Inversion of velocity ratio Vp/Vs from converted‐wave AVO

2007 ◽  
Author(s):  
Tiansheng Chen ◽  
Xiucheng Wei
Keyword(s):  
Velocity Ratio ◽  
Converted Wave

Wave-equation angle-domain common-image gathers for converted waves

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. S17-S26 ◽  
Author(s):  
Daniel A. Rosales ◽  
Sergey Fomel ◽  
Biondo L. Biondi ◽  
Paul C. Sava
Keyword(s):  
Seismic Data ◽  
Incidence Angle ◽  
Velocity Ratio ◽  
Real Data ◽  
Single Mode ◽  
Practical Application ◽  
Converted Wave ◽  
Reflection Angle ◽  
Wavefield Extrapolation ◽  
Local Image

Wavefield-extrapolation methods can produce angle-domain common-image gathers (ADCIGs). To obtain ADCIGs for converted-wave seismic data, information about the image dip and the P-to-S velocity ratio must be included in the computation of angle gathers. These ADCIGs are a function of the half-aperture angle, i.e., the average between the incidence angle and the reflection angle. We have developed a method that exploits the robustness of computing 2D isotropic single-mode ADCIGs and incorporates both the converted-wave velocity ratio [Formula: see text] and the local image dip field. It also maps the final converted-wave ADCIGs into two ADCIGs, one a function of the P-incidence angle and the other a function of the S-reflection angle. Results with both synthetic and real data show the practical application for converted-wave ADCIGs. The proposed approach is valid in any situation as long as the migration algorithm is based on wavefield downward continuation and the final prestack image is a function of the horizontal subsurface offset.

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.

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.

SV-P: An ignored seismic mode that has great value for interpreters

2014 ◽  
Vol 2 (2) ◽  
pp. SE17-SE27 ◽  
Author(s):  
Bob A. Hardage ◽  
Diana Sava ◽  
Don Wagner
Keyword(s):  
Velocity Ratio ◽  
Real Data ◽  
P Wave ◽  
Vertical Force ◽  
Horizontal Force ◽  
S Wave ◽  
Converted Wave ◽  
High Quality ◽  
First Case ◽  
Vsp Data

We show that SV-P reflectivity closely matches P-SV reflectivity; thus, in concept, an SV-P image should be as informative and as valuable as a P-SV image for seismic interpretation purposes. If the dip of rock layering is not severe, the length of the SV raypath involved in SV-P imaging is approximately the same as the length of the SV raypath in P-SV imaging; thus, the important lithology-sensitive [Formula: see text] velocity ratio determined with SV-P data should be approximately the same as the [Formula: see text] velocity ratio determined with P-SV data. We compare velocities used in P-SV imaging and SV-P imaging to emphasize the equivalence of P-SV and SV-P stacking velocities, and therefore seismic-derived [Formula: see text] velocity ratios, obtained with both converted-wave modes. We compare images of P-SV and SV-P data to illustrate the high-quality images that can be made with a SV-P mode. The SV-P data used in these comparisons are recorded by vertical geophones, whereas the P-SV data are recorded by horizontal geophones. In the real-data examples we present, the energy sources that produced the downgoing SV wavefield are vertical-force sources, not horizontal-force sources. A vertical vibrator is used in the first case, and shot-hole explosives are used in the second case. The interpretation technology described here thus introduces the option of extracting valuable S-wave information and images from legacy P-wave data generated by a vertical-force source and recorded with only 1C vertical geophones. We discuss several principles involved in constructing SV-P images from VSP data because of the importance that VSP technology has in calibrating depth-based geology with surface-recorded SV-P data. We emphasize that cautious and attentive data processing procedures are required to segregate SV-P reflections and P-P reflections in VSP data.

Numerical analysis and explore of asymmetrical fluid flow in a two-sided lid-driven cavity

2020 ◽  
Vol 14 (3) ◽  
pp. 7269-7281
Author(s):  
El Amin Azzouz ◽  
Samir Houat
Keyword(s):  
Velocity Ratio ◽  
Two Dimensional ◽  
Lower Side ◽  
Square Cavity ◽  
Driven Cavity ◽  
Parallel Motion ◽  
Bottom Cavity ◽  
Secondary Vortices ◽  
Volume Method ◽  
Fluid Characteristics

The two-dimensional asymmetrical flow in a two-sided lid-driven square cavity is numerically analyzed by the finite volume method (FVM). The top and bottom walls slide in parallel and antiparallel motions with various velocity ratio (UT/Ub=λ) where |λ|=2, 4, 8, and 10. In this study, the Reynolds number Re1 = 200, 400, 800 and 1000 is applied for the upper side and Re2 = 100 constant on the lower side. The numerical results are presented in terms of streamlines, vorticity contours and velocity profiles. These results reveal the effect of varying the velocity ratio and consequently the Reynolds ratio on the flow behaviour and fluid characteristics inside the cavity. Unlike conventional symmetrical driven flows, asymmetrical flow patterns and velocity distributions distinct the bulk of the cavity with the rising Reynolds ratio. For λ>2, in addition to the main vortex, the parallel motion of the walls induces two secondary vortices near the bottom cavity corners. however, the antiparallel motion generates two secondary vortices on the bottom right corner. The parallel flow proves affected considerably compared to the antiparallel flow.

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