Separating wave-modes of prestack elastic seismograms using pure mode wave propagators in anisotropic media

2012 ◽  
Author(s):  
Chenlong Wang ◽  
Jiubing Cheng ◽  
Wei Kang
Keyword(s):  
Anisotropic Media ◽  
Pure Mode ◽  
Mode Wave ◽  
Wave Modes

Simulating propagation of separated wave modes in general anisotropic media, Part I: qP-wave propagators

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. C1-C18 ◽  
Author(s):  
Jiubing Cheng ◽  
Wei Kang
Keyword(s):  
Wave Equation ◽  
Anisotropic Media ◽  
Pure Mode ◽  
Reverse Time ◽  
S Wave ◽  
Time Step ◽  
Flexible Tool ◽  
Mode Wave ◽  
Time Migration ◽  
Wave Modes

Wave propagation in an anisotropic medium is inherently described by elastic wave equations with P- and S-wave modes intrinsically coupled. We present an approach to simulate propagation of separated wave modes for forward modeling, migration, waveform inversion, and other applications in general anisotropic media. The proposed approach consists of two cascaded computational steps. First, we simulate equivalent elastic anisotropic wavefields with a minimal second-order coupled system (that we call here a pseudo-pure-mode wave equation), which describes propagation of all wave modes with a partial wave mode separation. Such a system for qP-wave is derived from the inverse Fourier transform of the Christoffel equation after a similarity transformation, which aims to project the original vector displacement wavefields onto isotropic references of the polarization directions of qP-waves. It accurately describes the kinematics of all wave modes and enhances qP-waves when the pseudo-pure-mode wavefield components are summed. The second step is a filtering to further project the pseudo-pure-mode wavefields onto the polarization directions of qP-waves so that residual qS-wave energy is removed and scalar qP-wave fields are accurately separated at each time step during wavefield extrapolation. As demonstrated in the numerical examples, pseudo-pure-mode wave equation plus correction of projection deviation provides a robust and flexible tool for simulating propagation of separated wave modes in transversely isotropic and orthorhombic media. The synthetic example of a Hess VTI model shows that the pseudo-pure-mode qP-wave equation can be used in prestack reverse-time migration applications.

Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact

1988 ◽  
Vol 415 (1849) ◽  
pp. 389-419 ◽  
Keyword(s):  
Anisotropic Media ◽  
Wave Mode ◽  
Sliding Contact ◽  
Stoneley Wave ◽  
Shear Stresses ◽  
Wave Problem ◽  
Numerical Computations ◽  
Cubic Symmetry ◽  
Anisotropic Elastic ◽  
Wave Modes

A variant of the Stoneley-wave problem, namely slip waves between two homogeneous elastic half-spaces whose interface is incapable of supporting shear stresses, is studied. For two isotropic half-spaces there is either no or one slip-wave mode. In the case of anisotropic half-spaces, the possibility of a new slip-wave mode, called the second slip-wave mode, arises. The case of two identical anisotropic half-spaces of the same orientation is discussed in detail; criteria for the existence of a second slip-wave mode in terms of the nature of the transonic state are developed. It is concluded that for many anisotropic media a second slip-wave mode will exist within certain ranges of orientation of the slip-wave geometry. Numerical computations for iron (cubic symmetry) demonstrate that second slip-wave modes indeed exist in this material.

Calculation of slowness vectors from ray directions for qP-, qSV-, and qSH-waves in tilted transversely isotropic media

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. C153-C160 ◽  
Author(s):  
Lijiao Zhang ◽  
Bing Zhou
Keyword(s):  
Ray Tracing ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Seismic Wave Propagation ◽  
Previous Method ◽  
New Methods ◽  
Slowness Vector ◽  
Isotropic Media ◽  
Tti Media ◽  
Wave Modes

Kinematic ray tracing is an effective way to simulate the seismic wave propagation in isotropic and anisotropic media. It is essential to know the ray velocity when tracing seismic rays. But in anisotropic media, the ray velocity is a function of the direction of the slowness vector instead of the ray direction and it often deviates from the phase velocity. In this case, it causes a critical problem for ray tracing, which is how to calculate the ray velocity from a known ray direction. If we could calculate the phase slowness vector from ray directions, the ray velocity could be computed. We have evaluated a previous method in the first place. Then, we developed two new methods to solve two existing problems of the previous method: (1) It leads to complex and multiple solutions of the slowness vector and (2) it mixes up the qP- and qSV-wave modes. Our first method solves the two problems by applying eigenvalues to separate the wave modes and decrease the two unknowns ([Formula: see text] and [Formula: see text]) to only one unknown in two equations. Our second method is based on the general relationship between the slowness and ray-velocity vectors and shows that only one unknown is involved in one equation for tilted transversely isotropic (TTI) media. After obtaining the slowness vector, the ray velocity can be computed easily. A 2D model is designed to test the feasibility of the new methods. Using the results for the model, we found that the presented approaches were applicable for ray tracing in TTI media.

Explicit expressions for prestack map time migration in isotropic and VTI media and the applicability of map depth migration in heterogeneous anisotropic media

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. S13-S28 ◽  
Author(s):  
Huub Douma ◽  
Maarten V. de Hoop
Keyword(s):  
Closed Form ◽  
Anisotropic Media ◽  
Velocity Model ◽  
Pure Mode ◽  
Anisotropic Parameter ◽  
Depth Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
The Common ◽  
Vti Media

We present 3D prestack map time migration in closed form for qP-, qSV-, and mode-converted waves in homogeneous transversely isotropic media with a vertical symmetry axis (VTI). As far as prestack time demigration is concerned, we present closed-form expressions for mapping in homogeneous isotropic media, while for homogeneous VTI media we present a system of four nonlinear equations with four unknowns to solve numerically. The expressions for prestack map time migration in VTI homogeneous media are directly applicable to the problem of anisotropic parameter estimation (i.e., the anellipticity parameter η) in the context of time-migration velocity analysis. In addition, we present closed-form expressions for both prestack map time migration and demigration in the common-offset domain for pure-mode (P-P or S-S) waves in homogeneous isotropic media that use only the slope in the common-offset domain as opposed to slopes in both the common-shot and common-receiver (or equivalently the common-offset and common-midpoint) domains. All time-migration and demigration equations presented can be used in media with mild lateral and vertical velocity variations, provided the velocity is replaced with the local rms velocity. Finally, we discuss the condition for applicability of prestack map depth migration and demigration in heterogeneous anisotropic media that allows the formation of caustics and explain that this condition is satisfied if, given a velocity model and acquisition geometry, one can map-depth-migrate without ambiguity in either the migrated location or the migrated orientation of reflectors in the image.

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.

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.

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