Jacob T. Fokkema

Bio: Jacob T. Fokkema is an academic researcher from Delft University of Technology. The author has contributed to research in topics: Reciprocity (electromagnetism) & Acoustic wave. The author has an hindex of 24, co-authored 131 publications receiving 3241 citations.

Green's function representations for seismic interferometry

Abstract: The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of time-reversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

Split-Step Fourier Migration

Abstract: The split‐step Fourier method is developed and applied to migrating stacked seismic data in two and three dimensions. This migration method, which is implemented in both the frequency‐wavenumber and frequency‐space domains, takes into account laterally varying velocity by defining a reference slowness (reciprocal of velocity) as the mean slowness in the migration interval and a perturbation term that is spatially varying. The mean slowness defines a reference vertical wavenumber which is used in the frequency‐wavenumber domain to downward continue the data across a depth interval as in constant‐velocity phase‐shift migration. The perturbation term is used to define a “source” contribution that is taken into account by the application of a second phase shift in the frequency‐space domain. Since the method does not include the effects of second and higher order spatial derivatives of the slowness field, the method theoretically is accurate only when there are no rapid lateral slowness variations combined wi...

Seismic applications of acoustic reciprocity

Abstract: Progress in seismic data processing requires the knowledge of all the theoretical aspects of the acoustic wave theory. We choose the reciprocity theorem as the central theme, because it constitutes the fundaments of the seismic wave theory (Fokkema and van den Berg, 1993). In essence, two states are distinguished in this theorem. These can be completely different, although they share the same time -invariant domgin of application and they are related via an interaction quantity. The particular choice of the two states determines the acoustic application. This makes it possible to formulate the seismic experiment in terme of a geological system response to a known source function.

Retrieving the Green’s function in an open system by cross correlation : A comparison of approaches (L)

Abstract: We compare two approaches for deriving the fact that the Green’s function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions. One approach is based on physical arguments, exploiting the principle of time-reversal invariance of the acoustic wave equation. The other approach is based on Rayleigh’s reciprocity theorem. Using a unified notation, we show that the result of the time-reversal approach can be obtained as an approximation of the result of the reciprocity approach.

Multiplicative regularization for contrast profile inversion

Abstract: [1] In this paper we discuss a new type of regularization technique for the nonlinear inverse scattering problem, namely the multiplicative technique. The main advantage is that we do not have to determine the regularization parameter before the inversion process is started. We consider different norms of the total variation as regularization factor. Specifically, we investigate a weighted L2-norm, and by using an appropriate updating scheme we show that this multiplicative regularization factor does not increase the nonlinearity of the inversion problem. Numerical examples using synthetic and experimental data demonstrate the robustness of the presented method.

The Rock Physics Handbook

Abstract: Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

Seismic Ray Theory

Abstract: Preface 1. Introduction 2. The elastodynamics and its simple solutions 3. Seismic rays and travel times 4. Dynamic ray tracing. Paraxial ray methods 5. Ray amplitudes 6. Ray synthetic seismograms Appendix. Fourier transform, Hilbert transform and analytical signals References Index.

Adaptive surface-related multiple elimination

Abstract: 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.

Global Optimization Methods in Geophysical Inversion

Abstract: Part 1 Preliminary statistics: random variables random nunmbers probability probability distribution, distribution function and density function joint and marginal probability distributions mathematical expectation, moments, variances and covariances conditional probability Monte Carlo integration importance sampling stochastic processes Markov chains homogeneous, inhomogeneous, irreducible and aperiodic Markov chains the limiting probability. Part 2 Direct, linear and iterative-linear inverse methods: direct inversion methods model based inversion methods linear/linearized inverse methods iterative linear methods for quasi-linear problems Bayesian formulation solution using probabilistic formulation. Part 3 Monte Carlo methods: enumerative or grid search techniques Monte Carlo inversion hybrid Monte Carlo-linear inversion directed Monte Carlo methods. Part 4 Simulated annealing methods: metropolis algorithm heat bath algorithm simulated annealing without rejected moves fast simulated annealing very fast simulated reannealing mean field annealing using SA in geophysical inversion. Part 5 Genetic algorithms: a classical GA schemata and the fundamental theorem of genetic algorithms problems combining elements of SA into a new GA a mathematical model of a GA multimodal fitness functions, genetic drift, GA with sharing, and repeat (parallel) GA uncertainty estimates evolutionary programming - a variant of GA. Part 6 Geophysical applications of SA and GA: 1-D seismic waveform inversion pre-stack migration velocity estimation inversion of resistivity sounding data for 1-D earth models inversion of resistivity profiling data for 2-D earth models inversion of magnetotelluric sounding data for 1-D earth models stochastic reservoir modelling seismic deconvolution by mean field annealing and Hopfield network. Part 7 Uncertainty estimation: methods of numerical integration simulated annealing - the Gibbs' sampler genetic algorithm - the parallel Gibbs' sampler numerical examples.