We present a 3D inversion methodology for multisource time-domain electromagnetic data. The forward model consists of Maxwell's equations in time where the permeability is fixed but electrical conductivity can be highly discontinuous. The goal of the inversion is to recover the conductivitygiven measurements of the electric and/or magnetic fields. The availability of matrix-factorization software and highperformance computing has allowed us to solve the 3D time domain EM problem using direct solvers. This is particularly advantageous when data from many transmitters and over many decades are available. We first formulate Maxwell's equations in terms of the magnetic field,H. The problem is then discretized using a finite volume technique in space and backward Euler in time. The forward operator is symmetric positive definite and a Cholesky decomposition can be performed with the work distributed over an array of processors. The forward modeling is quickly carried out using the factored operator. Time savings are considerable and they make 3D inversion of large ground or airborne data sets feasible. This is illustrated by using synthetic examples and by inverting a multisource UTEM field data set acquired at San Nicolás, which is a massive sulfide deposit in Mexico.
S U M M A R YWe present a general formulation for inverting time domain electromagnetic data to recover a 3-D distribution of electrical conductivity. The forward problem is solved using finite volume methods in the spatial domain and an implicit method (Backward Euler) in the time domain. A modified Gauss-Newton strategy is employed to solve the inverse problem. The modifications include the use of a quasi-Newton method to generate a pre-conditioner for the perturbed system, and implementing an iterative Tikhonov approach in the solution to the inverse problem. In addition, we show how the size of the inverse problem can be reduced through a corrective source procedure. The same procedure can correct for discretization errors that inevidably arise. We also show how the inverse problem can be efficiently carried out even when the decay time for the conductor is significantly larger than the repetition time of the transmitter wave form. This requires a second processor to carry an additional forward modelling. Our inversion algorithm is general and is applicable for any electromagnetic field (E, H, d B/dt) measured in the air, on the ground, or in boreholes, and from an arbitrary grounded or ungrounded source.Three synthetic examples illustrate the basic functionality of the algorithm, and a result from a field example shows applicability in a larger-scale field example.
We present an algorithm for inverting magnetotelluric data to recover a three-dimensional conductivity model of the Earth. The algorithm is an iterative, linearised, minimum-structure procedure within which the solution of the forward problem, the application of the Jacobian matrix of sensitivities, and the solution of the matrix equation are all done using sparse matrix-vector operations. Consequently, the algorithm is extremely efficient in its use of memory, making three-dimensional inversions feasible.
We present a practical formulation for forward modeling and inverting time domain data arising from multiple transmitters. The underpinning of our procedure is the ability to factor the forward modeling matrix and then solve our system using direct methods. We first formulate Maxwell's equations in terms of the magnetic field, H to provide a symmetric forward modeling operator. The problem is discretized using a finite volume technique in space and a backward Euler in time. The MUMPS software package is used to carry out a Cholesky decomposition of the forward operator, with the work distributed over an array of processors. The forward modeling is then quickly carried out using the factored operator. The time savings are considerable and they make the simulations of large ground or airborne data sets feasible and greatly increase our abilities to solve the 3D electromagnetic inverse problem in a reasonable time. The ability to use direct methods also greatly enhances our ability to carry out survey design problems.
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