Obtaining three‐dimensional velocity information directly from reflection seismic data: An inverse scattering formalism

Geophysics ◽  
1981 ◽  
Vol 46 (8) ◽  
pp. 1116-1120 ◽  
Author(s):  
A. B. Weglein ◽  
W. E. Boyse ◽  
J. E. Anderson
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Inverse Scattering ◽  
Seismic Data ◽  
A Priori ◽  
Three Dimensional ◽  
Quantum Scattering ◽  
Acoustic Wave Equation ◽  
Reflection Seismic ◽  
The One

We present a formalism for obtaining the subsurface velocity configuration directly from reflection seismic data. Our approach is to apply the results obtained for inverse problems in quantum scattering theory to the reflection seismic problem. In particular, we extend the results of Moses (1956) for inverse quantum scattering and Razavy (1975) for the one‐dimensional (1-D) identification of the acoustic wave equation to the problem of identifying the velocity in the three‐dimensional (3-D) acoustic wave equation from boundary value measurements. No a priori knowledge of the subsurface velocity is assumed and all refraction, diffraction, and multiple reflection phenomena are taken into account. In addition, we explain how the idea of slant stack in processing seismic data is an important part of the proposed 3-D inverse scattering formalism.

A brief comparison of some Kirchhoff integral formulas for migration and inversion

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1164-1169 ◽  
Author(s):  
Paul Docherty
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Reflection Coefficients ◽  
Acoustic Wave Equation ◽  
Inversion Formulas ◽  
Kirchhoff Migration ◽  
Integral Formulas ◽  
The One ◽  
And Inversion ◽  
Kirchhoff Integral

Kirchhoff migration has traditionally been viewed as an imaging procedure. Usually, few claims are made regarding the amplitudes in the imaged section. In recent years, a number of inversion formulas, similar in form to those of Kirchhoff migration, have been proposed. A Kirchhoff‐type inversion produces not only an image but also an estimate of velocity variations, or perhaps reflection coefficients. The estimate is obtained from the peak amplitudes in the image. In this paper prestack Kirchhoff migration and inversion formulas for the one‐parameter acoustic wave equation are compared. Following a heuristic approach based on the imaging principle, a migration formula is derived which turns out to be identical to one proposed by Bleistein for inversion. Prestack Kirchhoff migration and inversion are, thus, seen to be the same—both in terms of the image produced and the peak amplitudes of the output.

Hybrid Fourier finite-difference 3D depth migration for anisotropic media

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. S27-S34 ◽  
Author(s):  
Tong W. Fei ◽  
Christopher L. Liner
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Seismic Data ◽  
Transversely Isotropic ◽  
Acoustic Wave Equation ◽  
Near Surface ◽  
Depth Migration ◽  
Surface Distortions ◽  
Vti Media

When a subsurface is anisotropic, migration based on the assumption of isotropy will not produce accurate migration images. We develop a hybrid wave-equation migration algorithm for vertical transversely isotropic (VTI) media based on a one-way acoustic wave equation, using a combination of Fourier finite-difference (FFD) and finite-difference (FD) approaches. The hybrid method can suppress an additional solution that exists in the VTI acoustic wave equation, and it offers speed and other advantages over conventional FFD or FD methods alone. The algorithm is tested on a synthetic model involving log data from onshore eastern Saudi Arabia, including estimates of both intrinsic and layer-induced VTI parameters. Results indicate that VTI imaging in this region offers some improvement over isotropic imaging, primarily with respect to subtle structure and stratigraphy and to image continuity. These benefits probably will be overshadowed by perennial land seismic data issues such as near-surface distortions and multiples.

Computing Where Perturbations Affect the Acoustic Impulse Response in the Ocean

2018 ◽  
Vol 26 (02) ◽  
pp. 1850004
Author(s):  
John L. Spiesberger ◽  
Dmitry Yu Mikhin
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Impulse Response ◽  
Sound Speed ◽  
Acoustic Signals ◽  
Technological Advance ◽  
Propagation Model ◽  
Acoustic Wave Equation ◽  
Finite Frequency ◽  
The One

We compute accurate maps of oceanic perturbations affecting transient acoustic signals propagating from source to receiver. The technological advance involves coupling the one-way wave equation (OWWE) propagation model with the theory for the Differential Measure of Influence (DMI) yielding the map. The DMI requires two finite-frequency solutions of the acoustic wave equation obeying reciprocity: from source to receiver and vice versa. OWWE satisfies reciprocity at basin-scales with sound speed varying horizontally and vertically. At infinite frequency, maps of the DMI collapse into rays. Mapping the DMI is useful for understanding measurements of acoustic perturbations at finite frequencies.

NUMERICAL SOLUTION OF THE ACOUSTIC WAVE EQUATION AT THE LIMIT BETWEEN NEAR AND FAR FIELD PROPAGATION

2001 ◽  
Vol 12 (10) ◽  
pp. 1497-1507 ◽  
Author(s):  
ERICH STOLL ◽  
STEFAN DANGEL
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Waves ◽  
Near Field ◽  
Three Dimensional ◽  
Low Frequency ◽  
Far Field ◽  
Acoustic Wave Equation ◽  
Sound Sources ◽  
Continuous Waves

The acoustic wave equation is solved numerically for two and three-dimensional systems at the limit between near and far field propagation. Our results show that for large sound velocities, corresponding to wavelengths larger than the system, near field properties are dominant. When the near field conditions are no longer satisfied, standing waves close to the sound emitters and interference patterns between the near field and far field solutions appear. Our procedure is applied to sound sources, which broadcast coherent and continuous waves as well as to sources emitting bursts of incoherent and uncorrelated waves. Both cases can be used to simulate the spreading of low frequency seismic waves observed close to volcanoes and hydrocarbon reservoirs.

Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme

2015 ◽  
Vol 12 (3) ◽  
pp. 409-420 ◽  
Author(s):  
Xiao-Hui Cai ◽  
Yang Liu ◽  
Zhi-Ming Ren ◽  
Jian-Min Wang ◽  
Zhi-De Chen ◽  
...  
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Equation Modeling ◽  
Acoustic Wave Equation

Acoustic wave equation traveltime and waveform inversion of crosshole seismic data

1993 ◽  
Author(s):  
Changxi Zhou ◽  
Wenying Cai ◽  
Yi Luo ◽  
Gerard T. Schuster ◽  
Sia Hassanzadeh
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Acoustic Wave Equation
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