We present a continuous model capable of demonstrating some salient features of aeolian sand ripples: the realistic asymmetric ripple shape, coarsening of the ripple field at the nonlinear stage of ripple growth, saturation of ripple growth for homogeneous sand, typical size segregation of sand, and formation of armoring layers of coarse particles on ripple crests and windward slopes if the sand is inhomogeneous.

[1] High-resolution seismic reflection surveys across active fault zones are capable of supplying key structural information required for assessments of seismic hazard and risk.We have recorded a 360 m long ultrahigh-resolution seismic reflection profile across the Alpine Fault in New Zealand. The Alpine Fault, a continental transform that juxtaposes major tectonic plates, is capable of generating large (M > 7.8) damaging earthquakes. Our seismic profile across a northern section of the fault targets fault zone structures in Holocene to late Pleistocene sediments and underlying Triassic and Paleozoic basement units from 3.5 to 150 m depth. Since ultrashallow seismic data are strongly influenced by near-surface heterogeneity and source-generated noise, an innovative processing sequence and nonstandard processing parameters are required to produce detailed information on the complex alluvial, glaciofluvial and glaciolacustrine sediments and shallow to steep dipping fault-related features. We present high-quality images of structures and deformation within the fault zone that extend and complement interpretations based on shallow paleoseismic and ground-penetrating radar studies. Our images demonstrate that the Alpine Fault dips 75°-80°to the southeast through the Quaternary sediments, and there is evidence that it continues to dip steeply between the shallow basement units. We interpret characteristic curved basement surfaces on either side of the Alpine Fault and deformation in the footwall as consequences of normal drag generated by the reverse-slip components of displacement on the fault. The fault dip and apparent $35 m vertical offset of the late Pleistocene erosional basement surface across the Alpine Fault yield a provisional dip-slip rate of 2.0 ± 0.6 mm/yr. The more significant dextral-slip rate cannot be determined from our seismic profile.

Seismic full-waveform inversion (FWI) is potentially a powerful method for obtaining high-resolution subsurface images, but the results are often distorted by nonlinear effects and parameter trade-offs. Such distortions can be particularly severe in the case of multiparameter FWI, such as elastic FWI, in which inversion is performed simultaneously for P- and S-wave velocities and density. The problem can be alleviated by adding constraints in the form of plausible a priori information. A usually well-justified constraint includes the structural similarity of different model parameters; i.e., an anomalous body likely exhibits variations in all elastic properties, although their magnitudes may be different. To consider such types of a priori information, we have developed a structurally constrained elastic FWI, which is based on minimization of the cross products of gradients of different model parameters. Our synthetic 2D experiments show that structurally constrained FWI can significantly improve model reconstruction. It is also demonstrated that our approach still leads to improved results, even when the structural similarity between the individual parameter types is not exactly met. Inversions of field data show that in comparison to conventional FWI, structurally constrained FWI is able to match the field data equally well while requiring less structural complexity of the subsurface.

Full waveform inversion (FWI) is an increasingly popular tool for analysing seismic data. Current practise is to record seismic data sets that are suitable for reflection processing, that is, a very dense spatial sampling and a high fold are required. Using tools from optimized experimental design (ED), we demonstrate that such a dense sampling is not necessary for FWI purposes. With a simple noise-free acoustic example, we show that only a few suitably selected source positions are required for computing high-quality images. A second, more extensive study includes elastic FWI with noise-contaminated data and free-surface boundary conditions on a typical near-surface setup, where surface waves play a crucial role. The study reveals that it is sufficient to employ a receiver spacing in the order of the minimum shear wavelength expected. Furthermore, we show that horizontally oriented sources and multicomponent receivers are the preferred option for 2-D elastic FWI, and we found that with a small amount of carefully selected source positions, similarly good results can be achieved, as if as many sources as receivers would have been employed. For the sake of simplicity, we assume in our simulations that the full data information content is available, but data pre-processing and the presence of coloured noise may impose restrictions. Our ED procedure requires an a priori subsurface model as input, but tests indicate that a relatively crude approximation to the true model is adequate. A further pre-requisite of our ED algorithm is that a suitable inversion strategy exists that accounts for the non-linearity of the FWI problem. Here, we assume that such a strategy is available. For the sake of simplicity, we consider only 2-D FWI experiments in this study, but our ED algorithm is sufficiently general and flexible, such that it can be adapted to other configurations, such as crosshole, vertical seismic profiling or 3-D surface setups, also including larger scale exploration experiments. It also offers interesting possibilities for analysing existing large-scale data sets that are too large to be inverted. With our methodology, it is possible to extract a small (and thus invertible) subset that offers similar information content as the full data set.

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