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.

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.

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.

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.

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.

Elastic inversion of near- and postcritical reflections using phase variation with angle

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R149-R159 ◽  
Author(s):  
Xinfa Zhu ◽  
George A. McMechan
Keyword(s):  
Wave Velocity ◽  
Spherical Wave ◽  
Phase Variation ◽  
P Wave ◽  
Wide Angle ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Elastic Inversion

Near- and postcritical (wide-angle) reflections provide the potential for velocity and density inversion because of their large amplitudes and phase-shifted waveforms. We tested using phase variation with angle (PVA) data in addition to, or instead of, amplitude variation with angle (AVA) data for elastic inversion. Accurate PVA test data were generated using the reflectivity method. Two other forward modeling methods were also investigated, including plane-wave and spherical-wave reflection coefficients. For a two half-space model, linearized least squares was used to invert PVA and AVA data for the P-wave velocity, S-wave velocity, and the density of the lower space and the S-wave velocity of the upper space. Inversion tests showed the feasibility and robustness of PVA inversion. A reverse-time migration test demonstrated better preservation of PVA information than AVA information during wavefield propagation through a layered overburden. Phases of deeper reflections were less affected than amplitudes by the transmission losses, which makes the results of PVA inversion more accurate than AVA inversion in multilayered media. PVA brings useful information to the elastic inversion of wide-angle reflections.

Inversion of azimuthally dependent NMO velocity in transversely isotropic media with a tilted axis of symmetry

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 232-246 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Wave Velocity ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Model Parameters ◽  
Symmetry Direction ◽  
Time Migration ◽  
Inversion Procedure ◽  
Tti Media

Just as the transversely isotropic model with a vertical symmetry axis (VTI media) is typical for describing horizontally layered sediments, transverse isotropy with a tilted symmetry axis (TTI) describes dipping TI layers (such as tilted shale beds near salt domes) or crack systems. P-wave kinematic signatures in TTI media are controlled by the velocity [Formula: see text] in the symmetry direction, Thomsen’s anisotropic coefficients ε and δ, and the orientation (tilt ν and azimuth β) of the symmetry axis. Here, we show that all five parameters can be obtained from azimuthally varying P-wave NMO velocities measured for two reflectors with different dips and/or azimuths (one of the reflectors can be horizontal). The shear‐wave velocity [Formula: see text] in the symmetry direction, which has negligible influence on P-wave kinematic signatures, can be found only from the moveout of shear waves. Using the exact NMO equation, we examine the propagation of errors in observed moveout velocities into estimated values of the anisotropic parameters and establish the necessary conditions for a stable inversion procedure. Since the azimuthal variation of the NMO velocity is elliptical, each reflection event provides us with up to three constraints on the model parameters. Generally, the five parameters responsible for P-wave velocity can be obtained from two P-wave NMO ellipses, but the feasibility of the moveout inversion strongly depends on the tilt ν. If the symmetry axis is close to vertical (small ν), the P-wave NMO ellipse is largely governed by the NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η. Although for mild tilts the medium parameters cannot be determined separately, the NMO-velocity inversion provides enough information for building TTI models suitable for time processing (NMO, DMO, time migration). If the tilt of the symmetry axis exceeds 30°–40° (e.g., the symmetry axis can be horizontal), it is possible to find all P-wave kinematic parameters and construct the anisotropic model in depth. Another condition required for a stable parameter estimate is that the medium be sufficiently different from elliptical (i.e., ε cannot be close to δ). This limitation, however, can be overcome by including the SV-wave NMO ellipse from a horizontal reflector in the inversion procedure. While most of the analysis is carried out for a single layer, we also extend the inversion algorithm to vertically heterogeneous TTI media above a dipping reflector using the generalized Dix equation. A synthetic example for a strongly anisotropic, stratified TTI medium demonstrates a high accuracy of the inversion (subject to the above limitations).

Useful approximations for converted‐wave AVO

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1721-1734 ◽  
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.

scholarly journals Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. C279-C293 ◽  
Author(s):  
Ju-Won Oh ◽  
Tariq Alkhalifah
Keyword(s):  
Wave Velocity ◽  
Dimensionless Parameter ◽  
P Wave ◽  
Radiation Patterns ◽  
S Wave ◽  
Velocity Perturbation ◽  
Anisotropic Parameter ◽  
P Wave Velocity ◽  
Parameter Perturbations ◽  
Scattering Potential

The resolution of a multiparameter full-waveform inversion (FWI) is highly influenced by the parameterization used in the inversion algorithm, as well as the data quality and the sensitivity of the data to the elastic parameters because the scattering patterns of the partial derivative wavefields (PDWs) vary with parameterization. For this reason, it is important to identify an optimal parameterization for elastic orthorhombic FWI by analyzing the radiation patterns of the PDWs for many reasonable model parameterizations. We have promoted a parameterization that allows for the separation of the anisotropic properties in the radiation patterns. The central parameter of this parameterization is the horizontal P-wave velocity, with an isotropic scattering potential, influencing the data at all scales and directions. This parameterization decouples the influence of the scattering potential given by the P-wave velocity perturbation from the polar changes described by two dimensionless parameter perturbations and from the azimuthal variation given by three additional dimensionless parameters perturbations. In addition, the scattering potentials of the P-wave velocity perturbation are also decoupled from the elastic influences given by one S-wave velocity and two additional dimensionless parameter perturbations. The vertical S-wave velocity is chosen with the best resolution obtained from S-wave reflections and converted waves, and little influence on P-waves in conventional surface seismic acquisition. The influence of the density on observed data can be absorbed by one anisotropic parameter that has a similar radiation pattern. The additional seven dimensionless parameters describe the polar and azimuth variations in the P- and S-waves that we may acquire, with some of the parameters having distinct influences on the recorded data on the earth’s surface. These characteristics of the new parameterization offer the potential for a multistage inversion from high symmetry anisotropy to lower symmetry ones.

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