Bayesian-based signal processing is expected to dominate the future of model-based signal processing for years to come. This book develops the "Bayesian approach" to statistical signal processing for a variety of useful model sets with an emphasis on nonlinear/non-Gaussian problems, as well as classical techniques. Current applications and simple examples motivate the models and prepare the reader for developments in subsequent chapters. Although designed primarily as a graduate textbook, Bayesian Signal Processing is also useful to signal processing professionals and scientists.

Bayesian Signal Processing: Classical, Modern and Particle Filtering Methods

Seismic migration and inversion describe a class of closely related processes sharing common objectives and underlying physical principles. These processes range in complexity from the simple NMO‐stack to the complex, iterative, multidimensional, prestack, nonlinear inversion used in the elastic seismic case. By making use of amplitudes versus offset, it is, in principle, possible to determine the three elastic parameters from compressional data. NMO‐stack can be modified to solve for these parameters, as can prestack migration. Linearized, wave‐equation inversion does not inordinately increase the complexity of data processing. The principal part of a migration‐inversion algorithm is the migration. Practical difficulties are considerable, including both correctable and intrinsic limitations in data quality, limitations in current algorithms (which we hope are correctable), and correctable (or perhaps intrinsic) limitations in computer power.

Migration and inversion of seismic data

Methodology for using median filtering as one step in cepstral deconvolution or seismic signature estimation. The surprising conclusion from empirical studies on synthetic data is that in high-noise situations, cepstral-based median filtering appears to perform exceptionally well as a deconvolver but poorly as a signature estimator.--Modified journal abstract.

Applications of median filtering to deconvolution, pulse estimation, and statistical editing of seismic data

This heuristic paper presents several simple techniques for analyzing the stability of time-delay systems. It explains the Smith predictor control scheme for time-delay systems and shows how errors in modeling the plant parameters can cause instability. Then an adaptive controller is added to the Smith predictor system; this pedagogical example offers a complete derivation of a simple adaptive control system. Finally, a new control scheme is discussed that allows zero-latency tracking of predictable targets by a time-delay system.

A simple adaptive Smith-predictor for controlling time-delay systems: A tutorial

By rearranging the formulas for the responses of buried sources and receivers in the Kennett reflectivity algorithm, we have obtained a new algorithm that is very efficient for computing multioffset VSP synthetic seismograms. The rearrangement of the response formulas is quite general inasmuch as it applies to both isotropic and anisotropic Kennett codes. Our new algorithm and the original single‐receiver algorithm can both be made to run much faster on vector computers by taking the layer loop out of the p-loop, but leaving it inside the frequency loop. The resulting vector codes can still compute the response of media with frequency‐ dependent velocities.

Rapid computation of multioffset vertical seismic profile synthetic seismograms for layered media

This paper demonstrates some results obtained using state‐variable models and techniques on problems for which solutions either cannot be or are not easily obtained via more conventional input‐output techniques. After a brief introduction to state‐variable notions, the following seven problem areas are discussed: modeling seismic source wavelets, simultaneous deconvolution and correction for spherical divergence, simultaneous wavelet estimation and deconvolution, well log processing, design of recursive Wiener filters, Bremmer series decomposition of a seismogram (including suppression of multiples and vertical seismic profiling), and estimating reflection coefficients and traveltimes.

A novel approach to seismic signal processing and modeling

Vertical seismic profiles (VSPs) are, by definition, recordings of seismic signals (total upgoing and downgoing seismic wave fields) at different depth points, usually at equally spaced intervals zi=iΔ, i = 1, 2, …, I. In a nonnormal incidence (NNI) elastic model, where each layer is described by thickness, density, and P- and S-wave velocities, the mapping between time and depth needed to generate synthetic VSPs is not usually straightforward. In this paper we develop a relatively simple procedure for generating synthetic vertical and horizontal direction plane wave NNI VSPs. No spatial discretization is necessary. We (1) compute two surface seismograms, one vertical and the other horizontal, exactly as described in Aminzadeh and Mendel (1982); and (2) downward continue the surface seismograms to fixed VSP depth points. This paper demonstrates an algorithm for downward continuation of an elastic wave field using state‐space representation and gives simulations which illustrate both z- and x-direction pri...

Synthetic vertical seismic profiles for nonnormal incidence plane waves

We show how to include absorption effects in a normal incidence state‐space model of a layered media system. Two models are discussed: a convolutional state‐space model and a differential‐delay state‐space model. Extensive results are presented for the former model, whereas only formulative results are presented for the latter. For the convolutional state‐space model we develop absorption impulse responses in closed form for Gaussian and exponential absorption operators. Simulation results demonstrate that this model has the desired low‐pass filtering effect expected of a system with absorption losses. The differential‐delay state‐space model does not appear to have been applied before in the context of seismic modeling. We suggest it as a useful model.

Normal incidence layered system state-space models which include absorption effects

: The primary purpose of this paper is to extend a newly published normal incidence state space model to a non-normal incidence case. It also provides a synthetic seismogram for a two-dimensional point source and different offsets. The non-normal incidence state space model is structurally the same as the normal incidence state space model except that it has twice as many state variables. Because of the mode conversion in non-normal incidence, the scalar upgoing and downgoing waves and travel times in each layer as well as reflection and transmission coefficents at each interface are replaced by a vector of upgoing and downgoing waves, a vector of travel time, and matrices of reflection and transmission coefficents respectively. To obtain a two-dimensional point source synthetic generally used to express a three-dimensional point source in terms of a superposition of line sources. (Author)

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA064812&Location=U2&doc=GetTRDoc.pdf

Non-Normal Incidence State Space Model.

This paper is directed at modeling layered media. We extend the plane-wave normal-incidence state-space model developed by Mendel, Nahi and Chan in 1979, to the non-normal incidence case. To do this we introduce a shifting principle, a zero-offset wavefront, and zero-offset travel times for different layers. We also develop an algorithm for obtaining a synthetic line source reflection seismogram. In this algorithm non-normal incidence plane-wave seismograms are summed over a range of incident angles. The algorithm is based on a modified version of Sommerfield's (1896) theorem. Simulations of acoustic and elastic media are included which illustrate the applicability of our plane-wave and line source seismograms for both elastic and acoustic cases.

Fereydoun Aminzadeh

Papers

A novel approach to seismic signal processing and modeling

Synthetic vertical seismic profiles for nonnormal incidence plane waves

Normal incidence layered system state-space models which include absorption effects

Non-Normal Incidence State Space Model.

Non‐normal incidence state‐space model and line source reflection synthetic seismogram*