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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.

Seismic imaging provides much of our information about the Earth's crustal structure. The principal source of imaging errors derives from simplistic modelled predictions of the complex, scattered wavefields that interact with each subsurface point to be imaged. A new method of wavefield extrapolation based on inverse scattering theory in mathematical physics produces accurate estimates of these subsurface scattered wavefields, while still using relatively little information about the Earth's properties. We use it for the first time to create real target-oriented seismic images of a North Sea field. We synthesise underside illumination from surface reflection data, and use it to reveal subsurface features that are not present in an image from conventional migration of surface data. To reconstruct underside reflections, we rely on the so-called downgoing focusing function, whose coda consists entirely of transmission-born multiple scattering. As such, with the method presented here, we provide the first field data example of reconstructing underside reflections with contributions from transmitted multiples, without the need to first locate or image any reflectors in order to reconstruct multiple scattering effects.

Cross‐hole radar tomography is a useful tool for mapping shallow subsurface electrical properties viz. dielectric permittivity and electrical conductivity. Common practice is to invert cross‐hole radar data with ray‐based tomographic algorithms using first arrival traveltimes and first cycle amplitudes. However, the resolution of conventional standard ray‐based inversion schemes for cross‐hole ground‐penetrating radar (GPR) is limited because only a fraction of the information contained in the radar data is used. The resolution can be improved significantly by using a full‐waveform inversion that considers the entire waveform, or significant parts thereof. A recently developed 2D time‐domain vectorial full‐waveform cross‐hole radar inversion code has been modified in the present study by allowing optimized acquisition setups that reduce the acquisition time and computational costs significantly. This is achieved by minimizing the number of transmitter points and maximizing the number of receiver positions. The improved algorithm was employed to invert cross‐hole GPR data acquired within a gravel aquifer (4–10 m depth) in the Thur valley, Switzerland. The simulated traces of the final model obtained by the full‐waveform inversion fit the observed traces very well in the lower part of the section and reasonably well in the upper part of the section. Compared to the ray‐based inversion, the results from the full‐waveform inversion show significantly higher resolution images. At either side, 2.5 m distance away from the cross‐hole plane, borehole logs were acquired. There is a good correspondence between the conductivity tomograms and the natural gamma logs at the boundary of the gravel layer and the underlying lacustrine clay deposits. Using existing petrophysical models, the inversion results and neutron‐neutron logs are converted to porosity. Without any additional calibration, the values obtained for the converted neutron‐neutron logs and permittivity results are very close and similar vertical variations can be observed. The full‐waveform inversion provides in both cases additional information about the subsurface. Due to the presence of the water table and associated refracted/reflected waves, the upper traces are not well fitted and the upper 2 m in the permittivity and conductivity tomograms are not reliably reconstructed because the unsaturated zone is not incorporated into the inversion domain.

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.

High-contrast layers caused by porosity or clay content changes can have a dominant effect on hydraulic processes within an aquifer. These layers can act as low-velocity waveguides for GPR waves. We used a field example from a hydrological test site in Switzerland to show that fullwaveform inversion of crosshole GPR signals could image a subwavelength thickness low-velocity waveguiding layer. We exploited the full information content of the data, whereas ray-based inversion techniques are not able to image such thin waveguide layers because they only exploit the first-arrival times and first-cycle amplitudes. This lowvelocity waveguide layer is caused by an increase in porosity and indicates a preferential flow path within the aquifer. The waveguide trapping causes anomalously high amplitudes and elongated wavetrains to be observed for a transmitter within the waveguide and receivers straddling the waveguide depth range. The excellent fit of amplitudes and phase between the measured and modeled data confirms its presence. This new method enables detailed aquifer characterization to accurately predict transport and flow and can be applied to a wide range of geologic, hydrological, and engineering investigations.

Standard seismic processing steps such as velocity analysis and reverse time migration (imaging) usually assume that all reflections are primaries: Multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts. Many suppression methods are relatively ineffective for internal multiples. We show how to predict and remove internal multiples using Marchenko autofocusing and seismic interferometry. We first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected, up- and downgoing Green’s functions from virtual sources in the subsurface. We then generate the relevant up- and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing. Then, we convolve purely scattered components of up- and downgoing Green’s functions to reconstruct only the internal multiple field, which is adaptively subtracted from the measured data. Crucially, this is all possible without detailed modeled information about the earth’s subsurface. The method only requires surface reflection data and estimates of direct (nonreflected) arrivals between subsurface virtual sources and the acquisition surface. The method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used.

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