William J. Vetter

Spatial parameter estimation for ocean subsurface layered media

Discusses the problem of obtaining estimates of amplitude and delay parameters associated with the response to impulsive acoustic excitations of the ocean subbottom. The availability of the estimates is important for identifying properties and geometry of underwater sediments and rock formations. The authors detail the basic model for ocean bottom subsurface reflections and gives the mathematical basis for extraction of parameter estimates for the model by a correlation method. Some results are presented for estimates on field data. It is found that for the data records available the results after estimation only contain false events and unrecognized events. Spatial filtering and smoothing is suggested to improve estimates and their reliability.

Event enhancement of reflections from subsurface layered media

The problem of obtaining amplitude and delay parameters associated with the response of subsurface layered sedimentation to impulse-type acoustic excitations is considered. We use a linear lossless model which characterizes the subsurface in terms of layerwise homogeneous segments. The parameters of the model are the time delays associated with the wave propagation in the various layers and amplitude parameters which are functions of the reflection coefficients at the interfaces. With knowledge of the travel time in a sediment of rock layer, its thickness can be estimated if the medium velocity is known. This paper extends theory developed by the authors. In particular, a procedure to enhance the detection of reflection events is presented. The procedure utilizes a balance property shown by the derivative of the input waveform signal to obtain an improved display of reflection-event portions of the received signals. Computational results are given in the paper to illustrate the effectivess of the procedure.

Heave Compensation of Shallow Marine Seismic Reflection Records by Kalman Filtering

The purpose of this paper is to present a procedure for data filtering to compensate for the heaves effects of the towed body dynamics, in shallow marine seismic reflection records. The Fourier transform of the heave component record provides the basis for a proposed linear model for the heave motion. A formulation of the heave compensation requirement as a Kalman filtering problem in optimal linear estimation theory is presented. A discussion of the computational aspects and practical results are given to conclude this paper.

A Layer-Indexed Reflection Model for Multilayered Media

Models for acoustic reflections from multilayered media, such as marine sediments or geological strata, are important for interpretive work on actual reflection data. We present here a new formulation for the ideal reflection process for multiple layers and unequal travel times. Our formulation uses a superior index notation, and gives a very tractable and compact model structure. We generalise the reflection model to accommodate frequency dependent attenuation in the layers.

Reflector Extraction from Marine Shallow Seismic Broadband Data

A time domain synthetic reflection seismogram is detailed and, as a limiting condition on this model, the analytic reflection impulse response for a one-dimensional lossless acoustic medium with piecewise continuous acoustic impedance is obtained. This analytic impulse response solution provides insight to some of the poorly understood aspects of acoustic reflections from stratified and smoothly varying media. It offers as well an approach for the inverse problem of extracting acoustic impedance profiles from reflection response data.

The array matrix generalization for signal processing

The diversity of notation permeating the publications on signal processing suggests the need for some consolidation and standardization. We advocate here the array theory and notation of Tait as a standardizing framework for a smooth transition from the vector-matrix era to the array domain and array processing era. A duality between array domain and matrix domain operations blends the flexibility and power of the array domain with the compactness and overview attributes of matrix expressions. The notation facilitates tractability through the super- and subscript patterns for the indices and the range set of the indices. We introduce fundamentals from Taits work with some consolidation and exemplify notation and manipulations. The relevance for signal processing is demonstrated more fully in a companion paper [8].

Reflection response for normal incidence probing of vertically nonhomogeneous media

A time domain synthetic reflection seismogram is detailed and, as a limiting condition on this model, the analytic reflection impulse response for a one-dimensional lossless acoustic medium with piecewise continuous acoustic impedance is obtained. This analytic impulse response solution, in the structure of a sum of terms by order of reflection, provides insight to some of the poorly understood aspects of acoustic reflections from stratified and smoothly varying media as may be encountered in shallow marine sediments and elsewhere. It offers as well an approach for the inverse problem of extracting acoustic impedance profiles from reflection response data, though other effects (such as wavefront spreading, dispersive and absorptive attenuation, and wavelet broadening attendant with pulse propagation through a medium) need to be accommodated.

Acoustic Subbottom Sediment Reflections: Synthesized Responses from Core Parameter Profiles Compared with Observed Broadband Reflection Responses

A model for the acoustic response of a sedimentary ocean subbottom to pulse type excitation is detailed, which accommodates gradients of sound velocity and of density in the depth coordinate. Effects of spherical spreading, and of frequency and depth dependent attenuation are also included, the latter by a novel intepretation of the depth dependence as the response of a depth-varying linear filter. Synthesised responses, using parameter values from subbottom cores, are compared with the acoustic responses from the vicinity of the core stations.

Impulse response for the one-dimensional inhomogeneous medium with an approximation for attenuation and dispersion

The impulse response h(z,t) for the wave equation which models the propagation in a one-dimensional inhomogeneous lossless medium is detailed, Pulse spreading and pulse hight reduction versus travel distance are then accommodated as a superposition integral with the lossless response acting as an excitation function on a dispersion model g(z,t).

Source Heave Compensation for High Resolution Marine Seismic Profiling

In this paper several compensation schemes for removal of acoustic source heave affects from the seismic echo signal are described and examined. A new compensation method is proposed, in which heave distortion is continuously corrected, irrespective of towing height. This scheme is based on a nonlinear time base display or time varying sampling rate during acquisition of the seismic signal. The method proposed leads to a simple hardware implementation.