Interview
The SIGMA consortium brings together research projects and petroleum
companies, in order to validate certain mathematical models for the
propagation of acoustic waves used to gain a better knowledge of the
structure of the subsoil.
INEDIT: What were the reasons behind the creation of the SIGMA consortium?
The first goal is to exploit reflection seismic data by using an inverse
problem approach. The consortium is developing an original method, which
we called the MBTT (Migration Based Travel Time) method. The MBTT method
is based on the minimization of the usual cost function (the norm of the
difference between the data and the results computed from the model) using
local gradient algorithms. However, the optimization variables are novel
(kinematic parameters, reflectivity in time). In this way, we can recover
the subsoil velocity model, which yields excellent images that are both
sharp and well positioned. Since evaluating the cost function requires the
numerical simulation of the whole seismic data acquisition campaign, i.e.,
several hundred wave equations, and since the approach necessitates
numerous evaluations of the cost function, it is extremely costly in terms
of computational time.
To fix ideas, using the MBTT method and using the simplest possible wave
propagation models (Born + Rais), we are now able to invert data containing
millions of measurements of the vibratory state of the subsoil. This size
corresponds to the vibrations generated by about a hundred firings, recorded
at approximately fifty points on the ground.
A second objective of the consortium is to devise numerical algorithms for
acoustic wave propagation that have the best simulation quality over
computational time ratio. These algorithms will then be integrated into the
MBTT inversion methodology.
INEDIT: What are the mathematics involved?
The first goal is to exploit reflection seismic data by using an inverse
problem approach. The consortium is developing an original method, which
we called the MBTT (Migration Based Travel Time) method. The MBTT method
is based on the minimization of the usual cost function (the norm of the
difference between the data and the results computed from the model) using
local gradient algorithms. However, the optimization variables are novel
(kinematic parameters, reflectivity in time). In this way, we can recover
the subsoil velocity model, which yields excellent images that are both
sharp and well positioned. Since evaluating the cost function requires the
numerical simulation of the whole seismic data acquisition campaign, i.e.,
several hundred wave equations, and since the approach necessitates
numerous evaluations of the cost function, it is extremely costly in terms
of computational time.
To fix ideas, using the MBTT method and using the simplest possible wave
propagation models (Born + Rais), we are now able to invert data containing
millions of measurements of the vibratory state of the subsoil. This size
corresponds to the vibrations generated by about a hundred firings, recorded
at approximately fifty points on the ground.
A second objective of the consortium is to devise numerical algorithms for
acoustic wave propagation that have the best simulation quality over
computational time ratio. These algorithms will then be integrated into the
MBTT inversion methodology.
INEDIT: How is the consortium organized?
The consortium is a club whose membership entails payment of an entrance fee of 150kF. There is an annual meeting during which the research results are presented to the members. This is a classical type of collaboration between universities and oil companies. Current members are Amoco, Elf and Shell. We are actively trying to attract new members. Organizations of the same kind are envisioned in other scientific areas, such as finance mathematics.
http://www-rocq.inria.fr/sigma
Contact: François Clément, project Estime, INRIA Rocquencourt
Tel.: +33 1 39 63 58 46 - f
francois.clement@inria.fr