MONTE-CARLO ESTIMATION AND RESOLUTION ANALYSIS OF SEISMIC BACKGROUND VELOCITIES

The complete solution to an inverse problem, including information on accuracy and resolution, is given by the a posteriori probability density in the model space. By running a modified simulated annealing, samples from the model space can be drawn in such a way that their frequencies of occurrence approximate their a posteriori likelihoods. Using this method, maximum likelihood estimation and uncertainty analysis of seismic background velocity models are performed on multioffset seismic data. The misfit between observed and synthetic waveforms within the time windows along computed multioffset travel times, is used as an objective function for the simulated annealing approach. The real medium is modeled as a series of layers separated by curved interfaces. Lateral velocity variations within the layers are determined by interpolation from specified values at a number of sampling points. The input data consists of multioffset seismic data. Additionally, zero-offset times are used to migrate the reflectors in time to the depth domain. The multi-offset times are calculated by an efficient ray-tracing algorithm which allows inversion of a large number of seismograms. The a posteriori probability density for this problem is highly multidimensional and highly multimodal. Therefore, the information contained in this distribution cannot be adequately represented by standard deviations and covariances. However, by sequentially displaying a large number of images, computed from the a posteriori background velocity samples and the data, it is possible to convey to the spectator a better understanding of what information we really have on the subsurface.