Prestack scalar reverse-time depth migration of 3D elastic seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. S199-S207 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan ◽  
Chen-Shao Lee ◽  
Jinder Chow ◽  
Chen-Hong Chen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Seismic Data ◽  
P Wave ◽  
Scalar Wave ◽  
Reverse Time ◽  
S Wave ◽  
Absolute Value ◽  
S Waves ◽  
Finite Difference Solution

Using two independent, 3D scalar reverse-time depth migrations, we migrate the reflected P- and S-waves in a prestack 3D, three-component (3-C), elastic seismic data volume generated with a P-wave source in a 3D model and recorded at the top of the model. Reflected P- and S-waves are extracted by divergence (a scalar) and curl (a 3-C vector) calculations, respectively, during shallow downward extrapolation of the elastic seismic data. The imaging time for the migrations of both the reflected P- and P-S converted waves at each point is the one-way P-wave traveltime from the source to that point.The divergence (the extracted P-waves) is reverse-time extrapolated using a finite-difference solution of the 3D scalar wave equation in a 3D P-velocity modeland is imaged to obtain the migrated P-image. The curl (the extracted S-waves) is first converted into a scalar S-wavefield by taking the curl’s absolute value as the absolute value of the scalar S-wavefield and assigning a positive sign if the curl is counterclockwise relative to the source or a negative sign otherwise. This scalar S-wavefield is then reverse-time extrapolated using a finite-difference solution of the 3D scalar wave equation in a 3D S-velocity model, and it is imaged with the same one-way P-wave traveltime imaging condition as that used for the P-wave. This achieves S-wave polarity uniformity and ensures constructive S-wave interference between data from adjacent sources. The algorithm gives satisfactory results on synthetic examples for 3D laterally inhomogeneous models.

A method for correcting acoustic finite-difference amplitudes for elastic effects

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. T243-T255 ◽  
Author(s):  
James W. D. Hobro ◽  
Chris H. Chapman ◽  
Johan O. A. Robertsson
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Effective Means ◽  
Cost Effective ◽  
P Wave ◽  
S Waves ◽  
Velocity Models ◽  
Acoustic Simulation ◽  
Wide Range ◽  
Elastic Simulation

We present a new method for correcting the amplitudes of arrivals in an acoustic finite-difference simulation for elastic effects. In this method, we selectively compute an estimate of the error incurred when the acoustic wave equation is used to approximate the behavior of the elastic wave equation. This error estimate is used to generate an effective source field in a second acoustic simulation. The result of this second simulation is then applied as a correction to the original acoustic simulation. The overall cost is approximately twice that of an acoustic simulation but substantially less than the cost of an elastic simulation. Because both simulations are acoustic, no S-waves are generated, so dispersed converted waves are avoided. We tested the characteristics of the method on a simple synthetic model designed to simulate propagation through a strong acoustic impedance contrast representative of sedimentary geology. It corrected amplitudes to high accuracy for reflected arrivals over a wide range of incidence angles. We also evaluated results from simulations on more complex models that demonstrated that the method was applicable in realistic sedimentary models containing a wide range of seismic contrasts. However, its accuracy was reduced for wide-angle reflections from very high impedance contrasts such as a shallow top-salt interface. We examined the influence of modeling at coarse grid resolutions, in which converted S-waves in the equivalent elastic simulation are dispersed. These results provide some validation for the accuracy of the method when applied using finite-difference grids designed for acoustic modeling. The method appears to offer a cost-effective means of modeling elastic amplitudes for P-wave arrivals in a useful range of velocity models. It has several potential applications in imaging and inversion.

Scalar reverse‐time depth migration of prestack elastic seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1519-1527 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Seismic Waves ◽  
Velocity Model ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
S Wave ◽  
Wave Source ◽  
Reflected Waves ◽  
S Waves ◽  
Elastic Data

Reflected P‐to‐P and P‐to‐S converted seismic waves in a two‐component elastic common‐source gather generated with a P‐wave source in a two‐dimensional model can be imaged by two independent scalar reverse‐time depth migrations. The inputs to migration are pure P‐ and S‐waves that are extracted by divergence and curl calculations during (shallow) extrapolation of the elastic data recorded at the earth’s surface. For both P‐to‐P and P‐to‐S converted reflected waves, the imaging time at each point is the P‐wave traveltime from the source to that point. The extracted P‐wave is reverse‐time extrapolated and imaged with a P‐velocity model, using a finite difference solution of the scalar wave equation. The extracted S‐wave is reverse‐time extrapolated and imaged similarly, but with an S‐velocity model. Converted S‐wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources. Synthetic examples show that the algorithm gives satisfactory results for laterally inhomogeneous models.

Amplitude balancing in separating P- and S-waves in 2D and 3D elastic seismic data

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. S103-S113 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan ◽  
Han-Hsiang Chuang
Keyword(s):  
Wave Amplitude ◽  
Amplitude Ratio ◽  
Velocity Ratio ◽  
Displacement Component ◽  
P Wave ◽  
Elastic Displacement ◽  
Reverse Time ◽  
S Wave ◽  
Near Surface ◽  
S Waves

The reflected P- and S-waves in elastic displacement component data recorded at the earth’s surface are separated by reverse-time (downward) extrapolation of the data in an elastic computational model, followed by calculations to give divergence (dilatation) and curl (rotation) at a selected reference depth. The surface data are then reconstructed by separate forward-time (upward) scalar extrapolations, from the reference depth, of the magnitude of the divergence and curl wavefields, and extraction of the separated P- and S-waves, respectively, at the top of the models. A P-wave amplitude will change by a factor that is inversely proportional to the P-velocity when it is transformed from displacement to divergence, and an S-wave amplitude will change by a factor that is inversely proportional to the S-velocity when it is transformed from displacement to curl. Consequently, the ratio of the P- to the S-wave amplitude (the P-S amplitude ratio) in the form of divergence and curl (postseparation) is different from that in the (preseparation) displacement form. This distortion can be eliminated by multiplying the separated S-wave (curl) by a relative balancing factor (which is the S- to P-velocity ratio); thus, the postseparation P-S amplitude ratio can be returned to that in the preseparation data. The absolute P- and S-wave amplitudes are also recoverable by multiplying them by a factor that depends on frequency, on the P-velocity α, and on the unit of α and is location-dependent if the near-surface P-velocity is not constant.

SP- and SS-imaging for 3D elastic reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. A1-A6 ◽  
Author(s):  
Xufei Gong ◽  
Qizhen Du ◽  
Qiang Zhao
Keyword(s):  
Three Dimensional ◽  
Scalar Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Sh Waves ◽  
S Waves ◽  
Time Migration ◽  
Underlying Principle ◽  
Imaging Conditions

Three-dimensional elastic reverse time migration has been confronted with the problem of generating scalar images with vector S-waves. The underlying principle for solving this problem is to convert the vector S-waves into scalars. Previous methods were mainly focused on PS-imaging, but they usually cannot work properly on SP- and SS-cases. The complexity of SP- and SS-imaging arises from the fact that the incident S-wave has unpredictable relationship with the raypath plane. We have suggested that S-wave should be treated separately as SV- and SH-waves, which keep predictable relationships with the raypath plane. First, the elastic wavefield is separated into P- and S-waves using the Helmholtz decomposition. Then, we evaluate the normal direction of the raypath plane at each imaging grid. Next, we separate the vector S-wave obtained with curl operator into SH- and SV-waves, both of which are scalars. Finally, correlation imaging conditions are implemented to those scalar wave modes to produce scalar SV-P, SV-SV, and SH-SH images.

Separating P‐ and S‐waves in prestack 3D elastic seismograms using divergence and curl

Geophysics ◽  
2004 ◽  
Vol 69 (1) ◽  
pp. 286-297 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan ◽  
Hsu‐Hong Hsiao ◽  
Jinder Chow
Keyword(s):  
Wave Equation ◽  
Computational Model ◽  
Seismic Data ◽  
Velocity Model ◽  
Scalar Wave ◽  
Elastic Wave Equation ◽  
Seismic Section ◽  
P Waves ◽  
Scalar Wave Equation ◽  
S Waves

The reflected P‐ and S‐waves in a prestack 3D, three‐component elastic seismic section can be separated by taking the divergence and curl during finite‐difference extrapolation. The elastic seismic data are downward extrapolated from the receiver locations into a homogeneous elastic computational model using the 3D elastic wave equation. During downward extrapolation, divergence (a scalar) and curl (a three‐component vector) of the wavefield are computed and recorded independently, at a fixed depth, as a one‐component seismogram and a three‐component seismogram, respectively. The P‐ and S‐velocities in the elastic computational model are then split into two independent models. The divergence seismogram (containing P‐waves only) is then upward extrapolated (using the scalar wave equation) through the P‐velocity model to the original receiver locations at the surface to obtain the separated P‐waves. The x‐component, y‐component, and z‐component seismograms of the curl (containing S‐waves only) are upward extrapolated independently (using the scalar wave equation) through the S‐velocity model to the original receiver locations at the surface to obtain the separated S‐waves. Tests are successful on synthetic seismograms computed for simple laterally heterogeneous 2D models with a 3D recording geometry even if the velocities used in the extrapolations are not accurate.

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

scholarly journals Three-component amplitude versus offset analysis

1989 ◽  
Vol 20 (2) ◽  
pp. 257
Author(s):  
D.R. Miles ◽  
G. Gassaway ◽  
L. Bennett ◽  
R. Brown
Keyword(s):  
Seismic Data ◽  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
P Waves ◽  
S Waves ◽  
Avo Analysis ◽  
Avo Inversion ◽  
Amplitude Versus Offset ◽  
Converted Waves

Three-component (3-C) amplitude versus offset (AVO) inversion is the AVO analysis of the three major energies in the seismic data, P-waves, S-waves and converted waves. For each type of energy the reflection coefficients at the boundary are a function of the contrast across the boundary in velocity, density and Poisson's ratio, and of the angle of incidence of the incoming wave. 3-C AVO analysis exploits these relationships to analyse the AVO changes in the P, S, and converted waves. 3-C AVO analysis is generally done on P, S, and converted wave data collected from a single source on 3-C geophones. Since most seismic sources generate both P and S-waves, it follows that most 3-C seismic data may be used in 3-C AVO inversion. Processing of the P-wave, S-wave and converted wave gathers is nearly the same as for single-component P-wave gathers. In split-spread shooting, the P-wave and S-wave energy on the radial component is one polarity on the forward shot and the opposite polarity on the back shot. Therefore to use both sides of the shot, the back shot must be rotated 180 degrees before it can be stacked with the forward shot. The amplitude of the returning energy is a function of all three components, not just the vertical or radial, so all three components must be stacked for P-waves, then for S-waves, and finally for converted waves. After the gathers are processed, reflectors are picked and the amplitudes are corrected for free-surface effects, spherical divergence and the shot and geophone array geometries. Next the P and S-wave interval velocities are calculated from the P and S-wave moveouts. Then the amplitude response of the P and S-wave reflections are analysed to give Poisson's ratio. The two solutions are then compared and adjusted until they match each other and the data. Three-component AVO inversion not only yields information about the lithologies and pore-fluids at a specific location; it also provides the interpreter with good correlations between the P-waves and the S-waves, and between the P and converted waves, thus greatly expanding the value of 3-C seismic data.

Vector-wave-based elastic reverse time migration of ocean-bottom 4C seismic data

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. S333-S343 ◽  
Author(s):  
Pengfei Yu ◽  
Jianhua Geng ◽  
Jiqiang Ma
Keyword(s):  
Seismic Data ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Vector Wave ◽  
S Waves ◽  
Time Migration ◽  
Multicomponent Seismic ◽  
Wavefield Extrapolation

The acoustic-elastic coupled equation (AECE) has several advantages when compared with conventional scalar-wave-based elastic reverse time migration (ERTM) methods used to image ocean-bottom multicomponent seismic data. In particular, vector-wave-based ERTM requires vectorial P- and S-waves on the source and receiver sides, but these cannot be directly obtained from wavefield extrapolation using AECE. Therefore, we have developed a P- and S-wave vector decomposition (VD) approach within AECE; this approach enables the deduction of a novel VD-based AECE, from which vectorial P- and S-waves can be obtained directly via wavefield extrapolation. We are also able to derive a new formulation suitable for vector-wave-based ERTM of ocean-bottom multicomponent seismic data that can generate a phase-preserved PS-image. Three synthetic examples illustrate the validity and effectiveness of our new method.

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