Method of obtaining a model representative of a heterogeneous medium, and particularly the sub-soil

Claim 1

A method of obtaining an optimum model having at least two dimensions representing the variations of a physical parameter of a subterranean zone causing reflections by seismic waves transmitted into the earth, the model including a vertical dimension and a transverse dimension and closely agreeing with recordings of seismic data obtained by a set of sensors, disposed outside the subterranean zone and along the transverse direction, in response to seismic waves reflected from the zone due to the transmitted seismic waves, with values of the physical parameter chosen at different points of various depths in the zone as a result of measurements or evaluations, and with stratigraphic information, actual values of the physical parameter in the reference model, and the recorded seismic data having uncertainties therein, said method comprising the steps of: (a) constructing a reference model having values of the physical parameter adapted to the chosen values, and forming synthetic recordings representing the response of the reference model to the transmitted seismic waves; (b) optimizing the reference model by an iterative process including forming intermediate synthetic recordings to reach the optimum model, the optimizing including minimizing for the entire subterranean zone the differences between the values of the recorded seismic data and the intermediate synthetic recordings, while simultaneously minimizing the differences between the chosen values of the physical parameter and the values of the same physical parameter at any point of the reference model, the minimizing including applying to the differences operators selected for closely modelling variations in uncertainties, respectively, in the recorded seismic data and in the reference model, as well as for imposing on the optimum model a correlation between the values of the physical parameter at different points along directions different from the vertical.

Claim 2

A method of obtaining an optimum model having at least two dimensions representing the variations of a physical parameter of a subterranean zone causing reflections by seismic waves transmitted into the earth, the model including a vertical dimension and a transverse dimension and closely agreeing with recordings of seismic data obtained by a set of sensors, disposed outside the subterranean zone and along the transverse direction, in response to seismic waves reflected from the zone due to the transmitted seismic waves, with values of the physical parameter chosen at different points of various depths in the zone as a result of measurements or evaluations, and with stratigraphic information, actual values of the physical parameter in the reference model, and the recorded seismic data having uncertainties therein, said method comprising the steps of: (a) constructing a reference model having values of the physical parameter adapted to the chosen values, and forming synthetic recordings representing the response of the reference model to the transmitted seismic waves; (b) optimizing the reference model by an iterative process including forming intermediate synthetic recordings to reach the optimum model, the optimizing including minimizing for the entire subterranean zone the differences between the values of the recorded seismic data and the intermediate synthetic recordings, while simultaneously minimizing the differences between the chosen values of the physical parameter and the values of the same physical parameter at any point of the reference model, the minimizing including applying to the differences operators selected for closely modelling variations in uncertainties, respectively, in the recorded seismic data and in the reference model, as well as for imposing on the optimum model a correlation between the values of the physical parameter at different points along directions different from the vertical.