Abstract: A method of solving a geophysical inverse problem for estimating a physical parameter, the method comprising providing a model vector representing the physical parameter, transforming the model vector by a first operator to provide a first transformed model vector, solve the inverse problem for the first transformed model vector to provide a first solution, transforming the model vector by a second operator to produce a second transformed model vector, solve the inverse problem for the second transformed model vector to provide a second solution, calculating a weighted sum of the first solution and the second solution.

Abstract: A method of estimating a set of physical parameters, the method comprising iteratively inverting an equation to minimise an error between simulated data and measured data and to provide an estimated set of physical parameters, wherein said iteratively inverting comprises at least a first inversion step and a second inversion step and wherein the simulated data depend on a model vector representing the set of physical parameters, applying a compression operator to the model vector representing the set of physical parameters to reduce the number of free variables and to produce a compressed model vector and varying the compression operator between the first inversion step and the second inversion step.

Abstract: A method of estimating electromagnetic parameters of a geological structure, comprising: providing controlled source electromagnetic, CSEM, data of the structure, calculating a numerical model representing electromagnetic parameters of the structure and generating simulated CSEM data, discretising the numerical model based on prior knowledge of the structure, defining a functional for minimising the distance between said simulated CSEM data and said CSEM data, wherein the functional comprises a regularisation term which depends on prior knowledge of said structure.

Abstract: A method of estimating a set of physical parameters, the method comprising iteratively inverting an equation to minimise an error between simulated data and measured data and to provide an estimated set of physical parameters, wherein said iteratively inverting comprises at least a first inversion step and a second inversion step and wherein the simulated data depend on a model vector representing the set of physical parameters, applying a compression operator to the model vector representing the set of physical parameters to reduce the number of free variables and to produce a compressed model vector and varying the compression operator between the first inversion step and the second inversion step.

Abstract: A method of solving a geophysical inverse problem for estimating a physical parameter, the method comprising providing a model vector representing the physical parameter, transforming the model vector by a first operator to provide a first transformed model vector, solve the inverse problem for the first transformed model vector to provide a first solution, transforming the model vector by a second operator to produce a second transformed model vector, solve the inverse problem for the second transformed model vector to provide a second solution, calculating a weighted sum of the first solution and the second solution.

Abstract: A method of estimating electromagnetic parameters of a geological structure, comprising: providing controlled source electromagnetic, CSEM, data of the structure, calculating a numerical model representing electromagnetic parameters of the structure and generating simulated CSEM data, discretising the numerical model based on prior knowledge of the structure, defining a functional for minimising the distance between said simulated CSEM data and said CSEM data, wherein the functional comprises a regularisation term which depends on prior knowledge of said structure.