Method for partial differential equation inversion of data
AssigneeKing Abdullah University of Science and Technology
InventorTariq Ali Alkhalifah
Life of this patent
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Abstract
A method for partial differential equation inversion, the method including receiving measured data do; selecting an objective function having first and second measures N1 and N2, wherein the objective function depends on three independent variables V, u, and f, V being a perturbation of a wave equation operator L from a background operator L0, u being a wavefield that satisfies the wave equation operator L, and f being a source function that describes the source of the waves; optimizing with a processor the objective function by finding a minimum or a maximum using the inversion; calculating with the processor solutions V*, u*, and f* of the three independent variables V, u, and f; and generating with the processor an image of an object based on the solutions V*, u*, and f*.
Claims20
A method for partial differential equation inversion, the method comprising:
- receiving measured data do, wherein the measured data is a result of waves being emitted by a source, propagating through a medium toward an object, and being scattered from the object;
- selecting an objective function having first and second measures N1 and N2, wherein the objective function depends on three independent variables V, u, and f, V being a perturbation of a wave equation operator L from a background operator L0, u being a wavefield that satisfies the wave equation operator L, and f being a source function that describes the source of the waves;
- optimizing with a processor the objective function by finding a minimum or a maximum using the partial differential equation inversion;
- calculating with the processor solutions V*, u*, and f* of the three independent variables V, u, and f that minimizes or maximizes the objective function;
- and
- generating with the processor an image of the object from which the waves are scattered, based on the solutions V*, u*, and f*, so that a location of the object in the image is determined.
A method for partial differential equation inversion, the method comprising:
- receiving measured data d0, wherein the measured data is a result of waves being emitted by a source, propagating through a medium toward an object, and being scattered from the object;
- defining a force function fe based on three variables V, u, and f, where V is a perturbation of a wave equation operator L from a background operator L0, u is a wavefield that satisfies the wave equation operator L, and f is a source function that describes the source of the waves;
- selecting a first objective function having first and second measures N1 and N2, the first objective function depending on the wavefield u and the force function fe;
- optimizing with a processor the first objective function by finding a minimum or a maximum using the partial differential equation inversion;
- calculating with the processor solutions u* and fe* of the two independent variables u and fe that minimizes or maximizes the first objective function;
- selecting a second objective function having the first and second measures N1 and N2, the second objective function depending on the perturbation V and the source function f;
- optimizing with the processor the second objective function by finding a minimum or a maximum using the partial differential equation inversion;
- calculating with the processor solutions V* and f* of the two independent variables V and f that minimize or maximize the second objective function;
- and
- generating with the processor an image of the object from which the waves are scattered, based on the solutions V* and f*, so that a location of the object in the image is determined.
A method for partial differential equation inversion, the method comprising:
- receiving measured data d0, wherein the measured data is a result of waves being emitted by a source, propagating through a medium toward an object, and being scattered from the object;
- selecting a Green's function G, which generates estimated data ds when applied to a source function f, wherein the source function f describes the source of the waves;
- selecting an objective function having first and second measures N1 and N2, wherein the objective function depends on two independent variables G and f;
- optimizing with a processor the objective function by finding a minimum or a maximum using the partial differential equation inversion;
- calculating with the processor solutions G* and f* of the two independent variables G and f so that the objective function is minimized or maximized;
- and
- generating with the processor an image of the object from which the waves are scattered, based on the solutions G* and f*, so that a location of the object in the image is determined.
Dependencies are inferred from the claim text.