Path - integral seismic imaging

A B S T R A C T A new type of seismic imaging, based on Feynman path integrals for waveform modelling , is capable of producing accurate subsurface images without any need for a reference velocity model. Instead of the usual optimization for traveltime curves with maximal signal semblance, a weighted summation over all representative curves avoids the need for velocity analysis, with its common difficulties of subjective and time-consuming manual picking. The summation over all curves includes the stationary one that plays a preferential role in classical imaging schemes, but also multiple stationary curves when they exist. Moreover, the weighted summation over all curves also accounts for non-uniqueness and uncertainty in the stacking/migration velocities. The path-integral imaging can be applied to stacking to zero-offset and to time and depth migration. In all these cases, a properly defined weighting function plays a vital role: to emphasize contributions from traveltime curves close to the optimal one and to suppress contributions from unrealistic curves. The path-integral method is an authentic macromodel-independent technique in the sense that there is strictly no parameter optimization or estimation involved. Development is still in its initial stage, and several conceptual and implementation issues are yet to be solved. However , application to synthetic and real data examples shows that it has the potential for becoming a fully automatic imaging technique. First, we set aside seismic velocities and work in a macromodel-independent context. A detailed and accurate velocity is usually seen as a precondition for obtaining an optimally focused seismic image of the subsurface of the earth. A common approach to velocity estimation is to formulate a criterion to quantify the degree of focusing and from there to derive a mechanism to update velocities. Examples of such criteria are a maximal signal semblance in zero-offset imaging or flatness in common-image gathers (CIG) for time or depth migration. Key to such techniques is the picking of important seismic events in prestack gathers, either manually or by an automatic procedure. Manual picking is both time consuming and subjective. Automatic picking is practical and useful in many situations (Fomel 2003; Stinson et al. 2004), but there * are cases where picking a single event is not sufficient to determine a unique velocity. Complicated wave-propagation effects , such as multiple reflections, mode conversions and wave-front triplications, can often cause serious problems for the assumptions underlying the velocity-analysis technique. For instance, picking …