Three‐dimensional true‐amplitude zero‐offset migration

Abstract

The primary zero-offset reflection of a point source from a smooth reflector within a laterally inhomogeneous velocity earth model is (within the framework of ray theory) defined by parameters pertaining to the normal-incidence ray. The geometrical-spreading factor-usually computed along the ray by dynamic-ray tracing in a forward-modeling approach-can, in this case, be recovered from traveltime measurements at the surface. As a consequence, zero-offset reflections can be time migrated such that the geometrical-spreading factor for the normal-incidence ray is removed. This leads to a so-called "true-amplitude time migration." In this work, true-amplitude time-migrated reflections are obtained by nothing more than a simple diffraction stack essentially followed by a time derivative of the diffraction-stack traces. For small transmission losses of primary zero-offset reflections through intermediate-layer boundaries, the true-amplitude time-migrated reflection provides a direct measure of the reflection coefficient at the reflecting lower end of the normal-incidence ray. The time-migrated field can be easily transformed into a depth-migrated field with the help of image rays.

Geometrical spreading corrections of offset reflections in a laterally inhomogeneous earth

“…This will be described in a follow-up paper (Schleicher et al, 1992, currently under review), which can be looked upon as an extension to the offset data of the previous publication (Hubral et al, 1991) on 3-D true-amplitude zero-offset migration. In this context, we want to remark that trueamplitude migration methods are also the subject of investigations lately by Newman (1985Newman ( , 1989aNewman ( , 1989bNewman ( , 1990, Goldin (1989), and Kiehn (1990).…”

Numerical tests of 3D true‐amplitude zero‐offset migration1

“…rcl = 0. If only the vertical component of the displacement vector of the reflected wave at SG is considered in a zero-offset survey, the weight factor (4) is divided by cos a (Hubral et al 1991). Finally, variation in the factor l/vs can be neglected when the first layer is homogeneous, as in marine data.…”

“…The theory proposed by Hubral, Tygel and Zien (1991) has been implemented here along the lines indicated by these authors. However only a time migration of 3D synthetic zero-offset reflections is discussed below.…”

High Resolution/High Fidelity Seismic Imaging and Parameter Estimation for Geological Structure and Material Characterization

“…Therefore the imaging and image amplitude correction have to be done in the angle-domain, which makes ray-based methods more convenient than wave-equation based methods since the angle information is inherently embedded in ray-based methods. The theory and method of true-reflection imaging has been developed based on high-frequency asymptotic theory (ray theory) and is traditionally carried out through Kirchhoff prestack depth migration (e.g., Bleistein et al, 1987;Hubral et al, 1991;Hanitzsch, 1995;Xu et al, 2001;Audebert et al, 2002;Brandsberg-Dahl et al, 2003). However, the results may contain large errors in complex areas due to the high-frequency approximation and singularity problems therein.…”