Synthetic seismogram in depth domain based on the forward and inversion process of wave equation

2018 ◽  
Author(s):  
Zhang Hongjing ◽  
Liu Chaoying ◽  
Wang Xuehui ◽  
Tian Zhenpin ◽  
Huang Na
Keyword(s):  
Wave Equation ◽  
Synthetic Seismogram ◽  
Inversion Process ◽  
And Inversion

On the geometry and inversion process of PF3+· (X̃ 2A1)

1997 ◽  
Vol 273 (3-4) ◽  
pp. 199-204 ◽  
Author(s):  
Steven Creve ◽  
Minh Tho Nguyen
Keyword(s):  
Inversion Process ◽  
And Inversion

Crosshole seismics using vertical eigenstates

Geophysics ◽  
1990 ◽  
Vol 55 (7) ◽  
pp. 815-820 ◽  
Author(s):  
David M. Pai
Keyword(s):  
Wave Equation ◽  
Data Analysis ◽  
Phase Velocity ◽  
Linear Combination ◽  
Plane Waves ◽  
Basis Functions ◽  
Similar Role ◽  
Potential Applications ◽  
Data Expansion ◽  
And Inversion

This paper introduces the concept of vertical eigenstates to crosshole data analysis. In surface seismics, plane waves have played a fundamental role in many applications. This paper points out that for crosshole seismics, vertical eigenstates play a similar role. The vertical eigenstates separate the wave equation, and thus in terms of vertical eigenstate expansion the solution is a linear combination of modes, each mode traveling sideways with a distinct phase velocity. As a result, the vertical eigenstates form a natural set of basis functions for solution and data expansion, with potential applications to modeling, migration, and inversion.

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.

Nonlinear extended images via image-domain interferometry

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. SA105-SA115 ◽  
Author(s):  
Ivan Vasconcelos ◽  
Paul Sava ◽  
Huub Douma
Keyword(s):  
Wave Equation ◽  
Seismic Imaging ◽  
Theory And Practice ◽  
Seismic Interferometry ◽  
Image Domain ◽  
Velocity Inversion ◽  
Nonlinear Imaging ◽  
The One ◽  
Scattered Fields ◽  
And Inversion

Wave-equation, finite-frequency imaging and inversion still face many challenges in addressing the inversion of highly complex velocity models as well as in dealing with nonlinear imaging (e.g., migration of multiples, amplitude-preserving migration). Extended images (EIs) are particularly important for designing image-domain objective functions aimed at addressing standing issues in seismic imaging, such as two-way migration velocity inversion or imaging/inversion using multiples. General one- and two-way representations for scattered wavefields can describe and analyze EIs obtained in wave-equation imaging. We have developed a formulation that explicitly connects the wavefield correlations done in seismic imaging with the theory and practice of seismic interferometry. In light of this connection, we define EIs as locally scattered fields reconstructed by model-dependent, image-domain interferometry. Because they incorporate the same one- and two-way scattering representations usedfor seismic interferometry, the reciprocity-based EIs can in principle account for all possible nonlinear effects in the imaging process, i.e., migration of multiples and amplitude corrections. In this case, the practice of two-way imaging departs considerably from the one-way approach. We have studied the differences between these approaches in the context of nonlinear imaging, analyzing the differences in the wavefield extrapolation steps as well as in imposing the extended imaging conditions. When invoking single-scattering effects and ignoring amplitude effects in generating EIs, the one- and two-way approaches become essentially the same as those used in today’s migration practice, with the straightforward addition of space and time lags in the correlation-based imaging condition. Our formal description of the EIs and the insight that they are scattered fields in the image domain may be useful in further development of imaging and inversion methods in the context of linear, migration-based velocity inversion or in more sophisticated image-domain nonlinear inverse scattering approaches.

Solving the 3D acoustic wave equation on generalized structured meshes: A finite-difference time-domain approach

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. T363-T378 ◽  
Author(s):  
Jeffrey Shragge
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
3D Seismic ◽  
Acoustic Wave Equation ◽  
Structured Meshes ◽  
Cartesian Geometry ◽  
And Inversion ◽  
Difference Time

The key computational kernel of most advanced 3D seismic imaging and inversion algorithms used in exploration seismology involves calculating solutions of the 3D acoustic wave equation, most commonly with a finite-difference time-domain (FDTD) methodology. Although well suited for regularly sampled rectilinear computational domains, FDTD methods seemingly have limited applicability in scenarios involving irregular 3D domain boundary surfaces and mesh interiors best described by non-Cartesian geometry (e.g., surface topography). Using coordinate mapping relationships and differential geometry, an FDTD approach can be developed for generating solutions to the 3D acoustic wave equation that is applicable to generalized 3D coordinate systems and (quadrilateral-faced hexahedral) structured meshes. The developed numerical implementation is similar to the established Cartesian approaches, save for a necessary introduction of weighted first- and mixed second-order partial-derivative operators that account for spatially varying geometry. The approach was validated on three different types of computational meshes: (1) an “internal boundary” mesh conforming to a dipping water bottom layer, (2) analytic “semiorthogonal cylindrical” coordinates, and (3) analytic semiorthogonal and numerically specified “topographic” coordinate meshes. Impulse response tests and numerical analysis demonstrated the viability of the approach for kernel computations for 3D seismic imaging and inversion experiments for non-Cartesian geometry scenarios.

Near-real-time near-surface 3D seismic velocity and uncertainty models by wavefield gradiometry and neural network inversion of ambient seismic noise

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. KS13-KS27 ◽  
Author(s):  
Ruikun Cao ◽  
Stephanie Earp ◽  
Sjoerd A. L. de Ridder ◽  
Andrew Curtis ◽  
Erica Galetti
Keyword(s):  
Wave Equation ◽  
Real Time ◽  
Seismic Wave ◽  
Noise Level ◽  
Seismic Velocity ◽  
3D Seismic ◽  
Near Surface ◽  
Wave Velocities ◽  
Seismic Wave Velocities ◽  
And Inversion

With the advent of large and dense seismic arrays, novel, cheap, and fast imaging and inversion methods are needed to exploit the information captured by stations in close proximity to each other and produce results in near real time. We have developed a sequence of fast seismic acquisition for dispersion curve extraction and inversion for 3D seismic models, based on wavefield gradiometry, wave equation inversion, and machine-learning technology. The seismic array method that we use is Helmholtz wave equation inversion using measured wavefield gradients, and the dispersion curve inversions are based on a mixture of density neural networks (NNs). For our approach, we assume that a single surface wave mode dominates the data. We derive a nonlinear relationship among the unknown true seismic wave velocities, the measured seismic wave velocities, the interstation spacing, and the noise level in the signal. First with synthetic and then with the field data, we find that this relationship can be solved for unknown true seismic wave velocities using fixed point iterations. To estimate the noise level in the data, we need to assume that the effect of noise varies weakly with the frequency and we need to be able to calibrate the retrieved average dispersion curves with an alternate method (e.g., frequency wavenumber analysis). The method is otherwise self-contained and produces phase velocity estimates with tens of minutes of noise recordings. We use NNs, specifically a mixture density network, to approximate the nonlinear mapping between dispersion curves and their underlying 1D velocity profiles. The networks turn the retrieved dispersion model into a 3D seismic velocity model in a matter of seconds. This opens the prospect of near-real-time near-surface seismic velocity estimation using dense (and potentially rolling) arrays and only ambient seismic energy.

scholarly journals General representations for wavefield modeling and inversion in geophysics

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM5-SM17 ◽  
Author(s):  
Kees Wapenaar
Keyword(s):  
Wave Equation ◽  
Vector Wave ◽  
Geophysical Modeling ◽  
Vector Wave Equation ◽  
Symmetry Properties ◽  
Multiple Elimination ◽  
And Inversion ◽  
Matrix Vector ◽  
Wave Phenomena

Acoustic, electromagnetic, elastodynamic, poroelastic, and electroseismic waves are all governed by a unified matrix-vector wave equation. The matrices in this equation obey the same symmetry properties for each of these wave phenomena. This implies that the wave vectors for each of these phenomena obey the same reciprocity theorems. By substituting Green’s matrices in these reciprocity theorems, unified wavefield representations are obtained. Analogous to the well-known acoustic wavefield representations, these unified representations find applications in geophysical modeling, migration, inversion, multiple elimination, and interferometry.

Sign in / Sign up

Export Citation Format

Share Document