A rapid estimate of the position of geological surfaces from first arrival waves using the ellipsoid method.

in: Proc. 34th Gocad Meeting, Nancy

Abstract

The (inverse) problem of determining geological structures from seismic data is usually solved in a deterministic way, starting from a (hopefully not so bad) initial model and minimizing a cost function to end up with a better model. Because seismic waves have a limited frequency band, the resolution we can reach from such a kind of inversion is limited too, and the obtained models are necessarily smooth. In this paper, we envisage a probabilistic approach which uses seismic data to constrain the location of geological surfaces which may correspond to sharp contrasts of the seismic velocity field. The rough procedure consists of three steps: 1) generate a set of models from data which contain information on the position of geological surfaces (e.g from well data), 2) compute synthetic seismic data for each model and 3) compare the synthetics with real data. The expected result of this approach is an estimation of the uncertainty on the position of the discontinuities. Because the accurate simulation of seismic data for each model is computationally expensive, all the possible rapid tests allowing to remove some models from the initial data set are welcome. In this article, we focus on one possible test which involves travel time information from the first reflected waves. Using the ellipsoid method, weighted Hausdorf distances and random distributions of the seismic velocities, we show how travel time information allow to recover the position of the first reflector and, consequently, yield a rapid ranking of the models within the initial set.

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BibTeX Reference

@INPROCEEDINGS{KutsenkoGM2014,
    author = { Kutsenko, Anton and Cupillard, Paul and Caumon, Guillaume },
     title = { A rapid estimate of the position of geological surfaces from first arrival waves using the ellipsoid method. },
 booktitle = { Proc. 34th Gocad Meeting, Nancy },
      year = { 2014 },
  abstract = { The (inverse) problem of determining geological structures from seismic data is usually solved in a deterministic way, starting from a (hopefully not so bad) initial model and minimizing a cost function to end up with a better model. Because seismic waves have a limited frequency band, the resolution we can reach from such a kind of inversion is limited too, and the obtained models are necessarily smooth. In this paper, we envisage a probabilistic approach which uses seismic data to constrain the location of geological surfaces which may correspond to sharp contrasts of the seismic velocity field. The rough procedure consists of three steps: 1) generate a set of models from data which contain information on the position of geological surfaces (e.g from well data), 2) compute synthetic seismic data for each model and 3) compare the synthetics with real data. The expected result of this approach is an estimation of the uncertainty on the position of the discontinuities.
Because the accurate simulation of seismic data for each model is computationally expensive, all the possible rapid tests allowing to remove some models from the initial data set are welcome. In this article, we focus on one possible test which involves travel time information from the first reflected waves. Using the ellipsoid method, weighted Hausdorf distances and random distributions of the seismic velocities, we show how travel time information allow to recover the position of the first reflector and, consequently, yield a rapid ranking of the models within the initial set. }
}