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.

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.

Elastic inverse scattering for fluid variation with time-lapse seismic data

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. WA61-WA67 ◽  
Author(s):  
Zhaoyun Zong ◽  
Xingyao Yin ◽  
Guochen Wu ◽  
Zhiping Wu
Keyword(s):  
Shear Modulus ◽  
Inverse Scattering ◽  
Seismic Data ◽  
Scattering Theory ◽  
Time Lapse ◽  
Monitoring Data ◽  
Prestack Inversion ◽  
Fluid Factor ◽  
Reference Medium ◽  
The Difference

Elastic inverse-scattering theory has been extended for fluid discrimination using the time-lapse seismic data. The fluid factor, shear modulus, and density are used to parameterize the reference medium and the monitoring medium, and the fluid factor works as the hydrocarbon indicator. The baseline medium is, in the conception of elastic scattering theory, the reference medium, and the monitoring medium is corresponding to the perturbed medium. The difference in the earth properties between the monitoring medium and the baseline medium is taken as the variation in the properties between the reference medium and perturbed medium. The baseline and monitoring data correspond to the background wavefields and measured full fields, respectively. And the variation between the baseline data and monitoring data is taken as the scattered wavefields. Under the above hypothesis, we derived a linearized and qualitative approximation of the reflectivity variation in terms of the changes of fluid factor, shear modulus, and density with the perturbation theory. Incorporating the effect of the wavelet into the reflectivity approximation as the forward solver, we determined a practical prestack inversion approach in a Bayesian scheme to estimate the fluid factor, shear modulus, and density changes directly with the time-lapse seismic data. We evaluated the examples revealing that the proposed approach rendered the estimation of the fluid factor, shear modulus, and density changes stably, even with moderate noise.

scholarly journals Retrieval of the physical properties of an anelastic solid half space from seismic data

2013 ◽  
Vol 88 ◽  
pp. 70-82 ◽  
Author(s):  
Gaëlle Lefeuve-Mesgouez ◽  
Arnaud Mesgouez ◽  
Erick Ogam ◽  
Thierry Scotti ◽  
Armand Wirgin
Keyword(s):  
Physical Properties ◽  
Half Space ◽  
Seismic Data

Kirchhoff elastic wave migration for the case of noncoincident source and receiver

Geophysics ◽  
1984 ◽  
Vol 49 (8) ◽  
pp. 1223-1238 ◽  
Author(s):  
John T. Kuo ◽  
Ting‐fan Dai
Keyword(s):  
Elastic Wave ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Horizontal Layer ◽  
P Wave ◽  
Seismic Section ◽  
S Waves ◽  
Surface Data ◽  
Marine Seismic ◽  
Wave Migration

In taking into account both compressional (P) and shear (S) waves, more geologic information can likely be extracted from the seismic data. The presence of shear and converted shear waves in both land and marine seismic data recordings calls for the development of elastic wave‐migration methods. The migration method presently developed consists of simultaneous migration of P- and S-waves for offset seismic data based on the Kirchhoff‐Helmholtz type integrals for elastic waves. A new principle of simultaneously migrating both P- and S-waves is introduced. The present method, named the Kirchhoff elastic wave migration, has been tested using the 2-D synthetic surface data calculated from several elastic models of a dipping layer (including a horizontal layer), a composite dipping and horizontal layer, and two layers over a half‐space. The results of these tests not only assure the feasibility of this migration scheme, but also demonstrate that enhanced images in the migrated sections are well formed. Moreover, the signal‐to‐noise ratio increases in the migrated seismic section by this elastic wave migration, as compared with that using the Kirchhoff acoustic (P-) wave migration alone. This migration scheme has about the same order of sensitivity of migration velocity variations, if [Formula: see text] and [Formula: see text] vary concordantly, to the recovery of the reflector as that of the Kirchhoff acoustic (P-) wave migration. In addition, the sensitivity of image quality to the perturbation of [Formula: see text] has also been tested by varying either [Formula: see text] or [Formula: see text]. For varying [Formula: see text] (with [Formula: see text] fixed), the migrated images are virtually unaffected on the [Formula: see text] depth section while they are affected on the [Formula: see text] depth section. For varying [Formula: see text] (with [Formula: see text] fixed), the migrated images are affected on both the [Formula: see text] and [Formula: see text] depth sections.

Prestack 2D parsimonious Kirchhoff depth migration of elastic seismic data

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. S157-S164 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
P Wave ◽  
P Value ◽  
Common Source ◽  
S Wave ◽  
P Values ◽  
Depth Migration ◽  
Reflector Surface ◽  
Kirchhoff Depth Migration

We have extended prestack parsimonious Kirchhoff depth migration for 2D, two-component, reflected elastic seismic data for a P-wave source recorded at the earth’s surface. First, we separated the P-to-P reflected (PP-) waves and P-to-S converted (PS-) waves in an elastic common-source gather into P-wave and S-wave seismograms. Next, we estimated source-ray parameters (source p values) and receiver-ray parameters (receiver p values) for the peaks and troughs above a threshold amplitude in separated P- and S-wavefields. For each PP and PS reflection, we traced (1) a source ray in the P-velocity model in the direction of the emitted ray angle (determined by the source p value) and (2) a receiver ray in the P- or S-velocity model back in the direction of the emergent PP- or PS-wave ray angle (determined by the PP- or PS-wave receiver p value), respectively. The image-point position was adjusted from the intersection of the source and receiver rays to the point where the sum of the source time and receiver-ray time equaled the two-way traveltime. The orientation of the reflector surface was determined to satisfy Snell’s law at the intersection point. The amplitude of a P-wave (or an S-wave) was distributed over the first Fresnel zone along the reflector surface in the P- (or S-) image. Stacking over all P-images of the PP-wave common-source gathers gave the stacked P-image, and stacking over all S-images of the PS-wave common-source gathers gave the stacked S-image. Synthetic examples showed acceptable migration quality; however, the images were less complete than those produced by scalar reverse-time migration (RTM). The computing time for the 2D examples used was about 1/30 of that for scalar RTM of the same data.

Determination of background velocities by multiple migration fitting

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 476-490 ◽  
Author(s):  
Guy Chavent ◽  
Chester A. Jacewitz
Keyword(s):  
Numerical Investigation ◽  
Seismic Data ◽  
Synthetic Data ◽  
Similarity Index ◽  
Velocity Profiles ◽  
Additional Cost ◽  
Scalar Similarity ◽  
Local Gradient

We present an approach called multiple migration fitting (MMF) designed to automatically determine 2-D background velocities from prestack seismic data. In this approach, we maximize a scalar similarity index (SI) for a collection of migrated sections obtained by various illuminations of the same earth. Numerical investigation shows that this index is a rather smooth, nonoscillatory function of velocity that tends to be a maximum for good velocity profiles, and hence is amenable to maximization by local gradient techniques. This maximization will be practically feasible, as we prove that the exact gradient of SI can be computed at an additional cost of only twice that required for the computation of the collection of migrated sections, independently of the number of velocity unknowns. Application to synthetic data shows that MMF leads to enhanced background velocities and stacked migrated sections.

Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media

2016 ◽  
Vol 20 (2) ◽  
pp. 353-373 ◽  
Author(s):  
Jie Yao ◽  
Anne-Cécile Lesage ◽  
Fazle Hussain ◽  
Donald J. Kouri
Keyword(s):  
Scattering Theory ◽  
Incidence Angle ◽  
Neumann Series ◽  
Forward Scattering ◽  
Acoustic Medium ◽  
Inversion Method ◽  
Angle Of Incidence ◽  
Direct Inversion ◽  
Reference Medium ◽  
Density Perturbations

AbstractWe extend the full wavefield modeling with forward scattering theory and Volterra Renormalization to a vertically varying two-parameter (velocity and density) acoustic medium. The forward scattering series, derived by applying Born-Neumann iterative procedure to the Lippmann-Schwinger equation (LSE), is a well known tool for modeling and imaging. However, it has limited convergence properties depending on the strength of contrast between the actual and reference medium or the angle of incidence of a plane wave component. Here, we introduce the Volterra renormalization technique to the LSE. The renormalized LSE and related Neumann series are absolutely convergent for any strength of perturbation and any incidence angle. The renormalized LSE can further be separated into two sub-Volterra type integral equations, which are then solved noniteratively. We apply the approach to velocity-only, density-only, and both velocity and density perturbations. We demonstrate that this Volterra Renormalization modeling is a promising and efficient method. In addition, it can also provide insight for developing a scattering theory-based direct inversion method.

The domain of applicability of acoustic full-waveform inversion for marine seismic data

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC91-WCC103 ◽  
Author(s):  
Christophe Barnes ◽  
Marwan Charara
Keyword(s):  
Seismic Data ◽  
Seismic Inversion ◽  
Three Dimensions ◽  
Acoustic Medium ◽  
Physical Parameters ◽  
S Wave ◽  
Data Set ◽  
Reflection Seismic ◽  
Wave Inversion ◽  
Full Wave

Marine reflection seismic data inversion is a compute-intensive process, especially in three dimensions. Approximations often are made to limit the number of physical parameters we invert for, or to speed up the forward modeling. Because the data often are dominated by unconverted P-waves, one popular approximation is to consider the earth as purely acoustic, i.e., no shear modulus. The material density sometimes is taken as a constant. Nonlinear waveform seismic inversion consists of iteratively minimizing the misfit between the amplitudes of the measured and the modeled data. Approximations, such as assuming an acoustic medium, lead to incorrect modeling of the amplitudes of the seismic waves, especially with respect to amplitude variation with offset (AVO), and therefore have a direct impact on the inversion results. For evaluation purposes, we have performed a series of inversions with different approximations and different constraints whereby the synthetic data set to recover is computed for a 1D elastic medium. A series of numerical experiments, although simple, help to define the applicability domain of the acoustic assumption. Acoustic full-wave inversion is applicable only when the S-wave velocity and the density fields are smooth enough to reduce the AVO effect, or when the near-offset seismograms are inverted with a good starting model. However, in many realistic cases, acoustic approximation penalizes the full-wave inversion of marine reflection seismic data in retrieving the acoustic parameters.

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