Anisotropic Born scattering for the qP scalar wavefield using a low-rank symbol approximation

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Iury Araújo ◽  
Murillo Nascimento ◽  
Jesse Costa ◽  
Alan Souza ◽  
Jörg Schleicher
Keyword(s):  
Anisotropic Medium ◽  
Mathematical Formulation ◽  
Hamiltonian Formulation ◽  
Anisotropic Media ◽  
Low Rank ◽  
Direct Access ◽  
S Wave ◽  
Evolution Operators ◽  
Individual Parameter ◽  
Reflection Data

We present a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudo-acoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudo-acoustic evolution operators. Therefore it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information like its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversly isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to show that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudo-acoustic anisotropic media.

Pure P- and S-Wave Equations in Anisotropic Media

2020 ◽  
Author(s):  
A. Stovas ◽  
T. Alkhalifah ◽  
U. Bin Waheed
Keyword(s):  
Wave Equations ◽  
Anisotropic Media ◽  
S Wave

3D mapping of kinematic attributes in anisotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C159-C170 ◽  
Author(s):  
Yuriy Ivanov ◽  
Alexey Stovas
Keyword(s):  
Anisotropic Medium ◽  
Heterogeneous Media ◽  
Homogeneous Medium ◽  
Anisotropic Media ◽  
Transformation Matrix ◽  
3D Mapping ◽  
Slowness Surface ◽  
Point Correspondence ◽  
Geometric Spreading ◽  
Point To Point

Based on the rotation of a slowness surface in anisotropic media, we have derived a set of mapping operators that establishes a point-to-point correspondence for the traveltime and relative-geometric-spreading surfaces between these calculated in nonrotated and rotated media. The mapping approach allows one to efficiently obtain the aforementioned surfaces in a rotated anisotropic medium from precomputed surfaces in the nonrotated medium. The process consists of two steps: calculation of a necessary kinematic attribute in a nonrotated, e.g., orthorhombic (ORT), medium, and subsequent mapping of the obtained values to a transformed, e.g., rotated ORT, medium. The operators we obtained are applicable to anisotropic media of any type; they are 3D and are expressed through a general form of the transformation matrix. The mapping equations can be used to develop moveout and relative-geometric-spreading approximations in rotated anisotropic media from existing approximations in nonrotated media. Although our operators are derived in case of a homogeneous medium and for a one-way propagation only, we discuss their extension to vertically heterogeneous media and to reflected (and converted) waves.

scholarly journals Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. T63-T77 ◽  
Author(s):  
Jiubing Cheng ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Peng Zou ◽  
Chenlong Wang
Keyword(s):  
Elastic Waves ◽  
Vector Fields ◽  
Integral Operators ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Low Rank ◽  
Elastic Displacement ◽  
Low Rank Approximation ◽  
Time Step ◽  
Domain Integral

In elastic imaging, the extrapolated vector fields are decoupled into pure wave modes, such that the imaging condition produces interpretable images. Conventionally, mode decoupling in anisotropic media is costly because the operators involved are dependent on the velocity, and thus they are not stationary. We have developed an efficient pseudospectral approach to directly extrapolate the decoupled elastic waves using low-rank approximate mixed-domain integral operators on the basis of the elastic displacement wave equation. We have applied [Formula: see text]-space adjustment to the pseudospectral solution to allow for a relatively large extrapolation time step. The low-rank approximation was, thus, applied to the spectral operators that simultaneously extrapolate and decompose the elastic wavefields. Synthetic examples on transversely isotropic and orthorhombic models showed that our approach has the potential to efficiently and accurately simulate the propagations of the decoupled quasi-P and quasi-S modes as well as the total wavefields for elastic wave modeling, imaging, and inversion.

Wave characteristics in elliptical orthorhombic media

Geophysics ◽  
2021 ◽  
pp. 1-52
Author(s):  
Alexey Stovas ◽  
Yuriy Roganov ◽  
Vyacheslav Roganov
Keyword(s):  
Anisotropic Medium ◽  
Wave Equations ◽  
Reference Model ◽  
Relative Magnitude ◽  
P Wave ◽  
S Wave ◽  
Wave Characteristics ◽  
Singularity Point ◽  
Wave Properties ◽  
Wave Modes

An elliptical anisotropic medium is defined as a simplified representation of anisotropy in which the anelliptic parameters are set to zero in all symmetry planes. Despite of the fact that this model is rather seldom observed for real rocks, it is often used as a reference model. The P-wave equations for an elliptical anisotropic medium is well known. However, the S-wave equations have not been derived. Thus, we define all wave modes in elliptical orthorhombic models focusing mostly on the S-wave properties. We show that all wave modes in elliptical orthorhombic model are generally coupled and analyze the effect of additive coupling term. As the result, there is an S wave fundamental singularity point located in one of the symmetry planes depending on the relative magnitude of S wave stiffness coefficients.

Surface Seismic Measurements of Near-Surface P- and S-Wave Seismic Velocities at Earthquake Recording Stations, Seattle, Washington

1999 ◽  
Vol 15 (3) ◽  
pp. 565-584 ◽  
Author(s):  
Robert A. Williams ◽  
William J. Stephenson ◽  
Arthur D. Frankel ◽  
Jack K. Odum
Keyword(s):  
Seismic Refraction ◽  
Ground Surface ◽  
Industrial Area ◽  
High Amplitude ◽  
Seismic Velocities ◽  
S Wave ◽  
Near Surface ◽  
Sedimentary Deposits ◽  
Reflection Data ◽  
Seismic Reflections

We measured P- and S-wave seismic velocities to about 40-m depth using seismic-refraction/reflection data on the ground surface at 13 sites in the Seattle, Washington, urban area, where portable digital seismographs recently recorded earthquakes. Sites with the lowest measured Vs correlate with highest ground motion amplification. These sites, such as at Harbor Island and in the Duwamish River industrial area (DRIA) south of the Kingdome, have an average Vs in the upper 30 m (V¯s30) of 150 to 170 m/s. These values of V¯s30 place these sites in soil profile type E (V¯s30 < 180 m/s). A “rock” site, located at Seward Park on Tertiary sedimentary deposits, has a V¯s30 of 433 m/s, which is soil type C (V¯s30: 360 to 760 m/s). The Seward Park site V¯s30 is about equal to, or up to 200 m/s slower than sites that were located on till or glacial outwash. High-amplitude P- and S-wave seismic reflections at several locations appear to correspond to strong resonances observed in earthquake spectra. An S-wave reflector at the Kingdome at about 17 to 22 m depth probably causes strong 2-Hz resonance that is observed in the earthquake data near the Kingdome.

P-wave and S-wave azimuthal anisotropy at a naturally fractured gas reservoir, Bluebell‐Altamont Field, Utah

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1312-1328 ◽  
Author(s):  
Heloise B. Lynn ◽  
Wallace E. Beckham ◽  
K. Michele Simon ◽  
C. Richard Bates ◽  
M. Layman ◽  
...  
Keyword(s):  
Azimuthal Anisotropy ◽  
P Wave ◽  
Fracture Density ◽  
Wave Reflections ◽  
S Wave ◽  
Gas Reservoir ◽  
Green River ◽  
Wave Data ◽  
Reflection Data ◽  
Naturally Fractured

Reflection P- and S-wave data were used in an investigation to determine the relative merits and strengths of these two data sets to characterize a naturally fractured gas reservoir in the Tertiary Upper Green River formation. The objective is to evaluate the viability of P-wave seismic to detect the presence of gas‐filled fractures, estimate fracture density and orientation, and compare the results with estimates obtained from the S-wave data. The P-wave response to vertical fractures must be evaluated at different source‐receiver azimuths (travelpaths) relative to fracture strike. Two perpendicular lines of multicomponent reflection data were acquired approximately parallel and normal to the dominant strike of Upper Green River fractures as obtained from outcrop, core analysis, and borehole image logs. The P-wave amplitude response is extracted from prestack amplitude variation with offset (AVO) analysis, which is compared to isotropic‐model AVO responses of gas sand versus brine sand in the Upper Green River. A nine‐component vertical seismic profile (VSP) was also obtained for calibration of S-wave reflections with P-wave reflections, and support of reflection S-wave results. The direction of the fast (S1) shear‐wave component from the reflection data and the VSP coincides with the northwest orientation of Upper Green River fractures, and the direction of maximum horizontal in‐situ stress as determined from borehole ellipticity logs. Significant differences were observed in the P-wave AVO gradient measured parallel and perpendicular to the orientation of Upper Green River fractures. Positive AVO gradients were associated with gas‐producing fractured intervals for propagation normal to fractures. AVO gradients measured normal to fractures at known waterwet zones were near zero or negative. A proportional relationship was observed between the azimuthal variation of the P-wave AVO gradient as measured at the tops of fractured intervals, and the fractional difference between the vertical traveltimes of split S-waves (the “S-wave anisotropy”) of the intervals.

Integrating S‐wave seismic‐reflection data and cone penetration test data using a multiangle multiscale approach

Geophysics ◽  
2004 ◽  
Vol 69 (2) ◽  
pp. 440-459 ◽  
Author(s):  
Ranajit Ghose ◽  
Jeroen Goudswaard
Keyword(s):  
Wave Velocity ◽  
Seismic Reflection ◽  
Multiscale Analysis ◽  
S Wave ◽  
Cone Penetration ◽  
Seismic Reflection Data ◽  
Cone Resistance ◽  
Reflection Seismic ◽  
Reflection Data

A cone penetration test (CPT) is the most common geotechnical testing method used to estimate in situ the strength properties of soil. Although CPT provides valuable information, this information is restricted to the location of the measurement. We propose a new concept to integrate shallow S‐wave reflection seismic data with CPT data in order to obtain laterally continuous subsoil information. In this vein, a valid quantitative means to relate seismic reflections to CPT data is a primary requirement. The approach proposed here is based on the characterization of the scaling behavior of the local fine‐scale S‐wave velocity information extracted from the seismic reflection data and the same behavior of the CPT cone resistance. The local velocity contrast information is extracted by linearized Zoeppritz inversion of the amplitude‐preserved prestack reflection data. We have formulated a multiscale analysis approach employing the continuous wavelet transform in order to quantitatively characterize the nature of change at an interface of the local S‐wave velocity contrast and the CPT cone resistance and to illuminate any relation between these two. The multiscale analysis estimates the singularity parameter α, which indicates the nature of the interfacial change. The application of our method to the field data has uncovered a striking relation between the nature of variation of the local S‐wave velocity contrast and that of CPT cone resistance; otherwise, such a relation was not visible. Detailed analyses of two extensive field datasets have shown that the lateral fine‐scale variation of soil strength, as seen by CPT cone resistance, has a close resemblance with the variation of the local S‐wave velocity function as seen by angle‐dependent reflection measurements. This leads to a unique possibility to integrate two very different in‐situ measurements—reflection seismic and CPT—providing laterally continuous detailed information of the soil layer boundaries.

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