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1989 | Buch

Tau-p: a plane wave approach to the analysis of seismic data

herausgegeben von: Paul L. Stoffa

Verlag: Springer Netherlands

Buchreihe : Seismology and Exploration Geophysics

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Über dieses Buch

In exploration seismology, data are acquired at multiple source and receiver posi­ tions along a profile line. These data are subsequently processed and interpreted. The primary result of this process is a subsurface image of the exploration target. As part of this procedure, additional information is also obtained about the subsurface material properties, e.g., seismic velocities. The methods that are employed in the acquisition and processing of exploration seismic data are internally consistent. That is, principally near vertical incidence seismic waves are generated, recorded and subsequently imaged. The data processing methods commonly used are based upon a small angle of incidence approximation, thus making the imaging problem tractable for existing data processing technology. Although tremendously successful, the limitations of this method are generally recognized. Current and future exploration goals will likely require the use of additional seismic waves, i.e., both compressional and shear precritical and postcritical reflections and refractions. Also, in addition to making better use of seismic travel times, recent efforts to directly incorporate seismic amplitude variations show that the approach may lead to a better understanding of subsurface rock properties. In response to more demanding exploration goals, recent data acquisition techniques have improved significantly by increasing the spatial aperture and incorporating a large number of closely spaced receivers. The need for better subsurface resolution in depth and position has encouraged the use of 240, 512, and even 1024 recorded data channels with receiver separations of 5 to 25 m.

Inhaltsverzeichnis

Frontmatter
Cartesian and Cylindrical Slant Stacks
Abstract
The proper implementation of the τ-p method for surface data excited by a point source, requires the computation of a cylindrical slant stack. Usually, the common (Cartesian) slant stack is computed instead as an approximation to the geometrically-correct procedure. Here, we describe a formulation of the cylindrical slant stack as a weighted sum of Cartesian slant stacks which is accurate for all slownesses and efficient to perform.
As examples of the method, we show results computed from synthetic seismograms and from data recorded on the West Florida Shelf. Severe edge-effect noise which overwhelms the Cartesian slant stack, is attenuated by the cylindrical slant stack. Applications of the cylindrical slant stack to other seismological calculations, such as Lamb's problem, are also discussed. In particular, we show that the plane wave reflection coefficients apply exactly in the τ-p domain; hence an amplitude-versus-slowness analysis is unambiguous in this domain and requires no geometrical corrections to the data.
Douglas W. McCowan, Henry Brysk
Tau-p Filtering
Abstract
Examination, evaluation and processing of seismic data in the two-dimensional τ-p domain offers many advantages over analysis and processing in the originally recorded X-t domain or other transformed domains. Since the slowness p (1) is the reciprocal the horizontal phase velocity, (2) represents the apparent angle of emergence at the surface, and (3) in a flat-layered earth it is also a constant conserved quantity (the ray parameter) along the raypath, we can readily address (1) antenna and array problems, (2) angle of incidence effects, and (3) problems (such as multiples) associated with the ray geometry. Examples of these applications include attenuation of ground roll, separation of P and S-waves where the angle of incidence defines the efficiency of mode conversion, and more efficient attenuation of multiples where they are exactly periodic in the τ-p domain.
The present paper reviews and discusses some of these applications, with real data examples of each. It also discusses aspects of the τ-p transform relevant for such applications and an alteration of the forward transform that improves its filtering characteristics.
Robert H. Tatham
Tau-p Analysis in One, Two and Three Dimensions
Seismic inversion methods that are based on the analysis of traveltime rely on the most fundamental measurement of waveform and amplitude; either there is an arrival or there is not. Traveltime contains the basic information about an arrival's phase; the geometrical arrival time is equal to the stationary point of the phase term in the wave equation representation for any seismic arrival. Even when impedance and velocity series are determined from the amplitude and phase variations along a seismic trace, these can usually be interpreted only as fine scale deviations from a velocity function which changes relatively slowly as a function of depth. That 'long period' velocity function must itself be obtained by other means; typically from traveltime analysis.
John Diebold
Plane- Wave Decomposition: A Tool for Deconvolution
Abstract
Most (prestack) deconvolution methods for seismic shot records are based on simple stochastic models for the traces. They do not exploit the fact that these traces have to satisfy the wave equation. A plane-wave decomposition of a point-source seismogram recorded over a vertically inhomogeneous layered (acoustic) medium is a process based on the wave equation. It offers the possibility to extract both (a) the causal source pulse of arbitrary unknown shape and (b) the unknown broad-band plane-wave response (reflectivity) for any incidence angle or ray parameter. This was hitherto considered to be impossible but has become a reality if one exploits the wave theory that permits us to compose and decompose point-source responses from vertically inhomogeneous media in terms of plane waves. As starting point for constructing the seismogram by a plane-wave composition serves the Weyl Integral in either its time-harmonic or transient form. The central concept, on the other hand, upon which the plane-wave decomposition is based is the slant stack. The theory of plane-wave composition is briefly reviewed in order to establish the background for the new deconvolution procedure which essentially uses the properties that the reflectivity function (i.e. the reflection response of a layered medium for an incident plane wave) has for above-critical incidence angles.
M. Tygel, P. Hubral, F. Wenzel
Inversion of Common Mid Point Seismic Data
Abstract
Inversion of seismic reflection data is normally done by iterative forward model-ling. There are three problems with this approach. First, the choice of initial model and the number of parameters required to specify it are usually uncon-strained. Secondly, because of the lack of constraints, it becomes extremely difficult to find the optimum model. The optimum model is usually found by minimizing the error between the wavefield calculated from the model and the measured wavefield. The minimum reached is usually a local, rather than a global, minimum. Thirdly, the data are used only to calculate the error.
In our view, the choice of initial model should be inherently constrained by the data. We have developed a scheme that works in either the time domain or the frequency domain, for determining the acoustic parameters of the layered earth by directly inverting the CMP data, assuming that a CMP gather is equivalent to a shot gather over a horizontally-layered acoustic earth. The scheme is recursive, and is essentially the inverse of the forward reflectivity method. The recovered earth model is constructed from the top layer downwards, by stripping off the layers one by one. All interbed peg-leg multiples are included in the scheme. The result is an equivalent plane layered earth model for each CMP gather.
To apply the scheme in practice it is crucial to have accurate measurements of the source wavefield. If the source is not a point, the wavefield must be collapsed to that of a point source before transform of the data to plane wave components in the τ-p domain. The source wavelet and the influence of the free surface must be removed before applying the layer-stripping algorithm. The algorithm is un-stable in the presence of noise. Stabilization is achieved by limiting the magnitude of the recovered reflection coefficients, and by limiting the number of peg-leg multiples that are removed with each layer.
We show that the scheme works on synthetic data but, in the presence of noise, the recovered impedance profile is in error at low frequencies. This low frequency information can be obtained from the travel-time information using normal velocity analysis and an empirical velocity-density relation. Since this trend information is essentially independent of the layer-stripping results, it is probably better to use the frequency domain method, in which the trend information does not influence the layer-stripping scheme.
We have also applied our scheme to tank data and to a shot record from a data set shot in the North Sea. In both cases, the inversion works well and is stable. Addition of the trend information to recover the impedance must be done with great care. The recovery of the reflection coefficient series is robust and inde-pendent of the trend information. Comparison of the inverted North Sea data with a well-log is quite good. Errors in the inversion are caused both by lack of precision in the specification of the acquisition parameters, especially of the source wavefield, and in the removal of the free surface, which is done by predictive deconvolution. There are also errors in the log.
Anton Ziolkowski, Jacob T. Fokkema, Klaas-jan Koster, Arjen Confurius, Ruud Van Boom
Backmatter
Metadaten
Titel
Tau-p: a plane wave approach to the analysis of seismic data
herausgegeben von
Paul L. Stoffa
Copyright-Jahr
1989
Verlag
Springer Netherlands
Electronic ISBN
978-94-009-0881-9
Print ISBN
978-94-010-6884-0
DOI
https://doi.org/10.1007/978-94-009-0881-9