Abstract: Source-receiver compression is used to help design surveys and mitigate the computational costs of data set inversion. The source-receiver compression is based on data redundancy and sensitivity. More particularly, a compressed source array is produced for minimum redundancy and maximum sensitivity to reservoir model parameters. The synthesized transmitter array has a reduced number of sources, thereby reducing the number of forward model simulations needed to carry out the inversion. Furthermore, the data collected at the receivers employed in the survey can be compressed. This has the implication of reducing the computational cost of constructing the Jacobian matrix and inverting the corresponding Hessian matrix.

Abstract: A volume of data is partitioned into a plurality of domains. A multilevel preconditioner is applied in the plurality of domains to provide iterative approximate solutions for the domains, which are coupled with boundary conditions. The approximate solutions for the domains are stitched together to provide a solution for a wave equation which can be used in full waveform inversion.

Abstract: Source-receiver compression is used to help design surveys and mitigate the computational costs of data set inversion. The source-receiver compression is based on data redundancy and sensitivity. More particularly, a compressed source array is produced for minimum redundancy and maximum sensitivity to reservoir model parameters. The synthesized transmitter array has a reduced number of sources, thereby reducing the number of forward model simulations needed to carry out the inversion. Furthermore, the data collected at the receivers employed in the survey can be compressed. This has the implication of reducing the computational cost of constructing the Jacobian matrix and inverting the corresponding Hessian matrix.

Abstract: A method of determining the resistivity of an underground formation surrounding a cased borehole including the steps of: a) passing a current along a first pan of the casing and measuring the voltage; b) passing a current along a second part of the casing and measuring the voltage, the second part being spaced from the first part by an intermediate region; c) measuring voltages between the first part of the casing and a point in the intermediate region and between the second part of the casing and the same point; and d) using the measured voltages to derive the resistivity of the formation.