Resolution of slowness and reflectors in crosswell tomography with transmission and reflection traveltimes

We sometimes encounter situations in seismic imaging in which knowing the position of key reflectors between wells would be very useful. In many crosswell data sets, both transmission and reflection traveltimes for selected reflectors can be picked. We investigated the possibility that transmission- plus- reflection crosswell traveltime tomography can determine the position of these reflectors with a high level of accuracy, thereby providing an independent way of verifying (and perhaps improving) the position of these reflectors obtained from crosswell reflection imaging. We studied the effect of combining reflection traveltimes for selected reflectors with transmission traveltimes on the resolution of the interwell slowness field and depth determination of selected reflectors. We found that theoretically, the position of reflectors is determined uniquely from transmission and reflection traveltimes in a linearized continuum formulation of crosswell tomography. We also computed diagonal elements of the resolution matrix for two crosswell geometries based on field experiments conducted in a west Texas oil field to see what effect noise has on the accuracy of our determination of reflector depths. These computational results indicate that reflector positions are indeed very well determined for these geometries, with expected errors of similar to 0.5% of the well spacing when noise in traveltimes is similar to 2%. Because reflector- position parameters are so well determined, including reflection traveltimes does not degrade the resolution of the slowness field as a result of introducing additional reflector-depth parameters. Actually, the resolution of the slowness field, particularly near reflectors, improves by including reflection traveltimes, in spite of the fact that we must solve for these additional depth parameters. The improvement in slowness resolution should provide velocity models that can yield more accurate reflection images.