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SUMMARY Using the 2‐D DC‐resistivity tomography experiment as an example, we examine some of the difficulties inherently associated with constructing a single maximally smooth model as a solution to a geophysical inverse problem. We argue that this conventional approach yields at best only a single model from a myriad of possible models and at worst produces a model which, although having minimum structure, frequently has little useful relation to the earth that gave rise to the observed data. In fact in applied geophysics it is usual to have significant prior information which is to be supplemented by further geophysical experiments. With this perspective we suggest an alternate approach to geophysical inverse problems which emphasizes the prior information and includes the data from the geopysical experiment as a supplementary constraint. To this end we take all available prior information and construct an inversion algorithm which, given an arbitrary starting model and the absence of any data, will produce a preconceived earth model and then introduce the observed data into the inversion to determine how the prior earth model is influenced by the supplementary geophysical data.

We develop a new method for interpretation of tensor gravity field component data, based on regularized focusing inversion. The focusing inversion makes its possible to reconstruct a sharper image of the geological target than conventional maximum smoothness inversion. This new technique can be efficiently applied for the interpretation of gravity gradiometer data, which are sensitive to local density anomalies. The numerical modeling and inversion results show that the resolution of the gravity method can be improved significantly if we use tensor gravity data for interpretation. We also apply our method for inversion of the gradient gravity data collected by BHP Billiton over the Cannington Ag‐Pb‐Zn orebody in Queensland, Australia. The comparison with the drilling results demonstrates a remarkable correlation between the density anomaly reconstructed by the gravity gradient data and the true structure of the orebody. This result indicates that the emerging new geophysical technology of the airborne gravity gradient observations can improve significantly the practical effectiveness of the gravity method in mineral exploration.

S U M M A R YNumerical efficiency and efficacy of subspace methods for solving large-scale geophysical inverse problems are investigated. The primary advantage of subspace techniques over traditional Gauss-Newton algorithms lies in the need to invert only a matrix equal to the dimension of the subspace. The efficacy of the method lies in a judicious choice of basis vectors. Vectors associated with gradients of the data misfit or gradients of the model component of the objective function are of great utility, but substantial improvement in convergence rates can be obtained by using basis vectors associated with gradients of a segmented objective function. To quantify these benefits we invert data acquired in a synthetic dc resistivity experiment. 420 electric potentials obtained at the surface of a 2-D earth are inverted to recover estimates of the electrical conductivity of 1296 cells. The number of basis vectors range from two to 95 and convergence rates, model norms and final models are compared. In an effort to reduce the computations we investigate the possibility of using only linear information in the data-misfit objective function. This is shown to be effective at early iterations and is computationally efficient since it obviates the need to calculate curvature information in the data misfit and because it can also be implemented without a line search. The effects of using gradient vectors versus steepest descent vectors in the inversion are examined. Accordingly we introduce two methods by which approximate descent vectors can be fabricated from gradient vectors. They show that even simple preconditioning of gradient vectors can dramatically improve convergence rates provided that all vectors are preconditioned in the same manner.

SUMMARY A simple derivation is presented for the computation of sensitivities needed to solve parametric inverse problems in electromagnetic induction. It is shown that sensitivities for any component of an electromagnetic field can be obtained by solving two boundary‐value problems which are identical except for the specification of the source terms and (possibly) prescribed boundary conditions. The electric fields from these primal and auxiliary problems are multiplied and integrated to produce a numerical value for the sensitivity. Although the final formulae derived here are equivalent to those developed through the use of formal adjoint or Green's functions approaches, our work does not require explicit derivation of the adjoint operator and boundary conditions and does not formally invoke reciprocity.