The inverse problem of the density and bulk modulus profiles of a layered fluid

1982 ◽  
Vol 72 (3) ◽  
pp. 809-820
Author(s):  
Shimon Coen
Keyword(s):  
Inverse Problem ◽  
Bulk Modulus ◽  
Half Space ◽  
Seismic Data ◽  
Necessary Conditions ◽  
Vertical Component ◽  
Inversion Algorithm ◽  
Surface Data ◽  
Layered Half Space ◽  
Layered Fluid

abstract It is shown that the density and bulk modulus profiles of a layered fluid half-space are uniquely determined from the vertical component of the particle velocity on the surface due to an impulsive point source on the surface. In addition, an estimate of the highest acoustic wave velocity in the layered half-space is required as well. The necessary conditions for the existence of the solution are discussed and a direct (noniterative) inversion algorithm is developed which constructs the density and bulk modulus profiles of the half-space from the surface data. The main limitations of this theory to real seismic data are briefly discussed.

Velocity and density profiles of a layered acoustic medium from common source‐point data

Geophysics ◽  
1982 ◽  
Vol 47 (6) ◽  
pp. 898-905 ◽  
Author(s):  
Shimon Coen
Keyword(s):  
Half Space ◽  
Seismic Data ◽  
Scattering Theory ◽  
Velocity Profiles ◽  
Acoustic Medium ◽  
Common Source ◽  
Density Profiles ◽  
Source Point ◽  
Surface Data ◽  
Point Data

An inverse scattering theory is presented for the unique reconstruction of the density and velocity profiles of a layered acoustic half‐space from common source‐point surface data. The point source is either impulsive or is capable of vibrating at two arbitrary frequencies. An additional datum for the unique reconstruction of these profiles is an estimate of either the highest or lowest velocity within the inhomogeneous acoustic half‐space. Two direct (noniterative) inversion algorithms are developed which construct the density and velocity profiles of the inhomogeneous half‐space from these data. Analytical examples are presented in which all steps in the inversion algorithms are analytically determined. Finally, the paper discusses the potential application of the theory to real seismic data.

scholarly journals Inverse problem for wave propagation in a perturbed layered half-space

2007 ◽  
Vol 45 (1-2) ◽  
pp. 21-33 ◽  
Author(s):  
Robert Gilbert ◽  
Klaus Hackl ◽  
Yongzhi Xu
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Half Space ◽  
Layered Half Space

Restricted model domain time Radon transforms

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. A17-A21 ◽  
Author(s):  
Juan I. Sabbione ◽  
Mauricio D. Sacchi
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Computational Cost ◽  
Synthetic Data ◽  
Model Space ◽  
Radon Transforms ◽  
Iterative Solver ◽  
Hard Thresholding ◽  
Restricted Model ◽  
Marine Data

The coefficients that synthesize seismic data via the hyperbolic Radon transform (HRT) are estimated by solving a linear-inverse problem. In the classical HRT, the computational cost of the inverse problem is proportional to the size of the data and the number of Radon coefficients. We have developed a strategy that significantly speeds up the implementation of time-domain HRTs. For this purpose, we have defined a restricted model space of coefficients applying hard thresholding to an initial low-resolution Radon gather. Then, an iterative solver that operated on the restricted model space was used to estimate the group of coefficients that synthesized the data. The method is illustrated with synthetic data and tested with a marine data example.

scholarly journals Deblending by direct inversion

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. A9-A12 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Jan Thorbecke
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Iterative Procedure ◽  
Inversion Process ◽  
Direct Inversion ◽  
Source Data ◽  
Band Limited ◽  
Blended Data ◽  
Simultaneous Source ◽  
Additional Constraints

Deblending of simultaneous-source data is usually considered to be an underdetermined inverse problem, which can be solved by an iterative procedure, assuming additional constraints like sparsity and coherency. By exploiting the fact that seismic data are spatially band-limited, deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constraints. We applied the method with numerically modeled data and it suppressed the crosstalk well, when the blended data consisted of responses to adjacent, densely sampled sources.

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