SUMMARY Elastic Full Waveform Tomography (FWT) aims to reduce the misfit between recorded and modelled data, to deduce a very detailed model of elastic material parameters in the underground. The choice of the elastic model parameters to be inverted affects the convergence and quality of the reconstructed subsurface model. Using the Cross‐Triangle‐Squares (CTS) model three elastic parametrizations, Lamé parameters m1 = [λ, μ, ρ], seismic velocities m2 = [Vp, Vs, ρ] and seismic impedances m3 = [Ip, Is, ρ] for far‐offset reflection seismic acquisition geometries with explosive point sources and free‐surface condition are studied. In each CTS model the three elastic parameters are assigned to three different geometrical objects that are spatially separated. The results of the CTS model study reveal a strong requirement of a sequential frequency inversion from low to high frequencies to reconstruct the density model. Using only high‐frequency data, cross‐talk artefacts have an influence on the quantitative reconstruction of the material parameters, while for a sequential frequency inversion only structural artefacts, representing the boundaries of different model parameters, are present. During the inversion, the Lamé parameters, seismic velocities and impedances could be reconstructed well. However, using the Lamé parametrization ‐artefacts are present in the λ model, while similar artefacts are suppressed when using seismic velocities or impedances. The density inversion shows the largest ambiguity for all parametrizations. However, the artefacts are again more dominant, when using the Lamé parameters and suppressed for seismic velocity and impedance parametrization. The afore mentioned results are confirmed for a geologically more realistic modified Marmousi‐II model. Using a conventional streamer acquisition geometry the P‐velocity, S‐velocity and density models of the subsurface were reconstructed successfully and are compared with the results of the Lamé parameter inversion.

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We present a new global model of spherical gravimetric terrain corrections that take into account the gravitational attraction of Earth's global topographic masses at 3″ (~90 m) spatial resolution. The conversion of Shuttle Radar Topography Mission‐based digital elevation data to implied gravity effects relies on the global evaluation of Newton's law of gravitation, which represents a computational challenge for 3″ global topography data. We tackled this task by combining spatial and spectral gravity forward modeling techniques at the 0.2‐mGal accuracy level and used advanced computational resources in parallel to complete the 1 million CPU‐hour‐long computation within ~2 months. Key outcome is a 3″ map of topographic gravity effects reflecting the total gravitational attraction of Earth's global topography at ~28 billion computation points. The data, freely available for use in science, teaching, and industry, are immediately applicable as new in situ terrain correction to reduce gravimetric surveys around the globe.

Three‐dimensional elastic full‐waveform inversion aims to reconstruct elastic material properties of 3D structures in the subsurface with high resolution. Here we present an implementation of 3D elastic full‐waveform inversion based on the adjoint‐state method. The code is optimized regarding runtime and storage costs by using a time‐frequency approach. The gradient is computed from monochromatic frequency‐domain particle‐velocity wavefields calculated with a time‐domain velocity‐stress finite‐difference scheme. The 3D full‐waveform inversion was applied to data of a complex random medium model, which resembles a realistic crystalline rock environment. We show synthetic inversion results of P‐wave and S‐wave velocities for two transmission geometries: (1) a 3D acquisition geometry with planes of sources and receivers and (2) a 2D geometry with two lines of sources and receivers, resembling a realistic two‐borehole geometry. The 3D inversion of data acquired with 3D source‐receiver geometry is capable to reconstruct differently sized 3D structures of shear and compressional velocities with resolution of about a wavelength. The 3D random medium data recorded with 2D acquisition geometry were inverted using 3D inversion and 2D full‐waveform inversion for comparison. The 2D inversion suffers from strong artefacts that are caused by 3D scattering. The multiparameter 3D inversion, by contrast, is capable to invert the 3D scattered waves and to reconstruct 3D structures up to about 1–2 wavelengths adjacent to the plane between sources and receivers. The resolution is lower compared to the 3D acquisition geometry result. Still, a 3D inversion of cross‐hole data can be beneficial compared to a 2D inversion in the presence of complex 3D small‐scale heterogeneities, as it is capable to resolve 3D structures next to the source‐receiver plane.

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