Refraction traveltime tomography using damped monochromatic wavefield

For complicated earth models, wave-equation–based refraction-traveltime tomography is more accurate than ray-based tomography but requires more computational effort. Most of the computational effort in traveltime tomography comes from computing traveltimes and their Fr´echet derivatives, which for ray-based methods can be computed directly. However, in most wave-equation traveltime-tomography algorithms, the steepest descent direction of the objective function is computed by the backprojection algorithm, without computing a Fr ´echet derivative directly. We propose a new wave-based refraction-traveltime– tomography procedure that computes Fr´echet derivatives directly and efficiently. Our method involves solving a damped-wave equation using a frequency-domain, finite-element modeling algorithm at a single frequency and invoking the reciprocity theorem. A damping factor, which is commonly used to suppress wraparound effects in frequency-domain modeling, plays the role of suppressing multievent wavefields. By limiting the wavefield to a single first arrival, we are able to extract the first-arrival traveltime from the phase term without applying a time window. Computing the partial derivative of the damped wave-equation solution using the reciprocity theorem enables us to compute the Fr ´echet derivative of amplitude, as well as that of traveltime, with respect to subsurface parameters. Using the Marmousi-2 model, we demonstrate numerically that refraction traveltime tomography with large-offset data can be used to provide the smooth initial velocity model necessary for prestack depth migration.This work was financially supported by the National Laboratory Project of the Ministry of Science and Technology and the Brain Korea 21 project of the Ministry of Education. We are also grateful to Prof. K. J. Marfurt of the University of Houston and Dr. M. Schoenberger for editing our manuscript

Evaluation of Kirchhoff hyperbola in terms of partial derivative wavefield and virtual source

The Kirchhoff migration is computationally the most economic choice of migration currently available. From its beginning, the Kirchhoff migration has been developed and improved separately from wave-equation based migrations although they are founded on the same principle. In this paper, we reveal a link between the Kirchhoff depth migration and the wave-equation based migration such as reverse-time migration and least squares migration in terms of the partial derivative wavefield and the virtual source. The Kirchhoff prestack depth migration uses the partial derivative wavefield approximated by the Dirac delta function to migrate the seismic signals. Accordingly, the Kirchhoff hyperbola is defined as kinematic approximation of the partial derivative wavefield.This work was financially supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by Korea government (MOST) (No.R0A-2006-000-10291-0) and the Brain Korea 21 project of the Ministry of Education

Efficient electric resistivity inversion using adjoint state of mixed finite-element method for Poissons equation

We propose an electric resistivity inversion method that is similar to the reverse time migration technique applied to seismic data. For calculating model responses and inversion, we use the mixed finite-element method with the standard P1 P0 pair for triangular decompositions, which makes it possible to compute both the electric potential and the electric field vector economically. In order to apply the adjoint state of the Poisson equation in the resistivity inverse problem, we introduce an apparent electric field defined as the dot product between the computed electric field vector and a weighting factor and then defining a virtual source to compute the partial derivative of the electric field vector. We exploit the adjoint state (the symmetry of Green s function) of matrix equations derived from solving the Poisson equation by the mixed finiteelement method, for the calculation of the steepest descent direction of our objective function. By computing the steepest descent direction by a dot product of backpropagated residual and virtual source, we can avoid the cumbersome and expensive process of computing the Jacobian matrix directly. We calibrate our algorithm on a synthetic of a buried conductive block and obtain an image that is compatible with the limits of the resistivity method.The work of Ha was supported by the Korea Research Foundation Grant (KRF-2004-C00007) and the works of other people were financially supported by the National Research Laboratory Project of the Korea Ministry of Science and Technology, the Brain Korea 21 Project of the Korea Ministry of Education