Information about reservoir properties usually comes from two sources: seismic data and well logs. The former provide an indirect, low resolution image of rock velocity and density. The latter provide direct, high resolution (but laterally sparse) sampling of these and other rock parameters. An important problem in reservoir characterization is how best to combine these data sets, allowing the ...

Incomplete LU factorization is a valuable preconditioning approach for sparse iterative solvers. An “ideal” but inefficient preconditioner for the iterative solution of Ax = b is A−1 itself. This paper describes a preconditioner based on sparse approximations to partitioned representations of A−1, in addition to the results of implementation of the proposed method in a shared memory parallel en...

We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short H-matrices). These matrices form a subset of the set of all matrices and h...

Continuity along reflectors in seismic images is used via Curvelet representation to stabilize the convolution operator inversion. The Curvelet transform is a new multiscale transform that provides sparse representations for images that comprise smooth objects separated by piece-wise smooth discontinuities (e.g. seismic images). Our iterative Curvelet-regularized deconvolution algorithm combine...

Migration relies on multi-dimensional correlations between sourceand residual wavefields. These multi-dimensional correlations are computationally expensive because they involve operations with explicit and full matrices that contain both wavefields. By leveraging recent insights from compressive sampling, we present an alternative method where linear correlation-based imaging is replaced by im...

Even though contemporary methods for the removal of multiple events in seismic data due to a free-surface are built upon reciprocity relationships between wavefields, they are often still implemented as prediction-subtraction processes. The subtraction process does not always compensate for imperfect prediction of multiple events, and itself often leads to distortion of primary events. A recent...

All direct solvers described in this text make frequent use of matrix operations such as matrixmatrix multiplications, matrix inversions, LU factorizations, etc. The matrices that are manipulated are almost all dense, but fortunately, they will be either of small size, or will have internal structure that allows the required operations to be performed rapidly even though the matrices are dense....

A new method being developed for solving linear programs is discussed in this tutorial. This method uses matrix inversion operations sparingly, and it thus seems well suited to solve large-scale problems and those that may not have the property of being very sparse.