted waves. Most clear cut at present,however, is the discrimination between productive and non-productive reflectors. Looking next to Figure 12, the response phase H which has been modulated by the seismic signal f(t) amplitudes. This is done by coloring the 30 variable area lobe of the seismic trace with the color of the respective response phase ~.
Next looking at Figure 13, the response fre-quency v in Figure 12, the color scales range from white at 0 Hz through red, orange, yellow, green, blue, up to 35 90 Hz. The mean frequency for this bandpass is approxi-mately 30 Hz. It is noted that the reflector B-l response frequency v is a relatively low frequency event with respect to the nonproductive reflector B-2 and most of the other major reflectors. The productive reflector B-l is also associated with an underlying low response frequency anomaly. This is consistent with empirical resuits reported in the literature for analysis of gas zones using 5 instantaneous attributes.
It ls important to note the response phase ~
and response frequency ~ require excellent preprocessing to minimize noise effects and stabilize the stack trace waveform. The ability to quantify response waveform char-10 acteristics from seismic data is the main advantage ofusing complex seismic signal analysis. This is a prin-ciple upon which pattern recognition technology depends and which may be extended to more complicated computerized applications. With several elemental characteristics of a 15 signal, for example, phase frequency, pulse direction, amplitude, etc., one can uniquely characterize segments of seismic data and subject them to statistical analysis and correlation.
The foregoing describes a novel method for der-20 iving waveform characteristics for waveform analysis ofgeophysical data. The analysis technique provides a method whereby an operator can obtain quantitative meas-ures of the seismic signal and derive empirical relations between the seismic signal and the subterranean formation 25 to assist in determination of the formation geology and lithology. Changes may be made in combination and arrangement of the steps heretofore set forth in the spe-cification and shown in the drawing; it being understood that changes may be made without departing from the spirit 30 and scope of the invention as defined in the following claims.
Claims (24)
1. A method of processing seismic signals for empirical interpretation comprising steps of:
(a) forming a complex signal from a selected portion of the seismic signals;
(b) locating maxima in the amplitude envelope of the complex signals;
(c) determining a measure of at least one instantaneous attribute of the complex signal for each corresponding maxima in the amplitude envelope, and (d) displaying the measure of at least one instantaneous attribute as a constant across the envelope width of the amplitude envelope.
(a) forming a complex signal from a selected portion of the seismic signals;
(b) locating maxima in the amplitude envelope of the complex signals;
(c) determining a measure of at least one instantaneous attribute of the complex signal for each corresponding maxima in the amplitude envelope, and (d) displaying the measure of at least one instantaneous attribute as a constant across the envelope width of the amplitude envelope.
2. The method of Claim 1 wherein step (c) includes:
determining a measure of the instantaneous frequency attribute for each corresponding maxima in the amplitude envelope.
determining a measure of the instantaneous frequency attribute for each corresponding maxima in the amplitude envelope.
3. The method of Claim 1 wherein step (c) includes:
determining a measure of the instantaneous phase attribute for each corresponding maxima in the amplitude envelope.
determining a measure of the instantaneous phase attribute for each corresponding maxima in the amplitude envelope.
4. The method of Claim 1 further including the step of chromatically quantifying the measure of the instantaneous attribute.
5. The method of Claim 4 further including the step of modulating the intensity of the chromatically quantified instantaneous attribute.
6. A method for characterizing seismic data to enhance its evaluation and interpretation, comprising the steps of:
(a) producing a first instantaneous attri-bute representative of a seismic signal of the seis-mic data;
(b) producing a second instantaneous attribute representative of the seismic signal; and (c) producing a response waveform charac-teristic from the first and second instantaneous attributes, wherein the response wave form character-istic comprises a selected measure of the second instantaneous attribute for a corresponding selected measure of the first instantaneous attribute and the response waveform characteristic provides a measure of a dominant characteristic of the seismic signal.
(a) producing a first instantaneous attri-bute representative of a seismic signal of the seis-mic data;
(b) producing a second instantaneous attribute representative of the seismic signal; and (c) producing a response waveform charac-teristic from the first and second instantaneous attributes, wherein the response wave form character-istic comprises a selected measure of the second instantaneous attribute for a corresponding selected measure of the first instantaneous attribute and the response waveform characteristic provides a measure of a dominant characteristic of the seismic signal.
7. The method of Claim 6 wherein step (c) com-prises:
(a) locating maxima in the first instanta-neous attribute; and (b) producing response waveform character-istics from measures of the second instantaneous attribute corresponding to maxima in the first instantaneous attribute.
(a) locating maxima in the first instanta-neous attribute; and (b) producing response waveform character-istics from measures of the second instantaneous attribute corresponding to maxima in the first instantaneous attribute.
8. The method of Claim 7 further including the steps of:
(a) locating minima in the first instanta-neous attribute; and (b) characterizing a dominant character-istic of the seismic signal by setting the response waveform characteristics constant from minima to minima about each respective maxima.
(a) locating minima in the first instanta-neous attribute; and (b) characterizing a dominant character-istic of the seismic signal by setting the response waveform characteristics constant from minima to minima about each respective maxima.
9. The method of Claim 6 further including the steps of:
(a) producing at least two response wave-form characteristics from at least two or more instantaneous attributes of the seismic signals;
(b) assigning separate colors to each response waveform characteristic and modulating the intensity thereof with a measure of the seismic signal; and (c) combining the separately colored and modulated response waveform characteristic by chro-matic vector addition.
(a) producing at least two response wave-form characteristics from at least two or more instantaneous attributes of the seismic signals;
(b) assigning separate colors to each response waveform characteristic and modulating the intensity thereof with a measure of the seismic signal; and (c) combining the separately colored and modulated response waveform characteristic by chro-matic vector addition.
10. The method of Claim 1 further including the steps of:
(a) assigning separate colors to each response waveform characteristic; and (b) modulating the intensity of the col-ored response waveform characteristics with a measure of the seismic signal to enhance a dominant charac-teristic of the seismic signal.
(a) assigning separate colors to each response waveform characteristic; and (b) modulating the intensity of the col-ored response waveform characteristics with a measure of the seismic signal to enhance a dominant charac-teristic of the seismic signal.
11. The method of Claim 10 further including the step of:
(a) combining the separately colored and modulated colored response waveform characteristics by chromatic vector addition to locate predetermined combinations of response waveform characteristics.
(a) combining the separately colored and modulated colored response waveform characteristics by chromatic vector addition to locate predetermined combinations of response waveform characteristics.
12. The method of Claim 8 further including the step of:
displaying a measure of the response wave-form characteristics.
displaying a measure of the response wave-form characteristics.
13. The method of Claim 6 wherein the step of producing a first instantaneous attribute includes:
producing an instantaneous amplitude envel-ope attribute representation of the seismic signal.
producing an instantaneous amplitude envel-ope attribute representation of the seismic signal.
14. The method of Claim 13 wherein the step of producing a second instantaneous attribute includes:
producing an instantaneous frequency attri-bute representation of the seismic signal.
producing an instantaneous frequency attri-bute representation of the seismic signal.
15. The method of Claim 13 wherein the step of producing a second instantaneous attribute includes:
producing an instantaneous phase attribute representation of the seismic signal.
producing an instantaneous phase attribute representation of the seismic signal.
16. The method of Claim 14 wherein the step of producing response waveform characteristics includes:
determining a measure of the instantaneous frequency attribute at corresponding local maxima in the instantaneous amplitude envelope attribute.
determining a measure of the instantaneous frequency attribute at corresponding local maxima in the instantaneous amplitude envelope attribute.
17. The method of Claim 16 further including the step of:
displaying a measure of the response wave-form characteristics superimposed on a representation of the seismic signal.
displaying a measure of the response wave-form characteristics superimposed on a representation of the seismic signal.
18. The method of Claim 15 wherein the step of producing response waveform characteristics includes:
determining a measure of the instantaneous phase attribute at corresponding local maxima in the instantaneous amplitude envelope attribute.
determining a measure of the instantaneous phase attribute at corresponding local maxima in the instantaneous amplitude envelope attribute.
19. The method of Claim 18 further including the step of:
displaying a measure of the response wave-form characteristics superimposed on a representation of the seismic signal.
displaying a measure of the response wave-form characteristics superimposed on a representation of the seismic signal.
20. The method of Claim 6 further including chromatically quantifying the response waveform character-istics.
21. The method of Claim 20 further including modulating the intensity of the chromatically quantified response waveform characteristics.
22. The method of Claim 13 wherein the first and second instantaneous attributes representative of the seismic signal are the instantaneous amplitude envelope attribute.
23. The method of Claim 22 further including the step of:
determining a measure of the instantaneous amplitude envelope attribute at local maxima in the instantaneous amplitude envelope attribute.
determining a measure of the instantaneous amplitude envelope attribute at local maxima in the instantaneous amplitude envelope attribute.
24. The method of Claim 23 further including the step of:
displaying a measure of the response wave-form characteristics superimposed on a representation of seismic signal.
displaying a measure of the response wave-form characteristics superimposed on a representation of seismic signal.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US06/677,143 US4633447A (en) | 1984-12-03 | 1984-12-03 | Response waveform characterization of geophysical data |
| US677,143 | 1984-12-03 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1251550A true CA1251550A (en) | 1989-03-21 |
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ID=24717501
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000494631A Expired CA1251550A (en) | 1984-12-03 | 1985-11-05 | Response waveform characterization of geophysical data |
Country Status (4)
| Country | Link |
|---|---|
| US (1) | US4633447A (en) |
| CA (1) | CA1251550A (en) |
| EG (1) | EG17362A (en) |
| GB (1) | GB2168152B (en) |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4843599A (en) * | 1987-09-28 | 1989-06-27 | Amoco Corporation | Method for continuous color mapping of seismic data |
| US5197039A (en) * | 1988-03-29 | 1993-03-23 | Shell Oil Company | Methods for processing seismic data |
| US4964102A (en) * | 1988-04-19 | 1990-10-16 | Amoco Corporation | Method for enhancing and evaluating seismic data |
| US4964096A (en) * | 1988-05-24 | 1990-10-16 | Amoco Corporation | Method for inversion of seismic data to yield estimates of formation lithology |
| US4970699A (en) * | 1989-02-13 | 1990-11-13 | Amoco Corporation | Method for color mapping geophysical data |
| US5311484A (en) * | 1991-07-26 | 1994-05-10 | The Trustees Of Columbia University In The City Of New York | Method and apparatus for petroleum and gas exploration |
| US5226019A (en) * | 1992-01-10 | 1993-07-06 | Amoco Corporation | Method of geophysical exploration |
| US5383114A (en) * | 1992-10-05 | 1995-01-17 | Western Atlas International, Inc. | Method for displaying a volume of seismic data |
| US5995448A (en) * | 1996-11-20 | 1999-11-30 | Krehbiel; Steven | Method for mapping seismic reflective data |
| US5796678A (en) * | 1997-08-11 | 1998-08-18 | Trans Seismic International, Inc. | Method for determining the presence of fluids in a subterranean formation |
| US6985838B1 (en) | 2000-02-04 | 2006-01-10 | Apache Corporation | System for estimating thickness of thin subsurface strata |
| US6965830B1 (en) | 2000-09-13 | 2005-11-15 | Apache Corporation | System for estimating thickness of thin subsurface strata |
| US6487502B1 (en) | 2000-12-01 | 2002-11-26 | Rdsp I, L.P. | System for estimating the locations of shaley subsurface formations |
| CA2569102A1 (en) | 2004-06-07 | 2005-12-22 | Exxonmobil Upstream Research Company | Method for solving implicit reservoir simulation matrix equation |
| EP2247820A4 (en) | 2007-12-13 | 2016-02-24 | Exxonmobil Upstream Res Co | Parallel adaptive data partitioning on a reservoir simulation using an unstructured grid |
| MY170622A (en) * | 2012-03-08 | 2019-08-21 | Exxonmobil Upstream Res Co | Orthogonal source and receiver encoding |
| US20140019057A1 (en) * | 2012-07-16 | 2014-01-16 | Nanoseis Llc | Microseismic Event Verification Using Sub-stacks |
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| US4090145A (en) * | 1969-03-24 | 1978-05-16 | Webb Joseph A | Digital quadrature demodulator |
| US3938394A (en) * | 1973-11-30 | 1976-02-17 | Ird Mechanalysis, Inc. | Combination balance analyzer and vibration spectrum analyzer |
| GB1457153A (en) * | 1974-06-10 | 1976-12-01 | Geosource Inc | Method of seismic survexing by extracting and displaying seismic properties |
| US4279026A (en) * | 1978-08-31 | 1981-07-14 | Cities Service Company | Seismographic data color display |
| US4467461A (en) * | 1981-01-05 | 1984-08-21 | Conoco Inc. | Interactive color analysis of geophysical data |
| US4633399A (en) * | 1984-03-05 | 1986-12-30 | Conoco Inc. | Method of seismic data enhancement using a phase of rectified trace seismic parameter |
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- 1984-12-03 US US06/677,143 patent/US4633447A/en not_active Expired - Lifetime
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1985
- 1985-11-05 CA CA000494631A patent/CA1251550A/en not_active Expired
- 1985-12-03 GB GB08529751A patent/GB2168152B/en not_active Expired
- 1985-12-03 EG EG772/85A patent/EG17362A/en active
Also Published As
| Publication number | Publication date |
|---|---|
| GB8529751D0 (en) | 1986-01-08 |
| GB2168152A (en) | 1986-06-11 |
| GB2168152B (en) | 1988-08-03 |
| EG17362A (en) | 1989-06-30 |
| US4633447A (en) | 1986-12-30 |
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