Converted‐wave reflection seismology over inhomogeneous, anisotropic media

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 678-690 ◽  
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.

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

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U29-U36 ◽  
Author(s):  
Mirko van der Baan
Keyword(s):  
Wave Velocity ◽  
Velocity Ratio ◽  
P Wave ◽  
Pure Mode ◽  
S Wave ◽  
Converted Wave ◽  
Wave Data ◽  
Conversion Point ◽  
Isotropic Media ◽  
Zero Offset

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.

Anisotropic velocity updating for converted-wave prestack time migration

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. D29-D32 ◽  
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.

P–S converted wave: conversion point and zero-offset energy in anisotropic media

2004 ◽  
Vol 56 (3) ◽  
pp. 155-163 ◽  
Author(s):  
Fredy A.V. Artola ◽  
Ricardo Leiderman ◽  
Sergio A.B. Fontoura ◽  
Mércia B.C. Silva
Keyword(s):  
Anisotropic Media ◽  
Converted Wave ◽  
Conversion Point ◽  
Zero Offset ◽  
Wave Conversion

Comparison of imaging in anisotropic media using P‐wave and S‐wave data

1998 ◽  
Author(s):  
M. Graziella Kirtland Grech ◽  
J. Helen Isaac ◽  
Don C. Lawton
Keyword(s):  
Anisotropic Media ◽  
P Wave ◽  
S Wave ◽  
Wave Data

scholarly journals Effect of errors in the migration velocity model of PS-converted waves on traveltime accuracy in prestack Kirchhoff time migration in weak anisotropic media

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. S195-S205 ◽  
Author(s):  
Hengchang Dai ◽  
Xiang-Yang Li
Keyword(s):  
Wave Velocity ◽  
Vertical Velocity ◽  
Velocity Ratio ◽  
Anisotropic Media ◽  
Horizontal Distance ◽  
Converted Wave ◽  
Anisotropic Parameter ◽  
Effective Velocity ◽  
Time Migration ◽  
Converted Waves

We investigated the effect of errors in the migration-velocity model of PS-converted waves on the traveltime calculated in prestack Kirchhoff time migration in weak anisotropic media. The prestack-Kirchhoff-time-migration operator contains four parameters: the PS-converted-wave velocity, the vertical velocity ratio, the effective velocity ratio, and the anisotropic parameter. We derived four error factors that correspond to those parameters. Theoretical and numerical analyses of the error factors show them all to be inversely proportional to the velocity and to traveltime. Traveltime errors for shallow events usually are larger than for deep events. Error in PS-converted-wave velocity causes the largest traveltime error, and error in the vertical velocity ratio causes the smallest traveltime error. For a small horizontal-distance/depth ratio, the error in the effective velocity ratio affects traveltime more than does the anisotropic-parameter error. However, the anisotropic-parameter error affects traveltime more when the horizontal-distance/depth ratio is larger. Traveltime errors caused by errors in effective velocity ratio and the anisotropic parameter mainly stem from the converted-S-wave raypath of the PS-converted waves. To save processing time and cost, PS-wave velocity can be estimated accurately without an accurate vertical velocity ratio, effective velocity ratio, and anisotropic parameter. These findings are useful for understanding PS-wave behavior and for PS-wave imaging in anisotropic media.

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

Geophysics ◽  
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).

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

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 504-507 ◽  
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.

Traveltime and conversion‐point computations and parameter estimation in layered, anisotropic media by τ‐p transform

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 210-224 ◽  
Author(s):  
Mirko van der Baan ◽  
J.‐Michael Kendall
Keyword(s):  
Ray Tracing ◽  
Transverse Isotropy ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Seismic Wave Propagation ◽  
Pure Mode ◽  
Fast Method ◽  
Conversion Point ◽  
Arbitrary Strength ◽  
Taylor Series Expansions

Anisotropy influences many aspects of seismic wave propagation and, therefore, has implications for conventional processing schemes. It also holds information about the nature of the medium. To estimate anisotropy, we need both forward modeling and inversion tools. Forward modeling in anisotropic media is generally done by ray tracing. We present a new and fast method using the τ‐p transform to calculate exact reflection‐moveout curves in stratified, laterally homogeneous, anisotropic media for all pure‐mode and converted phases which requires no conventional ray tracing. Moreover, we obtain the common conversion points for both P‐SV and P‐SH converted waves. Results are exact for arbitrary strength of anisotropy in both HTI and VTI media (transverse isotropy with a horizontal or vertical symmetry axis, respectively). Since inversion for anisotropic parameters is a highly nonunique problem, we also develop expressions describing the phase velocities that require only a reduced number of parameters for both types of anisotropy. Nevertheless, resulting predictions for traveltimes and conversion points are generally more accurate than those obtained using the conventional Taylor‐series expansions. In addition, the reduced‐parameter expressions are also able to handle kinks or cusps in the SV traveltime curves for either VTI or HTI symmetry.

scholarly journals Advantages of Shear Wave Seismic in Morrow Sandstone Detection

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Paritosh Singh ◽  
Thomas Davis
Keyword(s):  
Shear Wave ◽  
Pure Shear ◽  
High Amplitude ◽  
Compressional Wave ◽  
Side Lobe ◽  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
P Waves ◽  
Wave Data

The Upper Morrow sandstones in the western Anadarko Basin have been prolific oil producers for more than five decades. Detection of Morrow sandstones is a major problem in the exploration of new fields and the characterization of existing fields because they are often very thin and laterally discontinuous. Until recently compressional wave data have been the primary resource for mapping the lateral extent of Morrow sandstones. The success with compressional wave datasets is limited because the acoustic impedance contrast between the reservoir sandstones and the encasing shales is small. Here, we have performed full waveform modeling study to understand the Morrow sandstone signatures on compressional wave (P-wave), converted-wave (PS-wave) and pure shear wave (S-wave) gathers. The contrast in rigidity between the Morrow sandstone and surrounding shale causes a strong seismic expression on the S-wave data. Morrow sandstone shows a distinct high amplitude event in pure S-wave modeled gathers as compared to the weaker P- and PS-wave events. Modeling also helps in understanding the adverse effect of interbed multiples (due to shallow high velocity anhydrite layers) and side lobe interference effects at the Morrow level. Modeling tied with the field data demonstrates that S-waves are more robust than P-waves in detecting the Morrow sandstone reservoirs.

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