Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

The problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory. In its roughest formulation, the inverse problem consists of obtaining the Earth model for which the predicted data best fit the observed data. If an adequate forward model is used, this best model will give the best images of the Earth’s interior. Three parameters are needed for describing a perfectly elastic, isotropic, Earth: the density ρ(x) and the Lame parameters λ(x) and μ(x), or the density ρ(x) and the P-wave and S-wave velocities α(x) and β(x). The choice of parameters is not neutral, in the sense that although theoretically equivalent, if they are not adequately chosen the numerical algorithms in the inversion can be inefficient. In the long (spatial) wavelengths of the model, adequate parameters are the P-wave and S-wave velocities, while in the short (spatial) wavelengths, P-wave impedance, S-wave impedance, and density are adequate. The problem of inversion o...

A strategy for nonlinear elastic inversion of seismic reflection data

Migration of an observed zero-offset wavefield can be performed as the solution of a boundary value problem in which the data are extrapolated backward in time. This concept is implemented through a finite-difference solution of the two-dimensional acoustic wave equation. All depths are imaged simultaneously at time 0 (the imaging condition), and all dips (right up to vertical) are correctly migrated. Numerical examples illustrate this technique in both constant and variable velocity media.

Migration by extrapolation of time‐dependent boundary values*

The major amount of multiple energy in seismic data is related to the large reflectivity of the surface. A method is proposed for the elimination of all surface-related multiples by means of a process that removes the influence of the surface reflectivity from the data. An important property of the proposed multiple elimination process is that no knowledge of the subsurface is required. On the other hand, the source signature and the surface reflectivity do need to be provided. As a consequence, the proposed process has been implemented adaptively, meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple-free data equals the inversion residue. Results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion.

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Adaptive surface-related multiple elimination

Preface 1. Introduction to rock physics 2. Rock physics interpretation of texture, lithology and compaction 3. Statistical rock physics: combining rock physics, information theory, and statistics to reduce uncertainty 4. Common techniques for quantitative seismic interpretation 5. Case studies: lithology and pore-fluid prediction from seismic data 6. Workflows and guide lines 7. Hands-on References Index.

Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk

The statics problem, whether short wavelength, long wavelength, residual, or trim, has always been one of the more time-consuming and problematic steps in seismic data processing. We routinely struggle with issues such as poor signal-to-noise (S/N) ratio, cycle skipping, truncated refractors, wavelets with ambiguous first arrival times, etc. Elevation variations create their own problems and impact the choice of datum—floating, phantom or recourse to a zero-velocity layer. Even if we can overcome some of these problems, we still have a “catch 22” situation in which accurate velocity estimation requires good statics, while good statics estimation requires accurate velocities. To characterize these ambiguities, we have come up the oxymoron “time-varying statics.”

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The dynamics of statics

Combining Full Wavefield Migration And Full Waveform Inversion

On the Information Content of P-P, P-SV, SV-SV , And SV-P Reflections

The acoustics in auditoria is determined by the properties of both direct sound and reflections. If electroacoustic means are used to optimize the acoustics, one has to cope with unfavorable side effects such as localization problems and artificial impression of the reverberant field. To avoid those side effects, the concept of electroacoustic wave‐front synthesis is introduced. The underlying theory is based on the Huygens–Rayleigh integral. In this concept, the wave fields of the sound sources on stage are measured by directive microphones; next they are extrapolated by means of an electronic processor, and finally, they are re‐emitted in the hall by one or more loudspeaker arrays. Depending on the processor design, the wave‐front systems can be used for direct sound enhancement, for simulation of discrete early reflections, or for generation of reverberation. Application of the wave‐front synthesis concept also opens the door to a new approach of sound recording and reproduction.

Wave Front Synthesis: A New Direction in Electroacoustics

In this paper we will discuss an approach to tissue characterization which was developed within our group. First our approach will be outlined.One of the basic steps we use here is a high resolution Synthetic Focusing procedure (Berkhout et al.,1982). For this procedure, and also for tissue characterization itself, correct knowledge of the sound propagation velocity is essential. In the second part of this paper a method will be put forward to determine values of the sound propagation velocity with little prior knowledge of the medium.This method is based on the minimization of the entropy of the synthetically focused image. Now an optimally focused image can be produced,which may be analysed in detail.In the final part of this paper we will discuss a method of analysis,based on two dimensional Fourier transformation of the r.f.data of part of the image.

A. J. Berkhout

Papers

The dynamics of statics

Combining Full Wavefield Migration And Full Waveform Inversion

On the Information Content of P-P, P-SV, SV-SV , And SV-P Reflections

Wave Front Synthesis: A New Direction in Electroacoustics

An Approach to Tissue Characterization Based on Wave Theory Using a New Velocity Analysis Technique