Solution of the VSP One‐dimensional Inverse Problem*

Macé, D.; Lailly, Patrick

doi:10.1111/j.1365-2478.1986.tb00510.x

Cited by 14 publications

(11 citation statements)

References 5 publications

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“…This would be the case for a reflection between a slow isotropic layer and a birefringent fast layer. Figure 19 shows both the reflection coefficients and the impedance deduced from a I-D full waveform inversion (Mace and Lailly, 1986) of each main component. (Brodov et al, 1990), a comparison with a layer stripping method has been performed (Lefeuvre et al, 1991) and the results have been compared with other tools of fracture detection like the investigation of the Stoneley wave behavior in full wave acoustic logs or like the televiewer data.…”

Section: Vr(t) =~*Dr(t)mentioning

confidence: 99%

Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications

et al. 1992

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An original method is presented that allows us to measure the local shear-wave birefringence properties over any depth interval. It requires the acquisition of two shear-wave vertical seismic profiles (VSPs), each with different initial polarizations of the shear wave. The method is based on the estimation of a two by two matrix (called the propagator matrix) that represents a linear operator between two states of polarization. No information is required about layering above the zone of interest (in particular, about the weathering zone). If these two states of polarization correspond to the direct downgoing shear wave at two different depths z 1 and z2, the operator represents the transmission properties between the two depths. Under the previous hypothesis, this operator is independent of the source polarization and can be accurately estimated by a least-squares method in the frequency domain. Physically, this operator is a multicomponent deconvolution, whose column vectors represent the state of polarizations at a depth Z2 for two linear and INTRODUCTION

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Section: Vr(t) =~*Dr(t)mentioning

confidence: 99%

Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications

et al. 1992

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“…For other models we refer the reader to [5][6][7]. For most classical partial differential equations, the reconstruction of source functions from the final data or a partial boundary data is an inverse problem with many applications in several branches of sciences and engineering, such as geophysical prospecting and pollutant detection [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

Zouyed

Djemoui

2015

Mathematical Problems in Engineering

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This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists) does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

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“…overpressured layers). The typical approach is to invert a VSP corridor stack trace for acoustic impedance in a one‐dimensional medium; for examples, see Kennett, Ireson and Conn (1980), Grivelet (1985), Mace and Lailly (1986), Payne (1994) and Borland et al (1998).…”

Section: Introductionmentioning

confidence: 99%

Monte‐Carlo Bayesian look‐ahead inversion of walkaway vertical seismic profiles

Malinverno

Leaney

2005

Geophysical Prospecting

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A B S T R A C TWe describe a method to invert a walkaway vertical seismic profile (VSP) and predict elastic properties (P-wave velocity, S-wave velocity and density) in a layered model looking ahead of the deepest receiver. Starting from Bayes's rule, we define a posterior distribution of layered models that combines prior information (on the overall variability of and correlations among the elastic properties observed in well logs) with information provided by the VSP data. This posterior distribution of layered models is sampled by a Monte-Carlo method. The sampled layered models agree with prior information and fit the VSP data, and their overall variability defines the uncertainty in the predicted elastic properties. We apply this technique first to a zero-offset VSP data set, and show that uncertainty in the long-wavelength P-wave velocity structure results in a sizable uncertainty in the predicted elastic properties. We then use walkaway VSP data, which contain information on the long-wavelength P-wave velocity (in the reflection moveout) and on S-wave velocity and density contrasts (in the change of reflectivity with offset). The uncertainty of the look-ahead prediction is considerably decreased compared with the zero-offset VSP, and the predicted elastic properties are in good agreement with well-log measurements.

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Solution of the VSP One‐dimensional Inverse Problem*

Cited by 14 publications

References 5 publications

Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications

Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications

An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

Monte‐Carlo Bayesian look‐ahead inversion of walkaway vertical seismic profiles

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