Seismic images provided by reverse time migration can be contaminated by artefacts associated with the migration of multiples. Multiples can corrupt seismic images, producing both false positives, that is by focusing energy at unphysical interfaces, and false negatives, that is by destructively interfering with primaries. Multiple prediction/primary synthesis methods are usually designed to operate on point source gathers and can therefore be computationally demanding when large problems are considered. A computationally attractive scheme that operates on plane-wave datasets is derived by adapting a data-driven point source gathers method, based on convolutions and cross-correlations of the reflection response with itself, to include plane-wave concepts. As a result, the presented algorithm allows fully data-driven synthesis of primary reflections associated with plane-wave source responses. Once primary plane-wave responses are estimated, they are used for multiple-free imaging via plane-wave reverse time migration. Numerical tests of increasing complexity demonstrate the potential of the proposed algorithm to produce multiple-free images from only a small number of plane-wave datasets.

In recent years, a variety of Marchenko methods for the attenuation of internal multiples has been developed. These methods have been extensively tested on two-dimensional synthetic data and applied to two-dimensional field data, but only little is known about their behaviour on three-dimensional synthetic data and three-dimensional field data. Particularly, it is not known whether Marchenko methods are sufficiently robust for sparse acquisition geometries that are found in practice. Therefore, we start by performing a series of synthetic tests to identify the key acquisition parameters and limitations that affect the result of three-dimensional Marchenko internal multiple prediction and subtraction using an adaptive double-focusing method. Based on these tests, we define an interpolation strategy and use it for the field data application. Starting from a wide azimuth dense grid of sources and receivers, a series of decimation tests are performed until a narrow azimuth streamer geometry remains. We evaluate the effect of the removal of sail lines, near offsets, far offsets and outer cables on the result of the adaptive double-focusing method. These tests show that our method is most sensitive to the limited aperture in the crossline direction and the sail line spacing when applying it to synthetic narrow azimuth streamer data. The sail line spacing can be interpolated, but the aperture in the crossline direction is a limitation of the acquisition. Next, we apply the adaptive Marchenko double-focusing method to the narrow azimuth streamer field data from the Santos Basin, Brazil. Internal multiples are predicted and adaptively subtracted, thereby improving the geological interpretation of the target area. These results imply that our adaptive double-focusing method is sufficiently robust for the application to three-dimensional field data, although the key acquisition parameters and limitations will naturally differ in other geological settings and for other types of acquisition.

Acoustic inversion in one-dimension gives impedance as a function of travel time. Inverting the reflection response is a linear problem. Recursive methods, from top to bottom or vice versa, are known and use a fundamental wave field that is computed from the reflection response. An integral over the solution to the Marchenko equation, on the other hand, retrieves the impedance at any vertical travel time instant. It is a non-recursive method, but requires the zero-frequency value of the reflection response. These methods use the same fundamental wave field in different ways. Combining the two methods leads to a non-recursive scheme that works with finite-frequency bandwidth. This can be used for target-oriented inversion. When a reflection response is available along a line over a horizontally layered medium, the thickness and wave velocity of any layer can be obtained together with the velocity of an adjacent layer and the density ratio of the two layers. Statistical analysis over 1000 noise realizations shows that the forward recursive method and the Marchenko-type method perform well on computed noisy data.

Seismic anisotropy is a unique observational tool for remotely studying deformation and stress within the Earth. Effects of anisotropy can be seen in seismic data; they are due to mineral alignment, fractures or layering. Seismic anisotropy is linked to local stress and strain, allowing modern geophysics to derive geomechanical properties from seismic data for supporting well planning and fracking. For unravelling anisotropic properties of the crust, the teleseismic receiver functions methodology has started to be widely applied recently due to its ability in retrieving the three-dimensional characteristics of the media sampled by the waves. The applicability of this technique is tested here by a field test carried out around the Kontinental Tiefbohrung site in southeastern Germany. We compare our results to previous investigations of the metamorphic rock pile of the Zone Erbendorf-Vohenstrauss, drilled down to 9 km depth, which sampled an alternating sequence of paragneiss and amphibolite, in which a strong foliation has been produced by ductile deformation. The application of the receiver functions reveals the presence of two distinct anisotropic layers within the metamorphic rock pile at 0-4 km and below 6 km depth, with up to 8% anisotropy; the depth of these two layers corresponds to the location of mica-rich paragneiss which show intense foliation, and finally proves the relation between the signal in the receiver functions, rock texture and presence of cracks. We have now the capability of providing insights from passive seismic data on geomechanical properties of the rocks, useful for geological exploration and engineering purposes, which will help influencing expensive drilling decisions thanks to future application of this seismic technique.

Passive seismic methods have been proven successful in recent years at retrieving information about the large-scale structure of a sedimentary basin. These methods are based on ambient noise recordings, and local and distant (teleseismic) earthquake data. In particular, it has been previously observed that the arrival time of teleseismic P-waves recorded inside a sedimentary basin shows time delays and polarization that both strongly depend on the basin properties and structure. In this paper, we present a new methodology for determining seismic P-wave velocity in a sedimentary basin, based on the time delay of a teleseismic P-wave travelling through the low-velocity basin infill, with respect to a teleseismic wave recorded outside the basin. The new methodology is developed in a Bayesian framework and, thus, it includes estimates of the uncertainties of the P-wave velocities. For this study, we exploit synchronous recordings of teleseismic P-wave arrivals at a dense linear array of broadband seismic stations, using data from two teleseismic events coming from two different incoming angles. The results obtained by the new proposed methodology are successfully compared to classical cross-correlation measurements, and are used to infer properties of a sedimentary basin, such as the basin bounding fault's geometry and the average P-wave velocity of the sedimentary basin fill.

A focussing function is a specially constructed field that focusses on to a purely downgoing pulse at a specified subsurface position upon injection into the medium. Such focussing functions are key ingredients in the Marchenko method and in its applications such as retrieving Green's functions, redatuming, imaging with multiples and synthesizing the response of virtual sources/receiver arrays at depth. In this study, we show how the focussing function and its corresponding focussed response at a specified subsurface position are heavily influenced by the aperture of the source/receiver array at the surface. We describe such effects by considering focussing functions in the context of time-domain imaging, offering explicit connections between time processing and Marchenko focussing. In particular, we show that the focussed response radiates in the direction perpendicular to the line drawn from the centre of the surface data array aperture to the focussed position in the time-imaging domain, that is, in time-migration coordinates. The corresponding direction in the Cartesian domain follows from the sum (superposition) of the time-domain direction and the directional change due to time-to-depth conversion. Therefore, the result from this study provides a better understanding of focussing functions and has implications in applications such as the construction of amplitude-preserving redatuming and imaging, where the directional dependence of the focussed response plays a key role in controlling amplitude distortions.