M. Turhan Taner

Velocity spectra-digital computer derivation and applications of velocity functions

Multifold ground coverage by seismic techniques such as the common reflection point method provides a multiplicity of wave travel path information which allows direct determination of root‐mean‐square velocities associated with such paths. Hyperbolic searches for semblance among appropriately gathered arrays of traces form the basis upon which velocities are estimated. Measured semblances are presented as a velocity spectral display. Interpretation of this information can give velocities with meaningful accuracy for primary as well as multiple events. In addition, the velocity data can help correctly label events. This paper outlines the fundamental principles for calculating velocity spectra displays. Examples are included which demonstrate the depth and detail of geological information which may be obtained from the interpretation of such displays.

Semblance and other coherency measures for multichannel data

The concept of semblance is introduced, along with a descriptive review of several of the more common likeness or coherence measures. Measures are considered from three points of view: the domain in which they are applied, the philosophy of their design, and the manner in which they are used.Crosscorrelation, the most familiar of the likeness criteria, is examined in detail. Differences of design philosophy are noted as expressing themselves by a change in the normalization. Semblance is shown to be related to an energy-normalized crosscorrelation and to share certain features of the summation method or stack which has been used recently as a coherence measure.Several coherence measures, including semblance, are considered in a problem environment--the determination of stacking velocities from multiple ground coverage seismic data. A noise-free synthetic example is studied in order to compare discrimination thresholds of the various methods. Semblance, when properly interpreted, proves to have the greatest power of discrimination among the candidates examined for the particular application.

Poststack velocity analysis by separation and imaging of seismic diffractions

Small geologic features manifest themselves in seismic data in the form of diffracted waves, which are fundamentally different from seismic reflections. Using two field-data examples and one synthetic example, we demonstrate the possibility of separating seismic diffractions in the data and imaging them with optimally chosen migration velocities. Our criteria for separating reflection and diffraction events are the smoothness and continuity of local event slopes that correspond to reflection events. For optimal focusing, we develop the local varimax measure. The objectives of this work are velocity analysis implemented in the poststack domain and high-resolution imaging of small-scale heterogeneities. Our examples demonstrate the effectiveness of the proposed method for high-resolution imaging of such geologic features as faults, channels, and salt boundaries.

ESTIMATION AND CORRECTION OF NEAR‐SURFACE TIME ANOMALIES

The problem of computing static corrections for CDP seismic reflection data is discussed. A new approach is presented and it is related to various existing approaches. The approach consists of using crosscorrelation computations to find time shifts which appear to align the traces of each common‐depth‐point. These shifts are expressed in terms of surface corrections, one for each source and receiver position; a residual NMO correction for each common‐depth‐point; and a fixed correction for each common‐depth‐point. These simultaneous equations form an overdetermined set which can be solved for the unknown static and NMO corrections. The least‐square‐error solution to these equations has an important indeterminancy which is discussed. Methods for its resolution are proposed. Application of the technique to real data is illustrated by several examples. Validity of the corrections is demonstrated by velocity analyses before and after correction of the traces.

Surface consistent corrections

Amplitudes of seismic reflections have been of interest since the first days of exploration seismology. Any change of amplitude or anomalous behavior may be significant, so it is important that the zones of interest be free from outside disturbances, such as those caused by the near‐surface layers. Surface consistent factors may be divided into source, receiver, offset, and subsurface components, and these may be divided further into amplitude and phase (or time shift) factors. Correction of trace amplitudes using multiplication by a scale factor is similar to correction of phase distortions by a static shift, and both corrections enhance seismic data. Displays of surface consistent components for time and amplitude corrections provide an additional diagnostic for the geophysicist.

A unified method for 2-D and 3-D refraction statics

Most of the seismic data processing procedures are divided into 2-D, 2.5-D, crooked lines or 3-D versions dictated by the differences in the shot and receiver configurations. In this paper, we introduce a tomographic approach that overcomes these geometrical difficulties and provides stable statics solutions from picked first-break times. We also show that the first-break picks contain both the short and the long wavelength surface statics. The solutions are obtained by solving a set of generalized surface-consistent delay-time equations using the method of weighted least squares and conjugate gradient. While iterating, each first-break pick is evaluated to ensure its consistency with the least-squares solution. Based on consistency, we weight the traveltime picks and use them in the next iteration. These weights also serve as an indicator of anomalous picks to the user. We show that long wavelength solutions leave large residual errors in the least-squares solutions. We also use the expected length of the Fresnel zone to differentiate between short and long wavelength static solutions. After removing the influence of long wavelength statics, we apply short wavelength statics to reduce the residual errors further. We demonstrate the validity of our unified method by applying it to actual data examples. The removal of both long and short wavelength statics improves the initial data set that produces a more consistent set of velocities and leaves only the short wavelength residual reflection statics, which are generally less than quarter wavelet period delays. This removes the most probable cause of the leg jump contamination and poor velocity estimates from the residual statics computations, especially from the 3-D data.

Separation and imaging of seismic diffractions using plane-wave decomposition

Summary We use the simulated plane wave section method to separate specular reflections and diffraction events. We show that plane wave sections naturally separate specular and diffracted events and allow us to use plane-wave distruction filters to suppress specular events resulting in plane-wave sections of diffractions. A synthetic example demonstrates the effectiveness of our method in imaging faults and small-scale discontinuities.

Limitations of the reflection seismic method; lessons from computer simulations

Piece‐wise local linearity of the subsurface reflectors and uniqueness of primary reflection travel path between particular source‐receiver pairs are two of the fundamental assumptions of multiple ground coverage reflection seismic techniques as currently employed. Some recent developments in seismic exploration which spring from the progress made in velocity determination techniques violate these fundamental assumptions with potentially serious consequences such as spurious geometries after migration and unrealistic interval velocities. In this paper we apply analytic techniques and computer simulation to linear and nonlinear subsurface models in order to obtain better definitions of the limitations of the reflection seismic method. The resulting lessons are of immediate practical value in seismic interpretation and clarify a variety of commonly occurring but puzzling situations such as phantom faults, incomplete contacts and segmented reflectors at unconformities, and apparent reversal of dip. In its ba...

Multi‐dimensional seismic imaging

Seismic traces synthesizing the response of subsurface formations to a cylindrical or plane wave are obtained for a succession of shotpoint locations along a seismic line of profile. The traces obtained are then wavefront steered and the steered traces and original trace for each shotpoint are summed. Groups of these traces for a line of profile are assembled to form a steered section. A number of these sections are then individually imaged or migrated, and the migrated sections are summed to form a migrated two-dimensional stack of data from cylindrical or plane wave exploration. Reflectors may then be located by finding common tangents. The traces for those shotpoints of the several lines which lie in planes perpendicular to the lines are then assembled and processed in the foregoing manner to obtain three dimension migrated seismic data.

The use of the conjugate-gradient algorithm in the computation of predictive deconvolution operators

A number of excellent papers have been published since the introduction of deconvolution by Robinson in the middle 1950s. The application of the Wiener‐Levinson algorithm makes deconvolution a practical and vital part of today’s digital seismic data processing. We review the original formulation of deconvolution, develop the solution from another perspective, and demonstrate a general and rigorous solution that could be implemented. By “general” we mean a deterministic time‐varying and multichannel operator design, and by “rigorous” we mean the straightforward least‐squares error solution without simplifying to a Toeplitz matrix. Also we show that the conjugate‐gradient algorithm used in conjunction with the least‐squares problem leads to a satisfactory simplification; that in the computation of the operators, the square matrix involved in the normal equations need not be computed. Furthermore, the product of this matrix with a column matrix can be obtained directly from the data as a result of two cascad...