Automatic velocity analysis by differential semblance optimization

Abstract

We present a method for automatic velocity analysis of seismic data based on differential semblance optimization (DSO). The data are mapped for each offset from the time domain to the depth domain by a Born migration scheme using ray tracing with the efficient wavefront construction method. The DSO cost functional is evaluated by taking differences of the migration images for neighboring offsets. The gradient of this functional with respect to the underlying velocity model is obtained by a first‐order approximation of the adjoint‐state method, leading to an optimal complexity: the cost of evaluating the gradient is about the same as that of evaluating the functional. The method has been applied to a marine line. Multiples turned out to be a problem, but were handled effectively by incorporating a multiple filter inside the DSO cost functional.

Coherence measures in automatic time migration velocity analysis

“…To solve this optimization problem, the adjoint-state method (Mulder and ten Kroode, 2002;Plessix, 2006) is very convenient to analytically calculate the gradient of the objective function. We start from the general migration-velocityanalysis functional for 2D or 3D time or depth migration as proposed by Mulder and ten Kroode (2002),…”

7. Migration Velocity Analysis

“…In contrast, the DSO method (Symes and Carazzone, 1991) defines an objective function that differs slightly from the one optimized by conventional MVA methods (see the earlier section titled "Objective function of tomographic migration velocity analysis" for a brief discussion of the DSO objective function). Mulder and ten Kroode (2002) showed that coherent noise (e.g., multiple reflections) can cause the presence of local minima in the DSO functional, but global convergence can be achieved if the effect of the multiple reflections is removed from the migrated CIGs. Chauris and Noble (1998) demonstrated that the DSO functional is convex in fairly simple cases.…”

Rigorous redatuming

“…For the model perturbation, an approach was taken that resembles the handling of real data. An initial, smooth velocity model was determined from the data by differential semblance optimization (Mulder & ten Kroode 2002). This model was used as a starting guess for an acoustic full‐waveform inversion.…”