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At interfaces between porous media acoustic energy can be converted into electromagnetic energy or vice versa by the electrokinetic effect. Operators exist describing this conversion, however these act on (one-way) upgoing and downgoing waves, while in nature only the total (two-way) wavefield exists. In this thesis mathematical formulations are developed for the source decomposition operator, describing the relation between the two-way source wavefield and the one-way downgoing wavefield, and for the receiver composition operator, describing the relation between the one-way upgoing wavefield and the two-way wavefield at the receivers. The behavior of these operators is visualized by numerical modeling.

Seismic interferometry is a technique by which the Green’s function (or impulse response) between two receivers can be acquired from the crosscorrelations of wavefield responses at these receivers. Recent developments of this method has led researchers to exploit active as well as passive seismic wavefields to retrieve surface wave Green’s functions by crosscorrelation. The primary objective of these applications has been to gain near surface resolution from the high frequency content of the active data while gaining greater depth resolution from the low frequency content of the passive data. In these applications however, a Green’s function is retrieved for each data type and therefore a matching filter or a form of joint inversion is required to benefit from the additional bandwidth of both data types. Interferometry by multidimensional deconvolution (MDD) is a relatively new method of Green’s function retrieval that provides several advantages over interferometry by crosscorrelation. This thesis proposes a new method of merging active and passive data during the process of MDD. A primary advantage of this method over the alternatives is that the source signatures are disregarded and only a single Green’s function with the combined characteristics of both the active and passive data is retrieved. Using numerical modelling it is demonstrated that a broadband Green’s function response can be retrieved from combined active and passive data without the need to compensate for the differences in source signatures or variations in amplitude. Merging active and passive data prior to deconvolution may in fact improve the retrieved response due to the additional illumination provided by the supplementary data. In addition to expanding the bandwidth of the retrieved response, this method is shown to be capable of using data from one source type to spatially infill gaps in illumination in another source type when the bandwidth of the two are comparable.

To evaluate the subsurface, seismic surveys are carried out. A requirement for the processing of these data is that it is dense and regularly sampled and it should also include the near-offsets. Because these data cannot be acquired in practice for towed marine surveys, it should be obtained by inter- and extrapolation. The first objective of this report was to give an overview of the methods which already exist for the inter- and extrapolation of seismic data. Only the most important methods are described, because the total number of methods is too large. They are first explained and finally classified into the three main categories: Wave-equation based methods, Domain transform methods and Prediction-Error-Filter methods. The other objective of this thesis was to explain and test the Mixed domain reconstruction method. It is based on the Polya-Plancherel theorem, which states that band-limited data in one domain has infinite support in the other domain. This theorem makes it possible to reconstruct the missing seismic data. A conjugate gradient method is used in the optimization part of the implementation. The method was tested for its interpolating qualities and it was shown that it works very well. For extrapolation, the data should be transformed into a ‘split-spread’ configuration instead of the ‘end-on’ configuration which is typical for towed marine surveys. With this transformation, the near-offset gap is filled accurately. It was also shown that the error increases for larger gaps and that the method is limited by the offset and not by the number of traces. The method works in the frequency domain, but a time domain implementation of the algorithm was generated which gave promising results. Finally, the method can handle a wide variety of datasets: low quality data, conflicting dip data, dual-sensor data and real data. The conclusion of this report is that the Mixed domain reconstruction method works very well and can be applied to many types of seismic data. It was demonstrated that a dense and regularly sampled dataset can be obtained which contains also the near-offset.

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.

We introduce seismic interferometry of passive data by multidimensional deconvolution (MDD) as an alternative to the crosscorrelation method. Interferometry by MDD has the potential to correct for the effects of source irregularity, assuming the first arrival can be separated from the full response. MDD applications can range from reservoir imaging using microseismicity to crustal imaging with teleseismic data.

Acoustic, electromagnetic, elastodynamic, poroelastic, and electroseismic waves are all governed by a unified matrix-vector wave equation. The matrices in this equation obey the same symmetry properties for each of these wave phenomena. This implies that the wave vectors for each of these phenomena obey the same reciprocity theorems. By substituting Green's matrices in these reciprocity theorems, unified wavefield representations are obtained. Analogous to the well-known acoustic wavefield representations, these unified representations find applications in geophysical modeling, migration, inversion, multiple elimination, and interferometry.

Abstract not available