Reverse‐time wave‐field extrapolation, imaging, and inversion

Geophysics ◽  
1988 ◽  
Vol 53 (7) ◽  
pp. 920-931 ◽  
Author(s):  
Cengiz Esmersoy ◽  
Michael Oristaglio
Keyword(s):  
Integral Representation ◽  
Wave Field ◽  
Incident Field ◽  
Perfect Reconstruction ◽  
Reconstructed Image ◽  
Closed Form Expression ◽  
Background Medium ◽  
Receiver Array ◽  
Scattering Potential ◽  
Imaging Algorithms

The scattered wave field propagated backward in time into an arbitrary background medium is related via a volume integral to perturbations in velocity about the background, which are expressed as a scattering potential. In general, there is no closed‐form expression for the kernel of this integral representation, although it can be expressed asymptotically as a superposition of plane waves backpropagated from the receiver array. When the receiver array completely surrounds the scatterer, the kernel reduces to the imaginary part of the Green’s function for the background medium. This integral representation is used to relate the images obtained by imaging algorithms to the actual scattering potential. Two such relations are given: (1) for the migrated image, obtained by deconvolving the extrapolated field with the incident field; and (2) for the reconstructed image, obtained by applying a one‐way wave operator to the extrapolated field and then deconvolving by the incident field. The migrated image highlights rapid changes in the scattering potential (interfaces), whereas the reconstructed image can, under ideal conditions, be a perfect reconstruction of the scattering potential. “Ideal” conditions correspond to (1) weak scattering about a smoothly varying background medium, (2) a receiver array with full angular aperture, and (3) data of infinite bandwidth. Images obtained from a multioffset vertical seismic profile (VSP) illustrate some of the practical differences between the two imaging algorithms. The reconstructed image shows a much clearer picture of the target (a reef structure), in part because the one‐way imaging operator eliminates artifacts caused by the limited aperture of the receiver array.

Vertical seismic profile migration using the Kirchhoff integral

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Near Field ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Processing Strategies ◽  
Receiver Array ◽  
Vsp Data ◽  
Kirchhoff Integral

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.

scholarly journals An iterative inversion of back‐scattered acoustic waves

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Ronan LeBras ◽  
Robert W. Clayton
Keyword(s):  
Wave Field ◽  
Born Approximation ◽  
Acoustic Waves ◽  
Integral Relation ◽  
Field Operator ◽  
Scattered Wave ◽  
Far Field ◽  
Direct Integral ◽  
Background Medium ◽  
Iterative Inversion

The application of the Born approximation to the scattered wave field, followed by a WKBJ and far‐field approximation on the propagation Green’s function for a slowly varying background medium, leads to a simple integral relation between the density and bulk‐modulus anomalies superimposed on the background medium and the scattered wave field. An iterative inversion scheme based on successive back‐projections of the wave field is used to reconstruct the two acoustic parameters. The scheme, when applied to data generated using the direct integral relation, shows that the variations of the parameters can be reconstructed. The procedure is readily applicable to actual data, since every iterative step is essentially a prestack Kirchhoff migration followed by the application of the direct Born approximation and far‐field operator.

scholarly journals Simulation of High-Frequency Rotational Motion in a Two-Dimensional Laterally Heterogeneous Half-Space

2021 ◽  
Author(s):  
Ivan Lokmer ◽  
Varun Kumar Singla ◽  
John McCloskey
Keyword(s):  
Wave Field ◽  
Half Space ◽  
High Frequency ◽  
Body Waves ◽  
Propagation Path ◽  
Small Scale ◽  
Two Dimensional ◽  
Engineering Structures ◽  
Background Medium ◽  
Body Forces

<p>The seismic waves responsible for vibrating civil engineering structures undergo interference, focusing, scattering, and diffraction by the inhomogeneous medium encountered along the source-to-site propagation path. The subsurface heterogeneities at a site can particularly alter the local seismic wave field and amplify the ground rotations, thereby increasing the seismic hazard. The conventional techniques to carry out full wave field simulations (such as finite-difference or spectral finite element methods) at high frequencies (e.g., 15 Hz) are computationally expensive, particularly when the size of the heterogeneities is small (e.g., <100 m). This study proposes an alternative technique that is based on the first-order perturbation theory for wave propagation. In this technique, the total wave field due to a particular source is obtained as a superposition of the ‘mean’ and ‘scattered’ wave fields. Whereas the ‘mean’ wave field is the response of the background (i.e., heterogeneity-free) medium due to the given source, the ‘scattered’ wave is the response of the background medium excited by fictitious body forces. For a two-dimensional laterally heterogeneous elastic medium, these body forces can be conveniently evaluated as a function of the material properties of the heterogeneities and the mean wave field. Since the problem of simulating high-frequency rotations in a laterally heterogeneous medium reduces to that of calculating rotations in the background medium subjected to the (1) given seismic source and (2) body forces that mathematically replace the small-scale heterogeneities, the original problem can be easily solved in a computationally accurate and efficient manner by using the classical (analytical) wavenumber-integration method. The workflow is illustrated for the case of a laterally heterogenous layer embedded in a homogeneous half-space excited by plane body-waves.</p>

MOTION OF AN ELASTIC SPHERE IN AN ACOUSTIC WAVE FIELD IN FLUIDS

Geophysics ◽  
1946 ◽  
Vol 11 (2) ◽  
pp. 178-182
Author(s):  
Alfred Wolf
Keyword(s):  
Acoustic Wave ◽  
Wave Field ◽  
Elastic Constants ◽  
Wave Length ◽  
Zero Order ◽  
Rigid Sphere ◽  
Elastic Sphere ◽  
Transverse Waves ◽  
Scattering Potential

The motion of an elastic sphere in an acoustic wave field in fluids is determined as function of the elastic constants of the sphere, its radius, and the frequency of the wave field. It is found that the motion differs but little from the motion of an infinitely rigid sphere when the wave length of transverse waves in the elastic sphere is at least as long as the circumference of the sphere. The coefficient of zero order scattering potential in the fluid is determined.

Scattering by periodic array of rectangular blocks

1995 ◽  
Vol 305 ◽  
pp. 263-279 ◽  
Author(s):  
M. Fernyhough ◽  
D. V. Evans
Keyword(s):  
Integral Representation ◽  
Linear Theory ◽  
Water Depth ◽  
Water Waves ◽  
Galerkin Approximation ◽  
Incident Field ◽  
Periodic Array ◽  
Two Dimensional ◽  
Matrix Formulation

Scattering properties of an incident field upon a periodic array of identical rectangular barriers, each extending throughout the water depth, are calculated based on a Galerkin approximation to an integral representation of the problem derived using the linear theory of water waves. The method incorporates full multi-modal scattring using the linear theory of water waves. The method incorporates full multi-modal scattering using a matrix formulation and is equivalent to a corresponding two-dimensional acoustics problem also discussed.

scholarly journals Three-Dimensional Near-Field Microwave Holography for Tissue Imaging

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Reza K. Amineh ◽  
Ali Khalatpour ◽  
Haohan Xu ◽  
Yona Baskharoun ◽  
Natalia K. Nikolova
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Near Field ◽  
Spherical Wave ◽  
Three Dimensional ◽  
Incident Field ◽  
Tissue Imaging ◽  
Imaging Results ◽  
Tem Horn ◽  
Imaging Algorithms

This paper reports the progress toward a fast and reliable microwave imaging setup for tissue imaging exploiting near-field holographic reconstruction. The setup consists of two wideband TEM horn antennas aligned along each other’s boresight and performing a rectangular aperture raster scan. The tissue sensing is performed without coupling liquids. At each scanning position, wideband data is acquired. Then, novel holographic imaging algorithms are implemented to provide three-dimensional images of the inspected domain. In these new algorithms, the required incident field and Green’s function are obtained from numerical simulations. They replace the plane (or spherical) wave assumption in the previous holographic methods and enable accurate near-field imaging results. Here, we prove that both the incident field and Green’s function can be obtained from a single numerical simulation. This eliminates the need for optimization-based deblurring which was previously employed to remove the effect of realistic non-point-wise antennas.

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