Particle swarm optimization (PSO) is a global optimization strategy that simulates the social behavior observed in a flock (swarm) of birds searching for food. A simple search strategy in PSO guides the algorithm toward the best solution through constant updating of the cognitive knowledge and social behavior of the particles in the swarm. To evaluate the applicability of PSO to inversion of geophysical data, we inverted three noise-corrupted synthetic sounding data sets over a multilayered 1D earth model by using DC, induced polarization (IP), and magnetotelluric (MT) methods. The results show that acceptable solutions can be obtained with a swarm of about 300 particles and that convergence occurs in less than 100 iterations. The time required to execute a PSO algorithm is comparable to that of a genetic algorithm (GA). Similarly, the models estimated from PSO and GA are close to the true solutions. Whereas a ridge regression (RR) algorithm converges in four to eight iterations, it yields satisfactory results only when the initial model is very close to the true model. Models estimated from PSO explain observed, vertical electric sounding (VES) and MT data, from Bhiwani district, Haryana, India, and the Chottanagpur gneissic complex, Dhanbad, India. The results are consistent with RR and GA inversions.

S U M M A R YWe show that the linearized reflection coefficients for arbitrary anisotropic media embedded in an isotropic background can be derived directly from a Born formalism. Due to rapidly varying phases of the scattered waves from first-order perturbations in density and elastic parameters, the major contributions to the observed wavefield for any source-receiver pair far from the volume of scatterers arise from the stationary points of a scattering integral, called the Born integral. For simple interface models, such integrals can be evaluated analytically using the method of stationary phase. The resulting scattering function relates linearly to the approximate (linearized) reflection coefficient through a scaling factor determined by the angle of incidence and the properties of the background medium. We consider a homogeneous isotropic background to express the approximate reflection coefficients as a sum of an isotropic and an anisotropic reflection coefficient. The isotropic coefficient is a weighted sum of density and isotropic perturbations about the background, whereas the anisotropic coefficient is a weighted sum of anisotropic perturbations where the weights depend on the angles of incidence, the properties of the background medium as well as the azimuth of the plane of reflection with respect to some symmetry plane of the weakly anisotropic medium.We derived expressions for approximate PP and PS reflection coefficients of a weakly isotropic medium, a weakly orthorhombic medium and a weak but arbitrarily anisotropic medium underlying an isotropic medium. Our expressions for PP reflection coefficients are exactly the same as those obtained from first-order perturbation theory which were previously derived by linearization of the exact reflection coefficients. For converted PS waves, our expressions are valid only for small angles of incidence, but have much simpler forms than those obtained by linearization of exact reflection coefficients.We also derive the approximate PP reflection coefficient of a transversely isotropic medium with a tilted axis of symmetry in an explicit form and investigate the effects of dip of the symmetry axis on these reflection coefficients. Numerical results demonstrate that neglecting the dip of a moderately dipping (30 • -60 • ) symmetry axis of a transversely isotropic medium yields significant errors in determining the weakly anisotropic parameters through an analysis of variations of amplitude with azimuth.

Walsh functions are a set of complete and orthonormal functions of nonsinusoidal waveform. In contrast to sinusoidal waveforms whose amplitudes may assume any value between −1 to +1, Walsh functions assume only discrete amplitudes of ±1 which form the kernel function of the Walsh transform. Because of this special nature of the kernel, computation of the Walsh transform of a given signal is simpler and faster than that of the Fourier transform. The properties of the Fourier transform in linear time are similar to those of the Walsh transform in dyadic time. The Fourier transform has been widely used in interpretation of geophysical problems. Considering various aspects of the Walsh transform, an attempt has been made to apply it to some gravity data. A procedure has been developed for automated interpretation of gravity anomalies due to simple geometrical causative sources, viz., a sphere, a horizontal cylinder, and a 2-D vertical prism of large depth extent. The technique has been applied to data from the published literature to evaluate its applicability, and the results are in good agreement with the more conventional ones.

Microstructural attributes of cracks and fractures, such as crack density, aspect ratio, and fluid infill, determine the elastic properties of a medium containing a set of parallel, vertical fractures. Although the tangential weakness [Formula: see text] of the fractures does not vary with the fluid content, the normal weakness [Formula: see text] exhibits significant dependence on fluid infill. Based on linear-slip theory, we used the ratio [Formula: see text] — termed the fluid indicator — as a quantitative measure of the fluid content in the fractures, with g representing the square of the ratio of S- and P-wave velocity in the unfractured medium. We used a Born formalism to derive the sensitivity to fracture weakness of PP- and PS-reflection coefficients for an interface separating an unfractured medium from a vertically fractured medium. Our formulae reveal that the PP-reflection coefficient does not depend on the 2D microcorrugation/surface roughness with ridges and valleys parallel to the fracture strike, whereas the PS-reflection coefficient is sensitive to this microstructural property of the fractures. Based on this formulation, we developed a method to compute the fluid indicator from wide-azimuth PP-AVOA data. Inversion of synthetic data corrupted with 10% random noise reliably estimates the normal and tangential fracture weaknesses and hence the fluid indicator can be determined accurately when the fractures are liquid-filled or partially saturated. As the gas saturation in the fractures increases, the quality of inversion becomes poorer. Errors of 15%–20% in g do not affect the estimation of fluid indicator significantly in case of liquid infill or partial saturation. However, for gas-saturated fractures, incorrect values of g may have a significant effect on fluid-indicator estimates.