Crosshole seismic tomography: working solutions to issues in real data travel time inversion

摘要

In travel time inversion of crosshole seismic tomography, when dealing with real data, the following three issues need to be addressed: how to suppress the effect of data errors, how to balance the data contribution and reference model, and how to properly set the geological constraints ( well logs) in an inversion. Signal-to-noise ratios of travel time data picked from real crosshole seismic surveys likely depend on the vertical offset between a source and a receiver, since the overall attenuation will typically be greater for a longer ray path. Therefore, to suppress the effect of data errors in a least-squares solution, a data confidence matrix is used in practice where the weighting is set logically based on the vertical offset. When a model constraint is adopted in the inversion to seek a solution with least deviation from some prescribed background that is most likely to have no spurious structure, a trade-off parameter is used to explicitly balance the dependence of the inversion solution to the data contribution and the reference model. The latter is built by combining sonic logging information, which is hard geological evidence at the vicinity of wells, and an initial estimate from the travel time back-projection, a preliminary solution of the travel time tomography. Geological constraints are set so that the inversion solution should have the least deviation from the hard geological evidence, and more deviation for the remaining part of the survey region, since the true velocity model might differ from such an initial estimate and the true ray paths might deviate from the initial ray paths.