· · · Institutional Repository

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.

Until now, seismic processing has been carried out by applying inverse filters in the forward data space. Because the acquired data of a seismic survey is always discrete, seismic measurements in the forward data space can be arranged conveniently in a data matrix (P). Each column in the data matrix represents one shot record. If we represent seismic data in the temporal frequency domain, then each matrix element consists of a complex-valued number. Considering the dominant role of multiple scattering in seismic data, it is proposed to replace data matrix P by its inverse P–1 before starting seismic processing. Making use of the feedback model for seismic data, multiple scattered energy is mapped onto the zero time axis of the inverse data space. The practical consequence of this remarkable property may be significant: multiple elimination in the inverse data space simplifies to removing data at zero time only. Moving to the inverse data space may cause a fundamental change in the way we preprocess and image seismic data.

The theory of iterative surface-related multiple elimination holds for 2D as well as 3D wavefields. The 3D prediction of surface multiples, however, requires a dense and extended distribution of sources and receivers at the surface. Since current 3D marine acquisition geometries are very sparsely sampled in the crossline direction, the direct Fresnel summation of the multiple contributions, calculated for those surface positions at which a source and a receiver are present, cannot be applied without introducing severe aliasing effects. In this newly proposed method, the regular Fresnel summation is applied to the contributions in the densely sampled inline direction, but the crossline Fresnel summation is replaced with a sparse parametric inversion. With this procedure, 3D multiples can be predicted using the available input data. The proposed method is demonstrated on a 3D synthetic data set as well as on a 3D marine data set from offshore Norway.

Removal of surface and internal multiples can be formulated by removing the influence of downward-scattering boundaries and downward-scattering layers. The involved algorithms can be applied in a model-driven or a data-driven way. A unified description is proposed that relates both types of algorithms based on wave theory. The algorithm for the removal of surface multiples shows that muted shot records play the role of multichannel prediction filters. The algorithm for the removal of internal multiples shows that muted CFP gathers play the role of multichannel prediction filters. The internal multiple removal algorithm is illustrated with numerical examples. The conclusion is that the layer-related version of the algorithm has significant practical advantages.

One application of seismic interferometry is to retrieve the impulse response (Green's function) from crosscorrelation of ambient seismic noise. Various researchers show results for retrieving the surface-wave part of the Green's function. However, reflection retrieval has proven more challenging. We crosscorrelate ambient seismic noise, recorded along eight parallel lines in the Sirte basin east of Ajdabeya, Libya, to obtain shot gathers that contain reflections. We take advantage of geophone groups to suppress part of the undesired surface-wave noise and apply frequency-wavenumber filtering before crosscorrelation to suppress surface waves further. After comparing the retrieved results with data from an active seismic exploration survey along the same lines, we use the retrieved reflection data to obtain a migrated reflection image of the subsurface.

We modeled time-domain EM measurements of induction currents for marine and land applications with a frequency-domain code. An analysis of the computational complexity of a number of numerical methods shows that frequency-domain modeling followed by a Fourier transform is an attractive choice if a sufficiently powerful solver is available. A recently developed, robust multigrid solver meets this requirement. An interpolation criterion determined the automatic selection of frequencies. The skin depth controlled the construction of the computational grid at each frequency. Tests of the method against exact solutions for some simple problems and a realistic marine example demonstrate that a limited number of frequencies suffice to provide time-domain solutions after piecewise-cubic Hermite interpolation and a fast Fourier transform.

A method for the efficient computation of multifrequency focal beams for 3D seismic acquisition geometry analysis has been developed. By computing them for all the frequency components of seismic data, single-frequency focal beams can be extended to multifrequency focal beams. However, this straightforward method involves considerable computer time and memory requirements, especially in complex media settings. Therefore, we propose a rapid 3D multifrequency focal beam method in which only a few single-frequency focal beam computations are followed by a number of smart interpolations. The 3D wavefield extrapolation in the focal beam analysis is conducted by the combined applications of a 3D degenerate Fourier migrator and a 3D Born-Kirchhoff interpolation operator, a process that reduces the computational cost for complex media. The multifrequency focal beam analysis is applied to a 3D model from an oil field of China, demonstrating how spatial sampling differences affect seismic imaging.

This paper focuses on the concept of using blended data and multiple scattering directly in the migration process, meaning that the blended input data for the proposed migration algorithm includes blended surface-related multiples. It also means that both primary and multiple scattering contribute to the seismic image of the subsurface. Essential in our approach is that multiples are not included in the Green's functions but are part of the incident wavefields, utilizing the so-called double illumination property. We find that complex incident wavefields, such as blended primaries and/or blended multiples, require a reformulation of the imaging principle in order to provide broadband angle-dependent reflection properties.

Deblending of simultaneous-source data is usually considered to be an underdetermined inverse problem, which can be solved by an iterative procedure, assuming additional constraints like sparsity and coherency. By exploiting the fact that seismic data are spatially band-limited, deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constraints. We applied the method with numerically modeled data and it suppressed the crosstalk well, when the blended data consisted of responses to adjacent, densely sampled sources

Accurate removal of surface-related multiples remains a challenge in many cases. To overcome typical inaccuracies in current multiple-removal techniques, we have developed a new primary-estimation method: estimation of primaries by sparse inversion (EPSI). EPSI is based on the same primary-multiple model as surface-related multiple elimination (SRME) and also requires no subsurface model. Unlike SRME, EPSI estimates the primaries as unknowns in a multidimensional inversion process rather than in a subtraction process. Furthermore, it does not depend on interpolated missing near-offset data because it can reconstruct missing data simultaneously. Sparseness plays a key role in the new primary-estimation procedure. The method was tested on 2D synthetic data.

Macroscopic measurements of electrical resistivity require frequency-dependent effective models that honor the microscopic effects observable in macroscopic measurements. Effective models based on microscopic physics exist alongside with empirical models. We adopted an empirical model approach to modify an existing physical model. This provided a description of electrical resistivity as a function of not only frequency, but also water saturation. We performed two-electrode laboratory measurements of the complex resistivity on a number of fine and medium-grained unconsolidated sand packs saturated with water of three different salinities. For frequencies between 0.1 and 1 MHz, the data were fitted with the new model and compared to fits with Archie’s law. Our model described the relaxation times and DC resistivity values as negative exponential functions with increasing water saturation. All data could be accurately described as a function of frequency and water saturation with nine parameters.

With seismic interferometry one can retrieve the response to a virtual source inside an unknown medium, if there is a receiver at the position of the virtual source. Using inverse scattering theory, we demonstrate that, for a 1D medium, the requirement of having an actual receiver inside the medium can be circumvented, going beyond seismic interferometry. In this case, the wavefield can be focused inside an unknown medium with independent variations in velocity and density using reflection data only.