The theory of seismic interferometry predicts that the cross-correlation (and possibly summation) between seismic recordings at two separate receivers allows the retrieval of an estimate of the inter-receiver response, or Green's function, from a virtual source at one of the receiver positions. Ideally, the recordings must consist of the responses from a homogeneous distribution of seismic sources that effectively surround the receivers. This principle has successfully been exploited to retrieve from recorded passive data more easily usable and interpretable responses. In fact, the retrieval of virtual-source responses has led to a wide range of applications, including for controlled-source seismic surveys. The latter is the case for data-driven methods for redatuming reflection data to a receiver level below the source-acquisition surface, or methods to suppress surface waves in land seismic data.
In this thesis, I studied the application of seismic interferometry to surface reflection data, that is, reflection data acquired with both sources and receivers at or near the earth's surface. This is a typical configuration for seismic exploration, either in land or marine surveys. The retrieval of additional virtual sources at receiver locations in that configuration would result in having effectively more shot points. Depending on whether the virtual-source responses contain relevant information, the combined source and virtual-source coverage could allow more complete illumination of the subsurface and so better imaging of its structures. This could be particularly the case for surveys with areas or directions poorly sampled by sources, including large gaps, but with receivers present. The main research questions are what are the conditions for retrieving useful virtual-source reflection responses and with what accuracy.
As I first show from mathematical derivations, the retrieval of virtual-source reflection responses from the application of seismic interferometry to exploration-type reflection data does not comply with several theoretical requirements. A major requirement is that the two considered receivers would need to be enclosed by a boundary of sources. This condition is obviously not fullfilled by the single-sided illumination as in exploration surveys. Consequently, as I show using modelled reflection data, the virtual-source reflection responses are retrieved with several distortions, including the presence of undesired non-physical reflection events.
Yet, in spite of the non-ideal single-sided configuration, cross-correlating the reflection records at receiver pairs and summing over source profiles allows retrieving virtual-source responses with relevant reflection signals. These virtual reflection signals are referred to as pseudo-physical reflections, as they share the same kinematics as physical reflections but contain distortions due to the {cross-correlation} process. By studying further the numerical examples, I determine the influence of several acquisition-related parameters and subsurface characteristics on the accuracy of the virtual-source reflection responses.
Then, based on a theoretical approach using the convolution-type reciprocity theorems, instead of the cross-correlation type, I show how part of the distortions in the virtual-source responses retrieved by cross-correlation could be reduced by performing a multidimensional-deconvolution operation. The potential benefits of multidimensional deconvolution are verified with a numerical example, showing that the obtained virtual-source reflection responses match better the reference physical responses.
In addition, I highlight the essential role of the surface-related multiples in the retrieval process of pseudo-physical reflections. In turn, the retrieved pseudo-physical reflections provide usable feedback about the surface multiples. In particular, I present a method based on the stationary-phase analysis of the retrieved pseudo-physical reflection arrivals for detecting surface-related multiple reflections in the acquired data. The results from tests on numerically modelled data show that this interferometric method allows identifying prominent surface multiples in a wide range of source-receiver offsets. Also, I determine that this correlation-based method performs still well even in the case of missing near-offset reflection data. This interesting property suggests that for robust prediction of multiples, the method could be further developed and complement convolution-based schemes which often suffer from missing near-offset data.
Still, the main objective in retrieving virtual-source responses is to obtain additional desirable shot points for improving processing or imaging. In general, interpolation techniques are applied to the seismic data to compensate for the irregularities of the acquisition geometry. However, most of the direct interpolation techniques do not allow retrieval of the missing data if the gap is larger than the Nyquist criterion. I show, using numerically modelled datasets, that in these challenging cases, decisive information for imaging may be obtained from the retrieval of virtual sources as long as surface-multiple energy is present in the shot records. In particular, I show that virtual images (obtained from retrieved virtual data) can reveal initially invisible structures in the images obtained from the uncomplete reflection data.
Finally, I apply seismic reflection interferometry on a 3D land seismic dataset to test further the practical feasibility of retrieving relevant virtual-source reflection responses. The survey was acquired at a mining site in a hard rock environment with recorded reflections characterized by a relatively poor signal-to-noise ratio. The first results presented in this thesis show evidences of retrieved pseudo-physical reflections. By testing different source contributions, these investigations also show that the retrieval of these desirable events may largely depend on the location and extent of the considered source patch with respect to the virtual source and receiver geometry.