Frequency-domain Acoustic Modeling and Inversion in the Logarithmic Grid Set

Since seismic modeling and inversion are performed using finite-sized models, boundary conditions are necessary to remove edge reflections arising from boundaries. Although several boundary conditions were developed and have been used for seismic modeling, it is not easy to remove edge reflections perfectly using those boundary conditions for some cases. In this study, we propose using the logarithmic grid set for an edge-reflection-free seismic modeling algorithm and apply it to acoustic modeling and inversion. For modeling and inversion in the logarithmic grid set, wave equation and source position should be converted to the logarithmic grid set and interpolation is required to convert data from the logarithmic grid set to the conventional grid set or reversely. The logarithmic grid set can allow us to achieve computational efficiency when the record length is not too long. Our algorithms are based on the finite-difference method, the gradient method using the new pseudo-Hessian matrix for scaling and the conjugate gradient method. We verify the acoustic modeling and inversion techniques performed in the logarithmic grid set for the Marmousi-2 model. Numerical results demonstrate that the modeling and inversion techniques for the logarithmic grid set give reasonable solutions.