Data-driven retrieval of primary plane-wave responses.

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.

Wavefield finite time focusing with reduced spatial exposure.

Wavefield focusing is often achieved by time-reversal mirrors, where wavefields emitted by a source located at the focal point are evaluated at a closed boundary and sent back, after time-reversal, into the medium from that boundary. Mathematically, time-reversal mirrors are derived from closed-boundary integral representations of reciprocity theorems. In heterogeneous media, time-reversal focusing theoretically involves in- and output signals that are infinite in time and the resulting waves propagate through the entire medium. Recently, integral representations have been derived for single-sided wavefield focusing. Although the required input signals for this approach are finite in time, the output signals are not and, similar to time-reversal mirroring, the resulting waves propagate through the entire medium. Here, an alternative solution for double-sided wavefield focusing is derived. This solution is based on an integral representation where in- and output signals are finite in time, and where the energy of the waves propagating in the layer embedding the focal point is smaller than with time-reversal focusing. The potential of the proposed method is explored with numerical experiments involving a head model consisting of a skull enclosing a brain.

Uncertainty loops in travel-time tomography from nonlinear wave physics.

Estimating image uncertainty is fundamental to guiding the interpretation of geoscientific tomographic maps. We reveal novel uncertainty topologies (loops) which indicate that while the speeds of both low- and high-velocity anomalies may be well constrained, their locations tend to remain uncertain. The effect is widespread: loops dominate around a third of United Kingdom Love wave tomographic uncertainties, changing the nature of interpretation of the observed anomalies. Loops exist due to 2nd and higher order aspects of wave physics; hence, although such structures must exist in many tomographic studies in the physical sciences and medicine, they are unobservable using standard linearized methods. Higher order methods might fruitfully be adopted.

Elastodynamic Green's function retrieval through single-sided Marchenko inverse scattering.

The solution of the inverse scattering problem for the one-dimensional Schrödinger equation is given by the Marchenko equation. Recently, a Marchenko-type equation has been derived for three-dimensional (3D) acoustic wave fields, whose solution has been shown to recover the Green's functions from points within the medium to its exterior, using only single-sided scattered data. Here we extend this approach to 3D vectorial wave fields that satisfy the elastodynamic wave equation and recover Green's functions from points interior to an elastic, solid-state medium from purely external and one-sided measurements. The method is demonstrated in a solid-earth-like model to construct Green's functions using only subsurface sources, from earth-surface force and deformation sources and particle velocity and stress measurements.

Physical and non-physical energy in scattered wave source-receiver interferometry.

Source-receiver interferometry allows Green's functions between sources and receivers to be estimated by means of convolution and cross-correlation of other wavefields. Source-receiver interferometry has been observed to work surprisingly well in practical applications when theoretical requirements (e.g., complete enclosing 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 in space which are controlled purely by medium heterogeneity and receiver locations. By contrast, application of source-receiver interferometry constructs at least kinematic information about physically scattered waves between a source and a receiver by cross-convolution of scattered waves propagating from and to any 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 energy in the constructed Green's function to be identified and ignored. Further, source-receiver interferometry (which includes a step of inter-receiver interferometry) turns all types of non-physical or spurious energy deriving from inter-receiver interferometry into what appears to be physical energy. This explains in part why source-receiver interferometry may perform relatively well compared to inter-receiver interferometry when constructing scattered wavefields.