Alexander Goertz

Aperture effects in 2.5D Kirchhoff migration: A geometrical explanation

Seismic images obtained by Kirchhoff time or depth migration are always accompanied by some artifacts known as migration noise, migration boundary effects, or diffraction smiles, which may severely affect the quality of the migration result. Most of these undesirable effects are caused by a limited aperture if the algorithms make no special disposition to avoid them. Strong amplitude variation along reflection events may cause similar artifacts. All of these effects can be explained mathematically by means of the method of stationary phase. However, such a purely theoretical explication is not always easily understood by applied geophysicists. A geometrical interpretation of the terms of the stationary-phase approximation in relation to the diffraction and reflection traveltime curves in the time domain can help to develop a more intuitive understanding of the migration artifacts. A simple numerical experiment for poststack (zero-offset) data indicates the problem and helps to demonstrate the effects and the methods to avoid them.

Optimized 3D VSP Survey Geometry Based On Fresnel Zone Estimates

Summary We present a method to optimize the acquisition geometry of 3D VSP data, that is, seismic data recording surface sources in large-aperture borehole receiver arrays. By estimating the Fresnel volume of specular rays at the target depth of interest, we are able to adapt the shooting geometry to the varying size of the Fresnel zone with offset from the well. Such an adaptive pattern of varying shot spacing helps to reduce illumination artifacts close to the receiver well and, at the same time, reduces the overall number of shotpoints, and thus, effort required to obtain the same image volume. We show a real data example where our approach has successfully been applied to optimize the shotpoint geometry.

Imaging walkaway VSP data using the common-reflection-surface stack

Images from walkaway VSP data are traditionally obtained by using either a VSP-CDP transform or a VSP Kirchhoff migration, which both heavily rely on the knowledge of a velocity model. The need for a velocity model is eliminated by using model-independent imaging methods, such as the common-reflection-surface (CRS) stack. The CRS stack is a data-driven time-domain stacking method that leads to images with a higher signal-to-noise ratio. Moreover, kinematic wavefield attributes (CRS attributes) determined in the process can be used for a variety of applications.

On the Aperture Effects In 2.5-D Kirchhoff Migration

Seismic images obtained by Kirchhoff time or depth migration are always accompanied by some artifacts known as “migration noise”, “migration boundary effects”, or “diffraction smiles”, which may severely affect the quality of the migration result. Most of these undesirable effects are caused by a limited aperture if the algorithms make no special disposition to avoid them. Likewise, strong amplitude variation along reflection events may also cause similar artifacts. All these effects can be explained mathematically by means of the Method of Stationary Phase. However, such a purely theoretical explication is not always easy to understand for applied geophysicists. By relating the terms of the stationary-phase approximation to simple geometrical situations, a more physical interpretation of the migration artifacts can be obtained. A simple numerical experiment for poststack (zero-offset) data indicates the problem and helps to develop an intuitive understanding of the effects and the methods to avoid them.

Cascaded Seismic Migration And Demigration

Summary We present a tool capable of performing 4D seismic monitoring investigations based on the so-called Unified Approach (Hubral et al. (1996),Tygel et al. (1996)). We show how inversion and forward modeling problems can be solved using the same algorithm: amplitude-preserving Kirchhoff-type depth migration enables to investigate reservoir properties, whereas the approach can also be used for forward modeling purposes (Santos et al., 1998). With this method, selected parts of the wavefield and/or selected target zones can be modeled in a fast, efficient and amplitude-preserving way which proves to be especially advantageous for poststack scenarios. Thus, time-dependent variations of subsurface properties can be investigated. The sensitivity to inconsistencies in selected target zones well below the surface (as is the case in e.g. subsalt imaging) can be tested by a repeated modeling and inversion procedure. In this paper, we present a practical implementation of the theory which enables us to perform prestack- and poststack migration and demigration within the same algorithm for arbitrary sourceand receiver configurations. We address practical problems occuring when implementing the method such as reducing necessary data volumes to a feasible minimum. The assemblage of summation operators requires the knowledge of an a-priori macro-velocity model. In order to reduce storage of wavefield attributes from this macro-velocity model, we present criteria, how sparse these informations can be sampled in the Green’s Function Table without losing resolution.