We describe the implementation of a versatile method for interpreting gravity and magnetic data in terms of 3D structures. The algorithm combines a number of features that have proven useful in other algorithms. To accommodate structures of arbitrary geometry, we define the subsurface using a large number of prisms, with the depths to the tops and bottoms as unknowns to be determined by optimization. Included in the optimization process are the three components of the magnetization vector and the density contrast, which is assumed to be a continuous function with depth. We use polynomial variations of the density contrast to simulate the natural increase of rock density with depth in deep sedimentary basins. The algorithm minimizes the quadratic norm of residuals combined with a regularization term. This term controls the roughness of the upper and lower topographies defined by the prisms. This results in simple shapes by penalizing the norms of the first and second horizontal derivatives of the prism depths and bottoms. Finally, with the use of quadratic programming, it is a simple matter to include a priori information about the model in the form of equality or inequality constraints. The method is first tested using a hypothetical model, and then it is used to estimate the geometry of the Ensenada basin by means of joint inversion of land and offshore gravity and land, offshore, and airborne magnetic data. The inversion helps constrain the structure of the basin and helps extend the interpretation of known surface faults to the offshore.

We consider that all types of electromagnetic measurements represent weighted averages of the subsurface electrical conductivity distribution, and that to each type of measurement there corresponds a different weighting function. We use this concept for the quantitative interpretation of dc resistivity, magnetometric resistivity, and low‐frequency electric and magnetic measurements at low induction numbers. In all three cases the corresponding inverse problems are nonlinear because the weighting functions depend on the unknown conductivity distribution. We use linear approximations that adapt to the data and do not require reference resistivity values. The problem is formulated numerically as a solution of a system of linear equations. The unknown conductivity values are obtained by minimizing an objective function that includes the quadratic norm of the residuals as well as the spatial derivatives of the unknowns. We also apply constraints through the use of quadratic programming. The final product is the flattest model that is compatible with the data under the assumption of the given weighting functions. This approximate inversion or imaging technique produces reasonably good results for low and moderate conductivity contrasts. We present the results of inverting jointly and individually different data sets using synthetic and field data.

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We apply a modified genetic algorithm, the "recombinant genetic analogue" (RGA) to the inversion of magnetotelluric (MT) data from two different geothermal areas, one in El Salvador and another in Japan. An accurate 2-D forward modelling algorithm suitable for very heterogeneous models forms the core of the inverse solver. The forward solution makes use of a gridding algorithm that depends on both model structure and frequency. The RGA represents model parameters as parallel sets of bit strings, and differs from conventional genetic algorithms in the ways in which the bit strings are manipulated in order to increase the probability of convergence to a global minimum objective function model. A synthetic data set was generated from a chessboard model, and the RGA was shown capable of reconstructing the model to an acceptable tolerance. The algorithm was applied to MT data from Ahuachapán geothermal area in El Salvador and compared with other interpretations. Data from the geothermal area of Minamikayabe in Japan served as a second test case. The RGA is highly adaptable and well suited to non-linear hypothesis testing as well as to inverse modelling.

We present a semi‐analytical, unifying approach for modelling the electromagnetic response of 3‐D bodies excited by low‐frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell’s equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green’s function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipole–dipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR‐TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR‐TE, where the mode of conduction is predominantly perpendicular to the profile.

[1] The attenuation effects predicted by Hickey's poroelastic theory (Hpt) are quantified by means of seismic modeling in an unbounded, homogeneous, isotropic porous model fully saturated with water and with oil. The numerical results are compared to those predicted by Biot poroelastic theory (Bpt). As opposed to Bpt, Hpt accounts for thermomechanical coupling and viscous fluid relaxation and adequately models the transient fluctuations of porosity and mass densities as the wave compresses and dilates the porous medium during propagation. Despite all these theoretical improvements over Bpt, the numerical results show that both theories produce remarkably similar waveforms. Without considering thermal relaxation, Hpt produces less than 1% higher-amplitude attenuation and velocity dispersion than Bpt. The major contrasts correspond to the slow P wave. Thermomechanical coupling affects the fast P wave: seismic amplitudes are 1% smaller and some dispersion for the oil-permeated case can be observed. It produces no effects on the fast S or the slow P wave. Therefore these numerical experiments appear to substantiate what Biot assumed at the outset of his theoretical developments: that the effects of transient oscillations of porosity during wave propagation are negligible in terms of velocity dispersion and amplitude attenuation. Furthermore it is confirmed that in a homogeneous porous medium, the combined dissipation mechanisms mentioned are not adequate to explain the total amount of energy dissipation observed in the field or laboratory.Citation: Quiroga-Goode, G., S. Jiménez-Hernández, M. A. Pérez-Flores, and R. Padilla-Hernández (2005), Computational study of seismic waves in homogeneous dynamic-porosity media with thermal and fluid relaxation: Gauging Biot theory,

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Although a comparative analysis of multiple images of a physical target can be useful, a joint image reconstruction approach should provide better interpretative elements for multi-spectral images. We present a generalized image reconstruction algorithm for the simultaneous reconstruction of bandlimited images based on the novel cross-gradients concept developed for geophysical imaging. The general problem is formulated as the search for those images that stay within their band limits, are geometrically similar and satisfy their respective data in a least-squares sense. A robust iterative quadratic programming scheme is used to minimize the resulting objective function. We apply the algorithm to synthetic data generated using linear mathematical functions and to comparative geophysical test data. The resulting images recovered the test targets and show improved structural semblance between the reconstructed images in comparison to the results from two other conventional approaches.