Some comments on common-asymptotic-conversion-point (CACP) sorting of converted-wave data in isotropic, laterally inhomogeneous media

Common-midpoint (CMP) sorting of pure-mode data in arbitrarily complex isotropic or anisotropic media leads to moveout curves that are symmetric around zero offset. This greatly simplifies velocity determination of pure-mode data. Common-asymptotic-conversion-point (CACP) sorting of converted-wave data, on the other hand, only centers the apexes of all traveltimes around zero offset in arbitrarily complex but isotropic media with a constant P-wave/S-wave velocity ratio everywhere. A depth-varying CACP sorting may therefore be required to position all traveltimes properly around zero offset in structurally complex areas. Moreover, converted-wave moveout is nearly always asymmetric and nonhyperbolic. Thus, positive and negative offsets need to be processed independently in a 2D line, and 3D data volumes are to be divided in common azimuth gathers. All of these factors tend to complicate converted-wave velocity analysis significantly.

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Converted‐wave reflection seismology over inhomogeneous, anisotropic media

Geophysics ◽

10.1190/1.1444577 ◽

1999 ◽

Vol 64 (3) ◽

pp. 678-690 ◽

Cited By ~ 155

Author(s):

Leon Thomsen

Keyword(s):

Velocity Ratio ◽

Anisotropic Media ◽

P Wave ◽

Image Point ◽

Physical Parameters ◽

Pure Mode ◽

Good Precision ◽

Converted Wave ◽

Wave Data ◽

Conversion Point

Converted‐wave processing is more critically dependent on physical assumptions concerning rock velocities than is pure‐mode processing, because not only moveout but also the offset of the imaged point itself depend upon the physical parameters of the medium. Hence, unrealistic assumptions of homogeneity and isotropy are more critical than for pure‐mode propagation, where the image‐point offset is determined geometrically rather than physically. In layered anisotropic media, an effective velocity ratio [Formula: see text] (where [Formula: see text] is the ratio of average vertical velocities and γ2 is the corresponding ratio of short‐spread moveout velocities) governs most of the behavior of the conversion‐point offset. These ratios can be constructed from P-wave and converted‐wave data if an approximate correlation is established between corresponding reflection events. Acquisition designs based naively on γ0 instead of [Formula: see text] can result in suboptimal data collection. Computer programs that implement algorithms for isotropic homogeneous media can be forced to treat layered anisotropic media, sometimes with good precision, with the simple provision of [Formula: see text] as input for a velocity ratio function. However, simple closed‐form expressions permit hyperbolic and posthyperbolic moveout removal and computation of conversion‐point offset without these restrictive assumptions. In these equations, vertical traveltime is preferred (over depth) as an independent variable, since the determination of the depth is imprecise in the presence of polar anisotropy and may be postponed until later in the flow. If the subsurface has lateral variability and/or azimuthal anisotropy, then the converted‐wave data are not invariant under the exchange of source and receiver positions; hence, a split‐spread gather may have asymmetric moveout. Particularly in 3-D surveys, ignoring this diodic feature of the converted‐wave velocity field may lead to imaging errors.

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Estimating shear‐wave velocities from P-wave and converted‐wave data

Geophysics ◽

10.1190/1.1444556 ◽

1999 ◽

Vol 64 (2) ◽

pp. 504-507 ◽

Cited By ~ 1

Author(s):

Franklyn K. Levin

Keyword(s):

Wave Velocity ◽

Seismic Data ◽

P Wave ◽

S Wave ◽

Converted Wave ◽

Wave Data ◽

Wave Velocities ◽

Shear Wave Velocities ◽

P Wave Velocity ◽

Growing Body

Tessmer and Behle (1988) show that S-wave velocity can be estimated from surface seismic data if both normal P-wave data and converted‐wave data (P-SV) are available. The relation of Tessmer and Behle is [Formula: see text] (1) where [Formula: see text] is the S-wave velocity, [Formula: see text] is the P-wave velocity, and [Formula: see text] is the converted‐wave velocity. The growing body of converted‐wave data suggest a brief examination of the validity of equation (1) for velocities that vary with depth.

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Anisotropic velocity updating for converted-wave prestack time migration

Geophysics ◽

10.1190/1.2435172 ◽

2007 ◽

Vol 72 (2) ◽

pp. D29-D32 ◽

Cited By ~ 6

Author(s):

Xiaogui Miao ◽

Torre Zuk

Keyword(s):

Wave Velocity ◽

Velocity Ratio ◽

Anisotropy Parameter ◽

Estimation Method ◽

P Wave ◽

Converted Wave ◽

Anisotropic Parameter ◽

Wave Data ◽

Time Migration ◽

Prestack Time Migration

The conventional method used to estimate velocities for converted-wave (C-wave) prestack time migration is awkward because the P-wave velocity [Formula: see text] comes from P-wave processing, the velocity ratio gamma [Formula: see text] is estimated from C-wave data, and the S-wave velocity [Formula: see text] is then derived from [Formula: see text] and gamma. Instead, by using the C-wave velocity [Formula: see text], effective gamma [Formula: see text], and anisotropy parameter [Formula: see text], velocity updating becomes straightforward and more reliable. To update [Formula: see text] for converted-wave time migration, one can carry out hyperbolic moveout analysis on the hyperbolic-moveout-migrated-common-midpoint (HMO-MCMP) gathers. However, the errors in initial [Formula: see text] and anisotropy parameter [Formula: see text] can only be corrected by trial and error. In this article, we propose to remove the effects of initial [Formula: see text] and [Formula: see text] in the HMO-MCMP gathers by inverting the moveout related to the initial [Formula: see text] and [Formula: see text]. This enables a full nonhyperbolic velocity analysis to update not only [Formula: see text] but also [Formula: see text] and [Formula: see text]. To obtain reliable [Formula: see text], we also develop a simultaneous PP/PS anisotropic-parameter estimation method so the [Formula: see text] estimated from P-wave data is compared immediately with the [Formula: see text] derived from [Formula: see text] by using C-wave data. This provides a better constraint for estimating anisotropy parameters. The method has been tested and shows consistent improvement in converted-wave prestack time-migration velocity estimations.

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Useful approximations for converted‐wave AVO

Geophysics ◽

10.1190/1.1487114 ◽

2001 ◽

Vol 66 (6) ◽

pp. 1721-1734 ◽

Cited By ~ 33

Author(s):

Antonio C. B. Ramos ◽

John P. Castagna

Keyword(s):

Wave Velocity ◽

Random Noise ◽

P Wave ◽

Rock Properties ◽

Negative Slope ◽

High Contrast ◽

Fractional Change ◽

S Wave ◽

Converted Wave ◽

Low Contrast

Converted‐wave amplitude versus offset (AVO) behavior may be fit with a cubic relationship between reflection coefficient and ray parameter. Attributes extracted using this form can be directly related to elastic parameters with low‐contrast or high‐contrast approximations to the Zoeppritz equations. The high‐contrast approximation has the advantage of greater accuracy; the low‐contrast approximation is analytically simpler. The two coefficients of the low‐contrast approximation are a function of the average ratio of compressional‐to‐shear‐wave velocity (α/β) and the fractional changes in S‐wave velocity and density (Δβ/β and Δρ/ρ). Because of its simplicity, the low‐contrast approximation is subject to errors, particularly for large positive contrasts in P‐wave velocity associated with negative contrasts in S‐wave velocity. However, for incidence angles up to 40° and models confined to |Δβ/β| < 0.25, the errors in both coefficients are relatively small. Converted‐wave AVO crossplotting of the coefficients of the low‐contrast approximation is a useful interpretation technique. The background trend in this case has a negative slope and an intercept proportional to the α/β ratio and the fractional change in S‐wave velocity. For constant α/β ratio, an attribute trace formed by the weighted sum of the coefficients of the low‐contrast approximation provides useful estimates of the fractional change in S‐wave velocity and density. Using synthetic examples, we investigate the sensitivity of these parameters to random noise. Integrated P‐wave and converted‐wave analysis may improve estimation of rock properties by combining extracted attributes to yield fractional contrasts in P‐wave and S‐wave velocities and density. Together, these parameters may provide improved direct hydrocarbon indication and can potentially be used to identify anomalies caused by low gas saturations.

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Converted-wave model building and imaging based on common-focus-point methodology

Geophysics ◽

10.1190/geo2019-0549.1 ◽

2020 ◽

Vol 85 (6) ◽

pp. U139-U149

Author(s):

Hongwei Liu ◽

Mustafa Naser Al-Ali ◽

Yi Luo

Keyword(s):

Elastic Wave ◽

Wave Velocity ◽

Seismic Data ◽

Model Building ◽

P Wave ◽

Rock Properties ◽

S Wave ◽

Converted Wave ◽

Seismic Images ◽

Focus Point

Seismic images can be viewed as photographs for underground rocks. These images can be generated from different reflections of elastic waves with different rock properties. Although the dominant seismic data processing is still based on the acoustic wave assumption, elastic wave processing and imaging have become increasingly popular in recent years. A major challenge in elastic wave processing is shear-wave (S-wave) velocity model building. For this reason, we have developed a sequence of procedures for estimating seismic S-wave velocities and the subsequent generation of seismic images using converted waves. We have two main essential new supporting techniques. The first technique is the decoupling of the S-wave information by generating common-focus-point gathers via application of the compressional-wave (P-wave) velocity on the converted seismic data. The second technique is to assume one common VP/ VS ratio to approximate two types of ratios, namely, the ratio of the average earth layer velocity and the ratio of the stacking velocity. The benefit is that we reduce two unknown ratios into one, so it can be easily scanned and picked in practice. The PS-wave images produced by this technology could be aligned with the PP-wave images such that both can be produced in the same coordinate system. The registration between the PP and PS images provides cross-validation of the migrated structures and a better estimation of underground rock and fluid properties. The S-wave velocity, computed from the picked optimal ratio, can be used not only for generating the PS-wave images, but also to ensure well registration between the converted-wave and P-wave images.

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High‐resolution crosswell imaging of a west Texas carbonate reservoir: Part 5—Core analysis

Geophysics ◽

10.1190/1.1443810 ◽

1995 ◽

Vol 60 (3) ◽

pp. 712-726 ◽

Cited By ~ 13

Author(s):

Richard C. Nolen‐Hoeksema ◽

Zhijing Wang ◽

Jerry M. Harris ◽

Robert T. Langan

Keyword(s):

Wave Velocity ◽

Field Experiments ◽

Velocity Ratio ◽

Carbonate Reservoir ◽

P Wave ◽

Core Analysis ◽

S Wave ◽

Traveltime Tomography ◽

West Texas ◽

P Wave Velocity

We conducted a core analysis program to provide supporting data to a series of crosswell field experiments being carried out in McElroy Field by Stanford University’s Seismic Tomography Project. The objective of these experiments is to demonstrate the use of crosswell seismic profiling for reservoir characterization and for monitoring [Formula: see text] flooding. For these west Texas carbonates, we estimate that [Formula: see text] saturation causes P‐wave velocity to change by −1.9% (pooled average, range = −6.3 to +0.1%), S‐wave velocity by +0.6% (range = 0 to 2.7%), and the P‐to‐S velocity ratio by −2.4% (range = −6.4 to −0.3%). When we compare these results to the precisions we can expect from traveltime tomography (about ±1% for P‐ and S‐wave velocity and about ±2% for the P‐to‐S velocity ratio), we conclude that time‐lapse traveltime tomography is sensitive enough to resolve changes in the P‐wave velocity, S‐wave velocity, and P‐to‐S velocity ratio that result from [Formula: see text] saturation. We concentrated here on the potential for [Formula: see text] saturation to affect seismic velocities. The potential for [Formula: see text] saturation to affect other seismic properties, not discussed here, may prove to be more significant (e.g., P‐wave and S‐wave impedance).

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The effects of transverse isotropy on reflection amplitude versus offset

Geophysics ◽

10.1190/1.1442325 ◽

1987 ◽

Vol 52 (4) ◽

pp. 564-567 ◽

Cited By ~ 56

Author(s):

J. Wright

Keyword(s):

Wave Velocity ◽

Transverse Isotropy ◽

Transversely Isotropic ◽

P Wave ◽

S Wave ◽

Reflection Amplitude ◽

Amplitude Versus Offset ◽

Transversely Isotropic Media ◽

P Wave Velocity ◽

Isotropic Media

Studies have shown that elastic properties of materials such as shale and chalk are anisotropic. With the increasing emphasis on extraction of lithology and fluid content from changes in reflection amplitude with shot‐to‐group offset, one needs to know the effects of anisotropy on reflectivity. Since anisotropy means that velocity depends upon the direction of propagation, this angular dependence of velocity is expected to influence reflectivity changes with offset. These effects might be particularly evident in deltaic sand‐shale sequences since measurements have shown that the P-wave velocity of shales in the horizontal direction can be 20 percent higher than the vertical P-wave velocity. To investigate this behavior, a computer program was written to find the P- and S-wave reflectivities at an interface between two transversely isotropic media with the axis of symmetry perpendicular to the interface. Models for shale‐chalk and shale‐sand P-wave reflectivities were analyzed.

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S-Zero Stack: A converted wave processing to extract subsurface density information

Geophysics ◽

10.1190/geo2013-0029.1 ◽

2014 ◽

Vol 79 (3) ◽

pp. N1-N10

Author(s):

Keshan Zou

Keyword(s):

Incident Angle ◽

Shear Velocity ◽

P Wave ◽

Density Contrast ◽

Richards Equation ◽

Maximum Magnitude ◽

S Wave ◽

Converted Wave ◽

Amplitude Variation With Offset ◽

Conversion Point

Analyzing the Aki-Richards equation for converted waves, I found that it is possible to decouple the effect of density contrast from that of shear velocity contrast. The two terms were mixed when the P-wave incident angle was less than 30°, but they started to separate at a middle angle range (approximately 40°). The term related to S-wave velocity contrast reached zero at an incident angle around 60°. However, the other term, which was related to the density contrast, did not reverse polarity until 90°. Furthermore, this density term reached almost the maximum (magnitude) around 60°. Based on those characteristics, I designed a new method called “S-Zero Stack” to capture the density contrast reliably at the subsurface interface without going to inversion. S-Zero Stack captured subsurface density anomalies using a special stacking method. It is simple but robust, even when there is noise in the common-conversion-point gathers. Combined with the traditional P-wave amplitude-variation-with-offset technique, S-Zero Stack of PS-waves may help discriminate commercial gas from fizz in gas sand and could be a useful tool in shale gas exploration to locate lower-density anomalies (sweet spots).

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Bayesian linearized AVO inversion

Geophysics ◽

10.1190/1.1543206 ◽

2003 ◽

Vol 68 (1) ◽

pp. 185-198 ◽

Cited By ~ 450

Author(s):

Arild Buland ◽

Henning Omre

Keyword(s):

Wave Velocity ◽

Posterior Distribution ◽

Acoustic Impedance ◽

Velocity Ratio ◽

P Wave ◽

Inversion Method ◽

Inversion Algorithm ◽

S Wave ◽

Data Set ◽

Avo Inversion

A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P‐wave velocity, S‐wave velocity, and density. Distributions for other elastic parameters can also be assessed—for example, acoustic impedance, shear impedance, and P‐wave to S‐wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance; hence, exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3‐D data set from the Sleipner field. The results show good agreement with well logs, but the uncertainty is high.

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Study on the Acoustic Characteristics of Rocks and Fracability in Wunan Oilfield

E3S Web of Conferences ◽

10.1051/e3sconf/20185303068 ◽

2018 ◽

Vol 53 ◽

pp. 03068

Author(s):

Guo Ziyi ◽

Hu Yongquan ◽

Zhang Yong ◽

Xiong Tingsong ◽

Mao Chun ◽

...

Keyword(s):

Wave Velocity ◽

Velocity Ratio ◽

P Wave ◽

S Wave ◽

Acoustic Characteristics ◽

Measured Velocity ◽

Average Value ◽

Parameter Test ◽

Rock Brittleness ◽

Theory Formula

The acoustic characteristics under P&S wave velocity of 56 samples from Low Youshashan Formation in Wunan Oilfield were tested by SCMS-E high temperature and high pressure core multi parameter test instrument, the measured velocity ratio of P wave and S wave is 1.32-1.67 and the conversion between the P and S wave velocity of rock sample was established. The corresponding dynamic elastic modulus and Poisson's ratio were obtained on the base of the elastic wave propagation theory formula. So, according to the transformation relationship between static and dynamic mechanical parameters, rock brittleness index is calculated and average value is only equal to 38. Therefore, it is difficult to form a fully developed network model during the hydraulic fracturing. These achievements provide a guiding significance for fracturing development at Low Youshashan Formation in Wunan Oilfield.

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