1-D layered media: Part 2, Layer‐based waveform inversion

Author:

Jurado Fabrice1,Cuer Michel2,Richard Vincent1

Affiliation:

1. Institut Français du Pétrole, B.P. 311, 92506 Rueil‐Malmaison, France

2. Université de Montpellier II, Laboratoire de Physique Mathématique, Place Eugène Bataillon, 34095 Montpellier, France

Abstract

We are interested here in the inversion of multioffset data to determine 1-D medium properties. The forward modeling technique accounts for 3-D wave propagation effects. The inversion is performed by minimizing the difference between modeled and reference data using a least‐squares technique. The gradient is computed by the adjoint state technique adapted to the first‐order hyperbolic system and to the Hankel transform. To reduce the number of optimization parameters and to optimize along reflected events from some selected interfaces, we propose a layer‐oriented reparameterization in the full‐waveform inversion. Then we discuss the effect on the inversion results of an incorrect number of layers. The local minima of the least‐squares functional are experimentally investigated and physically interpreted. This sensitivity study has shown that it is necessary to have an accurate initial model for the position of the layer interfaces. In principle, seismic data give access directly to this information. This is why we have formulated the inverse problem in one‐way vertical traveltime as opposed to depth. Using an example, we show that with this parameterization the variation of the least‐ squares misfit function when we change the interval velocity for a given layer tends to a quasi quadratic form. In practice, a layer‐based waveform inversion (LBWI) procedure is proposed to overcome the inherent problem of local minima. The procedure attempts to determine interval velocities, impedance contrasts, and interface positions for a limited number of layers to explain the major seismic events. The LBWI procedure is based on four key elements: traveltime formulation, layer‐based reparameterization, progressive enrichment of the model, and interpretative approach. This procedure is evaluated for a large‐scale acoustic synthetic example.

Publisher

Society of Exploration Geophysicists

Subject

Geochemistry and Petrology,Geophysics

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