C.P.A. Wapenaar

Adaptive surface‐related multiple elimination

The major amount of multiple energy in seismic data is related to the large reflectivity of the surface. A method is proposed for the elimination of all surface‐related multiples by means of a process that removes the influence of the surface reflectivity from the data. An important property of the proposed multiple elimination process is that no knowledge of the subsurface is required. On the other hand, the source signature and the surface reflectivity do need to be provided. As a consequence, the proposed process has been implemented adaptively, meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple‐free data equals the inversion residue. Results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion.

Angle‐dependent reflectivity by means of prestack migration

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 im...

Three-dimensional imaging of multicomponent ground-penetrating radar data

Scalar imaging algorithms originally developed for the processing of remote sensing measurements (e.g., the synthetic‐aperture radar method) or seismic reflection data (e.g., the Gazdag phase‐shift method) are commonly used for the processing of ground‐penetrating radar (GPR) data. Unfortunately, these algorithms do not account for the radiation characteristics of GPR source and receiver antennas or the vectorial nature of radar waves. We present a new multicomponent imaging algorithm designed specifically for vector electromagnetic‐wave propagation. It accounts for all propagation effects, including the vectorial characteristics of the source and receiver antennas and the polarization of the electromagnetic wavefield. A constant‐offset source‐receiver antenna pair is assumed to overlie a dielectric medium. To assess the performance of the scalar and multicomponent imaging algorithms, we compute their spatial resolution function, which is defined as the image of a point scatterer at a fixed depth using a ...

Amplitude preprocessing of single and multicomponent seismic data

Whenever the data acquisition is restricted to line surveys rather than areal surveys, seismic processing is necessarily in two dimensions. In this paper it is argued that two‐dimensional (2-D) processing is preferably applied after transforming the point source responses into line source responses. The effect of this transformation is a correction of the amplitudes in the data. For single‐component acoustic data as well as for multicomponent elastic data a line source response is nothing but a superposition of point source responses. Hence, in principle a line source response can be synthesized by integrating point source responses along the desired line source axis. In practice, however, this integration cannot be carried out due to the incompleteness of the data. It is shown that the integration along the source axis can be replaced by an integration along the receiver axis. The underlying assumption is that the wavefields exhibit a certain type of cylindrical symmetry. For horizontally layered acousti...

Adaptive decomposition of multicomponent ocean‐bottom seismic data into downgoing and upgoing P‐ and S‐waves

With wavefield decomposition, the recorded wavefield at a certain depth level can be separated into upgoing and downgoing wavefields as well as into P‐ and S‐waves. The medium parameters at the considered depth level (e.g., just below the ocean‐bottom) need to be known in order to be able to do a decomposition. In general, these parameters are unknown and, in addition, measurement‐related issues, such as geophone coupling and crosstalk between the different components, need to be dealt with. In order to apply decomposition to field data, an adaptive five‐stage decomposition scheme was developed in which these issues are addressed.In this study, the adaptive decomposition scheme is tested on a data example with a relatively shallow water depth (∼120 m), consisting recordings from of a full line of ocean‐bottom receivers. Although some of the individual stages in the decomposition scheme are more difficult to apply because of stronger interference between events compared to data acquired over deeper water, ...

Optimum seismic illumination of hydrocarbon reservoirs

A method is proposed for the design and application of a wave theory‐based synthesis operator, which combines shot records (2-D or 3-D) for the illumination of a specific part of the subsurface (target, reservoir) with a predefined source wavefield. After application of the synthesis operator to the surface data, the procedure is completed by downward extrapolation of the receivers. The output simulates a seismic experiment at the target, carried out with an optimum source wavefield. These data can be further processed by migration and/or inversion. The main advantage of the proposed method is that control of the source wavefield is put at the target, in contrast with the conventional wave stack procedures, where control of the source wavefield is put at the surface. Moreover, the proposed method allows true amplitude, three‐dimensional (3-D), prestack migration that can be economically handled on the current generation of supercomputers.

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

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 re...

Data-driven Green's function retrieval and application to imaging with multidimensional deconvolution

An iterative method is presented that allows one to retrieve the Greens function originating from a virtual source located inside a medium using reflection data measured only at the acquisition surface. In addition to the reflection response, an estimate of the travel times corresponding to the direct arrivals is required. However, no detailed information about the heterogeneities in the medium is needed. The iterative scheme generalizes the Marchenko equation for inverse scattering to the seismic reflection problem. To give insight in the mechanism of the iterative method, its steps for a simple layered medium are analyzed using physical arguments based on the stationary phase method. The retrieved Greens wavefield is shown to correctly contain the multiples due to the inhomogeneities present in the medium. Additionally, a variant of the iterative scheme enables decomposition of the retrieved wavefield into its downgoing and upgoing components. These wavefields then enable creation of a ghost-free image of the medium with either cross correlation or multidimensional deconvolution, presenting an advantage over standard prestack migration.

Representation of seismic sources in the one‐way wave equations

One‐way extrapolation of downgoing and upgoing acoustic waves plays an essential role in the current practice of seismic migration (Berkhout, 1985; Stolt and Benson, 1986; Claerbout, 1985; Gardner, 1985). Generally, one‐way wave equations are derived for the source‐free situation. Sources are then represented as boundary conditions for the one‐way extrapolation problem. This approach is valid provided the source representation is done with utmost care. For instance, it is not correct to represent a monopole source by a spatial delta function and to use this as input data for a standard one‐way extrapolation scheme. This yields an erroneous directivity pattern as illustrated below.

Improved Three-Dimensional Image Reconstruction Technique for Multi-Component Ground Penetrating Radar Data

For electromagnetic imaging the vectorial character of the emitted field and the radiation characteristics of both source and receiver play an important role. Recently, a new imaging algorithm was presented dedicated to the electromagnetic case. The radiation characteristics of GPR source and receiver antennas and the vectorial nature of the electromagnetic waves are taken into account for a monostatic fixed offset GPR survey. This resulted in a representative image of a point scatterer. Comparison with scalar imaging algorithms shows that for a homogeneous space the SAR image has an opposite sign compared to the multi-component image, whereas the Gazdag image has a phase shift of about 90° with respect to the multi-component image. In this paper, modified scalar imaging algorithms are introduced that minimize these differences. However, between the images obtained in a homogeneous half-space phase differences of 10–20° are still present. These differences indicate the possible error in nature of the physical property contrast when it is determined with the modified scalar imaging algorithms. The multi-component imaging algorithm returns a representative image because it uses the appropriate Greens functions to eliminate the propagation effects. For practical imaging strategies, only far-field radiation characteristics can be used to compensate for the propagation effects due to the large computing time needed to evaluate the total-field expressions. Synthetic analysis of the imaging of a point scatterer calculated using total-field expressions shows that using the far-field expressions in the multi-component imaging algorithm the images better approximate the actual contrast than using the modified scalar imaging algorithms. Experimental results are presented from imaging several buried objects with different medium properties and different orientations. The phase differences in the experimental data are similar to those obtained synthetically. This likeness indicates that using the multi-component imaging algorithm, a more reliable image is obtained than with the modified scalar imaging algorithms.