S U M M A R YClaerbout's daylight imaging concept is generalized to a theory of interferometric seismic imaging (II). Interferometric seismic imaging is defined to be any algorithm that inverts correlated seismic data for the reflectivity or source distribution. As examples, we show that II can image reflectivity distributions by migrating ghost reflections in passive seismic data and generalizes the receiver-function imaging method used by seismologists. Interferometric seismic imaging can also migrate free-surface multiples in common depth point (CDP) data and image source distributions from passive seismic data. Both synthetic and field data examples are used to illustrate the different possibilities of II. The key advantage of II is that it can image source locations or reflectivity distributions from passive seismic data where the source position or wavelet is unknown. In some cases it can mitigate defocusing errors as a result of statics or an incorrect migration velocity. The main drawback with II is that severe migration artefacts can be created by partial focusing of virtual multiples.

We develop a waveform-tomography method for estimating the velocity distribution that minimizes the waveform misfit between the predicted and observed early arrivals in space-time seismograms. By fitting the waveforms of early arrivals, early arrival waveform tomography (EWT) naturally takes into account more general wave-propagation effects compared to the high-frequency method of traveltime tomography, meaning that EWT can estimate a wider range of slowness wavenumbers. Another benefit of EWT is more reliable convergence compared to full-waveform tomography, because an early-arrival misfit function contains fewer local minima. Synthetic test results verify that the waveform tomogram is much more accurate than the traveltime tomogram and that this algorithm has good convergence properties. For marine data from the Gulf of Mexico, the statics problem caused by shallow, gassy muds was attacked by using EWT to obtain a more accurate velocity model. Using the waveform tomogram to correct for statics, the stacked section was significantly improved compared to using the normal move-out (NMO) velocity, and moderately improved compared to using the traveltime tomogram. Inverting high-resolution land data from Mapleton, Utah, showed an EWT velocity tomogram that was more consistent with the ground truth (trench log) than the traveltime tomogram. Our results suggest that EWT can provide supplemental, shorter-wavelength information compared to the traveltime tomogram for both shallow and moderately deep seismic data.

The theory and practice of refraction interferometry is presented. We show that the crosscorrelation between a nearby pair of refraction traces yields a head wave event kinematically equivalent to one generated by a source at position x along the refractor. This redatumed source location x is independent of the surface source location, so that all head waves arrive at the same time in a redatumed common geophone-pair gather (CPG). Thus, the traces in a redatumed CPG can be stacked together to yield an N-fold refraction trace, and combining different trace pairs yields N-fold refraction shot gathers. The benefits are that traveltime picking errors can be greatly reduced for noisy head wave arrivals such as far offset refraction events or secondary head-wave arrivals. We also show that head-wave events in a redatumed common geophonepair gather will follow a flat trajectory in offset-time coordinates compared to the curved trajectory of a diving wave event. Thus, head waves can be distinguished from diving waves using redatumed CPGs, with the possibility of estimating the type of velocity gradient along an interface. This might be important for determining the lithology associated with important interfaces such as the Moho or an oil/gas bearing boundary.

A B S T R A C TMultiples contain valuable information about the subsurface, and if properly migrated can provide a wider illumination of the subsurface compared to imaging with VSP primary reflections. In this paper we review three different methods for migrating multiples. The first method is model-based, and it is more sensitive to velocity errors than primary migration; the second method uses a semi-natural Green's function for migrating multiples, where part of the traveltimes are computed from the velocity model, and part of the traveltimes (i.e., natural traveltimes) are picked from the data to construct the imaging condition for multiples; the third method uses cross-correlation of traces. The last two methods are preferred in the sense that they are significantly less sensitive to velocity errors and statics because they use "natural data" to construct part of the migration imaging conditions. Compared with the interferometric (i.e., crosscorrelation) imaging method the semi-natural Green's function method is more computationally efficient and is sometimes less prone to migration artifacts.Numerical tests with 2-D and 3-D VSP data show that a wider subsurface coverage, higher-fold and more balanced illumination of the subsurface can be achieved with multiple migration compared with migration of primary reflections only. However, there can be strong interference from multiples with different orders or primaries when multiples of high order are migrated. One possible solution is to filter primaries and different orders of multiples before migration, and another possible solution is least squares migration of all events. A limitation of multiple migration is encountered for subsalt imaging. Here, the multiples must pass through the salt body more than twice, which amplifies the distortion of the image.