Automatic crosswell tomography by differential semblance optimization

Abstract

In this paper, a method for automatic tomography based on semblance and differential semblance is presented. The method determines the background velocity from the first arrivals. A semblance panel is built by back-propagating all the seismic data traces towards zero time. If the background velocity is close to the true one, all the first-arrivaltransmitted waves are lined up at zero time and the backpropagated traces are almost identical. The velocity model is then updated either by maximizing the norm of the stack of all the back-propagated traces (semblance optimization) or by minimizing the norm of the difference between two adjacent traces (differential semblance optimization).

On the gradient artifacts in migration velocity analysis based on differential semblance optimization

“…The basic idea is that when velocity is correct, the normed difference between neighboring traces along the "redundant" axis (e.g., offset or angle) in a prestack common image gather should be minimal. Several authors have since developed inversion algorithms based on the DSO concept (Shen et al, 2003, Chauris and Noble, 2001, Plessix, et al, 2000. DSO-MVA uses (one-way) wave equation migration as the engine to calculate gathers and update the velocity model, with the gradient of the objective function being calculated by the adjoint state method.…”

Seismic velocity analysis in the scattering‐angle/azimuth domain

“…With the above assumptions, we have paved the way for a velocity analysis scheme that is easily adapted to a variety of coherence‐based optimization techniques. The following techniques measure coherence in the common‐image gathers: differential semblance (DS) (Symes and Carazzone 1991; Plessix, ten Kroode and Mulder 2000), which is the preferred choice since it smoothly depends on the velocity and the data; semblance (Taner and Koehler 1969); stack‐power (SP) (Ursin 1977; Faye and Jeannot 1986). The DS measure assesses the similarity between neighbouring traces in the CIGs using differentiation of the scattering‐angle/azimuth coordinates.…”

“…The observed characteristics of DS and SP suggest the following strategy for the optimization: In the first stage, when the background model is very different from the true model, apply the DS measure. Then, when the DS measure falls below a prescribed threshold, change to the SP measure (see also Plessix et al 2000).…”