Adaptive ensemble-based method and device for highly-nonlinear problems

A computing device for generating an image of a subsurface of the earth to represent a physical reality thereof, the computing device comprising:

• an input/output circuitry configured to receive data acquired over the subsurface;
• and
• a processor connected to the interface and configured to,
• generate an ensemble of realizations based on the data,
• generating simulated data by running a forward model for members of the ensemble of realizations and computing an objective function for each of the members to estimate a mismatch with the corresponding simulated data;
• iteratively, until at least one convergence criterion is met:
• calculate a plurality of sensitivity matrices that are linearizations of a forward model for different subsets of samples,
• select a best sensitivity matrix for improving a mismatch between the data and the simulated data according to a given criterion from the plurality of sensitivity matrices,
• update the forward model (f), based on the best sensitivity matrix, and then regenerating simulated data by running the updated forward model for the members of the ensemble of realizations and recomputing the objective function for each of the members using the corresponding updated simulated data, and
• generate an image of the subsurface based on the data related to the subsurface of the earth and the updated forward model,
• wherein
• the image is useable to assess an oil and/or gas reservoir in the subsurface.

A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a computer, implement a method for generating an image of a subsurface of the earth to represent physical reality thereof, the method comprising:

• generating an ensemble of realizations based on data acquired over the subsurface;
• generating simulated data by running a forward model for members of the ensemble of realizations and computing an objective function for each of the members using the corresponding simulated data;
• iteratively, until at least one convergence criterion is met:
• calculating a plurality of sensitivity matrices that are linearizations of the forward model for different subsets of samples,
• selecting a best sensitivity matrix for improving a mismatch between the data and the simulated data according to a given criterion, from the plurality of sensitivity matrices, and
• updating the forward model, based on the best sensitivity matrix, regenerating simulated data by running the updated forward model for the members of the ensemble of realizations and recomputing the objective function for each of the members using the corresponding updated simulated data;
• and
• generating an image of the subsurface based on the data related to the subsurface of the earth and the updated forward model,
• wherein
• the image is useable to assess an oil and/or gas reservoir in the subsurface.