Wave field datuming for land prestack migration

Angle‐dependent reflectivity by means of prestack migration

Geophysics ◽

10.1190/1.1442938 ◽

1990 ◽

Vol 55 (9) ◽

pp. 1223-1234 ◽

Cited By ~ 168

Author(s):

C. G. M. de Bruin ◽

C. P. A. Wapenaar ◽

A. J. Berkhout

Keyword(s):

Reflection Coefficient ◽

Wave Field ◽

Grid Point ◽

Depth Level ◽

Wave Fields ◽

Prestack Migration ◽

Reflected Wave ◽

Zero Offset ◽

Source Wave ◽

Angle Dependent Reflectivity

Most present day seismic migration schemes determine only the zero‐offset reflection coefficient for each grid point (depth point) in the subsurface. In matrix notation, the zero‐offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source‐wave field into a reflected‐wave field. However, angle dependent reflectivity information is contained in the full reflectivity matrix. Our objective is to obtain angle‐dependent reflection coefficients from seismic data by means of prestack migration (multisource, multioffset). After downward extrapolation of source and reflected wave fields to one depth level, the rows of the reflectivity matrix (representing angle‐dependent reflectivity information for each grid point at that depth level) are recovered by deconvolving the reflected wave fields with the related source wave fields. This process is carried out in the space‐frequency domain. In order to preserve the angle‐dependent reflectivity in the imaging we must not only add all frequency contributions but we should extend the imaging principle by adding along lines of constant angle in the wavenumber‐frequency domain. This procedure is carried out for each grid point. The resulting amplitude information provides a rigorous approach to amplitude‐versus‐offset related methods. The new imaging technique has been tested on media with horizontal layers. However, with our shot‐record oriented algorithm it is possible to handle any subsurface geometry. The first tests show excellent results up to high angles, both in the acoustic and in the elastic case. With angle‐dependent reflectivity information it becomes feasible to derive detailed velocity and density information in a subsequent stratigraphic inversion step.

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Principle of prestack migration based on the full elastic two‐way wave equation

Geophysics ◽

10.1190/1.1442291 ◽

1987 ◽

Vol 52 (2) ◽

pp. 151-173 ◽

Cited By ~ 26

Author(s):

C. P. A. Wapenaar ◽

N. A. Kinneging ◽

A. J. Berkhout

Keyword(s):

Wave Equation ◽

Elastic Wave ◽

Wave Field ◽

Particle Velocity ◽

Synthetic Data ◽

Matrix Operator ◽

Shear Stresses ◽

Elastic Wave Equation ◽

Seismic Migration ◽

Prestack Migration

The acoustic approximation in seismic migration is not allowed when the effects of wave conversion cannot be neglected, as is often the case in data with large offsets. Hence, seismic migration should ideally be founded on the full elastic wave equation, which describes compressional as well as shear waves in solid media (such as rock layers, in which shear stresses may play an important role). In order to cope with conversions between those wave types, the full elastic wave equation should be expressed in terms of the particle velocity and the traction, because these field quantities are continuous across layer boundaries where the main interaction takes place. Therefore, the full elastic wave equation should be expressed as a matrix differential equation, in which a matrix operator acts on a full wave vector which contains both the particle velocity and the traction. The solution of this equation yields another matrix operator. This full elastic two‐way wave field extrapolation operator describes the relation between the total (two‐way) wave fields (in terms of the particle velocity and the traction) at two different depth levels. Therefore it can be used in prestack migration to perform recursive downward extrapolation of the surface data into the subsurface (at a “traction‐free” surface, the total wave field can be described in terms of the detected particle velocity and the source traction). Results from synthetic data for a simplified subsurface configuration show that a multiple‐free image of the subsurface can be obtained, from which the angle‐dependent P-P and P-SV reflection functions can be recovered independently. For more complicated subsurface configurations, full elastic migration is possible in principle, but it becomes computationally complex. Nevertheless, particularly for the 3-D case, our proposal has improved the feasibility of full elastic migration significantly compared with other proposed full elastic migration or inversion schemes, because our method is carried out per shot record and per frequency component.

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