Image space SRMP produces a multiple prediction by convolving the data with itself at every subsurface depth level during the course of a shot-profile migration. The result is the same as migrating the conventional SRMP multiple prediction. This method will only work with shot-profile migration strategies since the convolution operation must operate on distinct gathers rather than the combinations thereof produced by resorting to CMP coordinates. The simplicity of this approach can immediately be leveraged to manufacture the image-space multiple prediction directly from any shot-profile migration program. The method is immediately applicable to 3D, and non-zero subsurface-offset and angle. Any migration algorithm that maintains separate up-coming and down-going wavefields and uses a combinatory imaging condition (e.g. planewave and reverse-time migrations) can also be easily modified to produce an IS-SRMP volume.
Importantly, split-spread gathers must be pre-computed via reciprocity for data collected with off-end acquisition geometries. Off-end gathers will not contain (nor therefore predict) emerging rays which pierce the acquisition surface in front of the boat. This may increase the size of the computational domain used for propagating each individual shot-record. The cost increase by performing two imaging conditions is not severe, as the cost of calculating an imaging condition with in-line is usually a fraction of the cost of a shot-profile migration. Therefore, whenever a shot-profile migration is being performed, it may be advantageous to generate the IS-SRMP even if a data-space elimination effort has already been performed.
Given a reasonably accurate velocity model for migration, it is only necessary to compute O(10) subsurface offsets. This results in many fewer traces involved in calculating the multiple prediction than the O(1000) offsets collected at the surface. This savings will be offset however by the need to convolve the traces at every depth level, O(100), of the image-space rather than just at the surface. Whatever the balance of floating-point operations for a particular survey, the convenience of being able to manufacture the multiple prediction during another required processing step will save file manipulation, sorting, and overhead costs. Further, this technique can also be used in a target oriented fashion by simply not calculating the multiple prediction where it is not needed, e.g. at shallow depths.
The quality of the multiple prediction produced in the image-space with this technique is independent of the accuracy of the velocity model used during the migration. The multiple prediction, propagated with the same velocity model, will be kinematically accurate with the location of any multiples in the migrated image. Though both the image and the multiple prediction may be incorrect due to the use of an inaccurate velocity model, it has to correspond with the image constructed with the same extrapolation operators and velocity model. Due to the squaring of the wavelet when convolving the data, the multiple prediction can not be directly subtracted from the data or the image. However, deconvolution imaging conditions or a-priori wavelet deconvolution can make great strides in this direction.
While IS-SRMP, by definition, produces only surface-related multiples, the technique could be manipulated to address strong multiple generators in the subsurface. A topic for further research, we believe a layer-stripping type approach could be used when the location of problematic multiple generators is well constrained. By redatuming to the top of a multiple generator, the technique described above can be started at this deeper depth with the modeled multiples now referencing the new datum surface rather than the acquisition surface.