Geophysical Prospecting - Volume 40, Issue 4, 1992

Seismic reflection data in the southern Gulf of Suez, offshore Egypt, are commonly severely affected by shallow velocity inhomogeneities in the form of diapiric salt bodies, and depth migration techniques must be used in order to image the presalt structure correctly. Frequently the diapir and the underlying prospective structure are three dimensional rather than two dimensional and thus require 3D techniques to resolve them. In addition, the severity of the problem is sometimes such that the common midpoint (CMP) stack assumptions are invalid and prestack depth migration is therefore required.

In 1990, Unocal developed a practical 3D prestack depth‐migration scheme, which was applied to a data set in the Gulf of Suez. The prospect was subsequently drilled and results proved the effectiveness of the technique.

This paper describes the use of the technique in the form of a case history. It is expected that the technique will be routinely used to solve similar problems.

Methods for predicting and attenuating water‐bottom multiples by wavefield extrapolation have been discussed by several investigators. Because these prediction methods operate on shot records, boundary conditions must be specified for every shot record.

The approach presented operates in the common‐offset plane; a model of expected water‐bottom multiples is generated from the observed surface wavefield using a finite‐difference wave‐equation migration algorithm with an offset term. An accurate water‐depth profile is required, but there is no restriction on the shape of the water bottom other than a dip limit of approximately 18–20°. In generating a multiple model, the water‐bottom primary and each water‐bottom multiple reflection of the observed surface wavefield are extrapolated to a higher order. Thus, the extrapolated water‐bottom primary of the model is lined up with a water‐bottom multiple in the data and each multiple in the model is lined up with a higher‐order (or later) multiple in the data.

Prestack multiple attenuation is achieved, for one offset at a time, by first adapting the model of expected multiples to the observed data and then subtracting the predicted multiple energy. An error‐constrained adaptation algorithm is proposed in order to control instabilities. No assumptions are made about primary reflections and no subwater‐bottom velocities are required.

Computational efficiency of modelling and adaptation can be improved by applying this method only to near and intermediate offsets as the stacking process usually provides sufficient multiple attenuation at far offsets. A field data example demonstrates the potential of the proposed method for improving the primary‐to‐multiple ratio in prestack and post‐stack data.

Gravity data inversion can provide valuable information on the structure of the underlying distribution of mass.

The solution of the inversion of gravity data is an ill‐posed problem, and many methods have been proposed for solving it using various systematic techniques.

The method proposed here is a new approach based on the collocation principle, derived from the Wiener filtering and prediction theory.

The natural multiplicity of the solution of the inverse gravimetric problem can be overcome only by assuming a substantially simplified model, in this case a two‐layer model, i.e. with one separation surface and one density contrast only. The presence of gravity disturbance and/or outliers in the upper layer is also taken into account.

The basic idea of the method is to propagate the covariance structure of the depth function of the separation surface to the covariance structure of the gravity field measured on a reference plane.

This can be done since the gravity field produced by the layers is a functional (linearized) of the depth.

Furthermore, in this approach, it is possible to obtain the variance of the estimation error which indicates the precision of the computed solution.

The method has proved to be effective on simulated data, fulfilling the a priori hypotheses.

In real cases which display the required statistical homogeneity, good preliminary solutions, useful for a further quantitative interpretation, have also been derived.

A case study is discussed.

Some factors affecting the resolution and accuracy of resistivity tomography are examined using numerical simulation. The inversion method used is based on smoothness‐constrained least‐squares and finite‐element methods. An appropriate block discretization is obtained by dividing the target region into square blocks of size equal to half the minimum electrode spacing. While the effect of the damping factor on the resolution is significant, the resolution is not very sensitive to Gaussian noise as long as the damping factor is properly chosen, according to the noise level. The issue of choosing an optimum electrode array should be considered at the planning stage of a survey.

When the instrumental accuracy is high, the dipole‐dipole array is more suitable for resolving complex structures than the pole‐pole array. The pole‐dipole array gives somewhat less resolution than the dipole‐dipole array but yields greater signal strength; thus, the pole‐dipole array may be a good compromise between resolution and signal strength. The effect of an inhomogeneity located outside the target region may be very small if block discretization is done so as to represent the resistivity variations in both the target and outside regions.

Elastic redatuming can be carried out before or after decomposition of the multicomponent data into independent PP, PS, SP, and SS responses. We argue that from a practical point of view, elastic redatuming is preferably applied after decomposition. We review forward and inverse extrapolation of decomposed P‐ and S‐wavefields. We use the forward extrapolation operators to derive a model of discrete multicomponent seismic data. This forward model is fully described in terms of matrix manipulations.

By applying these matrix manipulations in reverse order we arrive at an elastic processing scheme for multicomponent data in which elastic redatuming plays an essential role. Finally, we illustrate elastic redatuming with a controlled 2D example, consisting of simulated multicomponent seismic data.