Velocity macro-model estimation from seismic reflection data by stereotomography

We introduce a new tomographic method for estimating velocity macro-models from seismic reflection data. In addition to traveltimes picked on locally coherent reflected events, the method requires that the associated local slopes of the events be picked simultaneously in the common-shot and common-receiver trace gathers. The data then consist of a discrete collection of traveltimes, positions and slopes for selected reflected events. Unlike traveltime tomography, picked events are only required to be locally coherent. It is not necessary to follow continuous arrivals all over the trace gathers. Indeed, the method does not require the introduction of interfaces in the model description. Several approaches of tomography using the slope have already been proposed. We present a unified formulation for slope tomography methods, in which the model is described by the velocity field and a set of ray-segment pairs associated with the reflected/diffracted events. We propose a new robust slope tomography method, which we call 'stereotomography'. It consists of fitting all observed data (positions, slopes and traveltimes) to data calculated by ray tracing. There are no theoretical limitations in stereotomography for laterally heterogeneous velocity macro-models. Practically, traveltimes and slopes are picked on local slant stack panels. Ray multipathing can be accounted for since paths are discriminated by their associated slopes. The non-linear inverse problem is iteratively resolved by a local optimization. The Fréchet derivatives are estimated by paraxial ray tracing. Validation tests on 1-D and 2-D synthetic data are analysed. In the first 1-D example, we study the sensitivity of the method to model parameters (using a singular-value decomposition). The second 1-D example evaluates picking precision and shows that it is sufficient for constraining the velocity field. The last example is a 2-D application in which data are calculated directly by ray tracing. It shows the performance of the method in the presence of strong lateral velocity variations.