##### Depth imaging of offset vertical seismic profile data

Authors:
Lasse Amundsen, Børge Arntsen and Rune Mittet

Journal name: Geophysical Prospecting

Issue: Vol 41, No 8, November 1993 pp. 1009 - 1031

DOI: 10.1111/j.1365-2478.1993.tb00896.x

Organisations:
Wiley

Language: English

Info: Article, PDF ( 1.2Mb )

Summary:

Depth migration consists of two different steps: wavefield extrapolation and imaging. The wave propagation is firmly founded on a mathematical frame-work, and is simulated by solving different types of wave equations, dependent on the physical model under investigation. In contrast, the imaging part of migration is usually based on *ad hoc*‘principles’, rather than on a physical model with an associated mathematical expression. The imaging is usually performed using the U/D concept of Claerbout (1971), which states that reflectors exist at points in the subsurface where the first arrival of the downgoing wave is time-coincident with the upgoing wave.

Inversion can, as with migration, be divided into the two steps of wavefield extrapolation and imaging. In contrast to the imaging principle in migration, imaging in inversion follows from the mathematical formulation of the problem. The image with respect to the bulk modulus (or velocity) perturbations is proportional to the correlation between the time derivatives of a forward-propagated field and a backward-propagated residual field (Lailly 1984; Tarantola 1984).

We assume a physical model in which the wave propagation is governed by the 2D acoustic wave equation. The wave equation is solved numerically using an efficient finite-difference scheme, making simulations in realistically sized models feasible. The two imaging concepts of migration and inversion are tested and compared in depth imaging from a synthetic offset vertical seismic profile section. In order to test the velocity sensitivity of the algorithms, two erroneous input velocity models are tested. We find that the algorithm founded on inverse theory is less sensitive to velocity errors than depth migration using the more *ad hoc* U/D imaging principle.

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