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.
By solving a Marchenko equation, Green's functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are to be collected at the top of the medium. So far, an exact solution could only be obtained if the medium obeys stringent monotonicity conditions and if all forward-scattered (non-converted and converted) transmissions between the acquisition level and the inner depth level are known a-priori. We introduce an alternative Marchenko equation by revising the window operators that are applied in its derivation. We also introduce an auxiliary equation for transmission data, which are to be collected at the bottom of the medium, and a coupled equation, which is based on both reflection and transmission data. We show that the joint system of the Marchenko equation, the auxiliary equation and the coupled equation can be succesfully inverted when broadband reflection and transmission data are available. This results in a novel methodology for elastodynamic Green's function retrieval from two-sided data. Apart from these data, our approach requires P- and S-wave transmission times between the inner depth level and the top of the medium, as well as two angle-dependent amplitude scaling factors, which can be estimated from the data by enforcing energy conservation.
We show how to ‘fingerprint’ individual diffractors inside an acoustic medium using interrogative wave energy from arrays of sources and receivers. For any recorded multiply diffracted wave observed between any source and any receiver, the set of such fingerprints is sufficient information to identify all diffractors involved in the corresponding diffraction path, and the sequential order in which diffractors are encountered. The method herein thus decomposes complex, multiply diffracted wavefields into constituent, single-diffraction interactions.
Seismic interferometry comprises a suite of methods to redatum recorded wavefields to those that would have been recorded if different sources (so-called virtual sources) had been activated. Seismic interferometry by cross-correlation has been formulated using either two-way (for full wavefields) or one-way (for directionally decomposed wavefields) representation theorems. To obtain improved Green's function estimates, the cross-correlation result can be deconvolved by a quantity that identifies the smearing of the virtual source in space and time, the so-called point-spread function. This type of interferometry, known as interferometry by multidimensional deconvolution (MDD), has so far been applied only to one-way directionally decomposed fields, requiring accurate wavefield decomposition from dual (e.g. pressure and velocity) recordings. Here we propose a form of interferometry by multidimensional deconvolution that uses full wavefields with two-way representations, and simultaneously invert for pressure and (normal) velocity Green's functions, rather than only velocity responses as for its one-way counterpart. Tests on synthetic data show that two-way MDD improves on results of interferometry by cross-correlation, and generally produces estimates of similar quality to those obtained by one-way MDD, suggesting that the preliminary decomposition into up- and downgoing components of the pressure field is not required if pressure and velocity data are jointly used in the deconvolution. We also show that constraints on the directionality of the Green's functions sought can be added directly into the MDD inversion process to further improve two-way multidimensional deconvolution. Finally, as a by-product of having pressure and particle velocity measurements, we adapt one- and two-way representation theorems to convert any particle velocity receiver into its corresponding virtual dipole/gradient source by means of MDD. Thus data recorded from standard monopolar (e.g. marine) pressure sources can be converted into data from dipolar (derivative) sources at no extra acquisition cost.
Source-receiver interferometry is a technique that allows the Green’s functions between sources and receivers to be estimated by means of convolution and cross-correlation of other recorded wavefields. Source-receiver interferometry has been observed to work surprisingly well in practical applications when theoretical requirements (e.g. closed surrounding boundaries of other sources and receivers) are contravened: this paper contributes to explain why this may be true. Commonly-used inter-receiver interferometry requires wavefields to be generated around specific stationary points on the boundaries which are controlled purely by medium heterogeneity and receiver locations. By contrast, we show that source-receiver interferometry constructs at least kinematically correct physically scattered waves between a source and receiver by convolution of scattered data from and to any and all points on the boundary. This reduces the ambiguity in interpreting wavefields generated using source-receiver interferometry with only partial boundaries (as is standard in practical applications), as it allows spurious or non-physical events in the constructed Green’s function to be identified and either interpreted or ignored.
Summary The Marchenko method is capable to create virtual sources inside a medium that is only accessible from an open-boundary. The resulting virtual data can be used to retrieve images free of artefacts caused by internal multiples. Conventionally, the Marchenko method retrieves a so-called focusing wavefield that focuses the data from the recording surface to a point inside the medium. Recently, it was suggested to modify the focusing condition such that the new focusing wavefield creates a virtual plane wave source inside the medium, instead of a virtual point source. The virtual plane wave data can be used to image an entire surface inside the medium in a single step rather than imaging individual points on the surface. Consequently, the imaging process is accelerated significantly. We provide an extension of plane wave Marchenko redatuming for elastodynamic waves and demonstrate its performance numerically.
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