Depth imaging with multiples is a prestack depth migration method that uses multiples as the signal for more accurate boundary mapping and amplitude recovery. The idea is partially related to model‐based multiple‐suppression techniques and reverse‐time depth migration. Conventional reverse‐time migration uses the two‐way wave equation for the backward wave propagation of recorded seismic traces and ray tracing or the eikonal equation for the forward traveltime computation (the excitation‐time imaging principle). Consequently, reverse‐time migration differs little from most other one‐way wave equation or ray‐tracing migration methods which expect only primary reflection events. Because it is almost impossible to attenuate multiples without degrading primaries, there has been a compelling need to devise a tool to use multiples constructively in data processing rather than attempting to destroy them. Furthermore, multiples and other nonreflecting wave types can enhance boundary imaging and amplitude recovery if a full two‐way wave equation is used for migration. The new approach solves the two‐way wave equation for both forward and backward directions of wave propagation using a finite‐difference technique. Thus, it handles all types of acoustic waves such as reflection (primary and multiples), refraction, diffraction, transmission, and any combination of these waves. During the imaging process, all these different types of wavefields collapse at the boundaries where they are generated or altered. The process goes through four main steps. First, a source function (wavelet) marches forward using the full two‐way scalar wave equation from a source location toward all directions. Second, the recorded traces in a shot gather march backward using the full two‐way scalar wave equation from all receiver points in the gather toward all directions. Third, the two forward‐ and backward‐propagated wavefields are correlated and summed for all time indices. And fourth, a Laplacian image reconstruction operator is applied to the correlated image frame. This technique can be applied to all types of seismic data: surface seismic, vertical seismic profile (VSP), crosswell seismic, vertical cable seismic, ocean‐bottom cable (OBC) seismic, etc. Because it migrates all wave types, the input data require no or minimal preprocessing (demultiple should not be done, but near‐surface or acquisition‐related problems might need to be corrected). Hence, it is only a one‐step process from the raw field gathers to a final depth image. External noise in the raw data will not correlate with the forward wavefield except for some coincidental matching; therefore, it is usually unnecessary to do signal enhancement processing before the depth imaging with multiples. The input velocity model could be acquired from various methods such as iterative focusing analysis or tomography, as in other prestack depth migration methods. The new method has been applied to data sets from a simple multiple‐generating model, the Marmousi model, and a real offset VSP. The results show accurate imaging of primaries and multiples with overall significant improvements over conventionally imaged sections.
Computation of Farfield Radiation Patterns by Use of a General Integral Solution to the Time‐Dependent Scalar Wave Equation