Finite-difference methods for modeling seismic waves are known to be inaccurate when including a realistic topography, due to the large dispersion errors that appear in the modelled surface waves and the scattering introduced by the staircase approximation to the topography. As a consequence, alternatives to finite-difference methods have been proposed to circumvent these issues. We present a new numerical scheme for 3D elastic wave propagation in the presence of strong topography. This finite-difference scheme is based upon a staggered grid of the Lebedev type, or fully staggered grid (FSG). It uses a grid deformation strategy to make a regular Cartesian grid conform to a topographic surface. In addition, the scheme uses a mimetic approach to accurately solve the free-surface condition and hence allows for a less restrictive grid spacing criterion in the computations. The scheme can use high-order operators for the spatial derivatives and obtain low-dispersion results with as few as six points per minimum wavelength. A series of tests in 2D and 3D scenarios, in which our results are compared to analytical and numerical solutions obtained with other numerical approaches, validate the accuracy of our scheme. The resulting FSG mimetic scheme allows for accurate and efficient seismic wave modelling in the presence of very rough topographies with the advantage of using a structured staggered grid.
Full waveform inversion (FWI) is one of the most challenging procedures to obtain quantitative information of the subsurface. For elastic inversions, when both compressional and shear velocities have to be inverted, the algorithmic issue becomes also a computational challenge due to the high cost related to modelling elastic rather than acoustic waves. This shortcoming has been moderately mitigated by using high-performance computing to accelerate 3D elastic FWI kernels. Nevertheless, there is room in the FWI workflows for obtaining large speedups at the cost of proper grid pre-processing and data decimation techniques. In the present work, we show how by making full use of frequency-adapted grids, composite shot lists and a novel dynamic offset control strategy, we can reduce by several orders of magnitude the compute time while improving the convergence of the method in the studied cases, regardless of the forward and adjoint compute kernels used.
Geophysics 2 ABSTRACTFull Waveform Inversion (FWI) in seismic scenarios continues to be a complex procedure for subsurface imaging that might require extensive human interaction, in terms of model setup, constraints and data preconditioning. The underlying reason is the strong non-linearity of the problem that forces the addition of a priori knowledge (or bias) in order to obtain geologically sound results. In particular, when the use of long offset receiver is not possible or may not favor the reconstruction of the fine structure of the model, one needs to rely on reflection data. As a consequence, the inversion process is more prone to get stuck into local minima. It is then possible to take advantage of the cross-correlation error functional, less subject to starting models error, in order to output a suitable background model for inversion of reflection data. By combining these functionals, high-frequency data content with poor initial models can be successfully inverted. If we can find simple parameterizations for such functionals we can can reduce the amount of uncertainty and manual work related to tuning FWI. Thus FWI might become a semi-automatized imaging tool. I NTRODUCTIONFull Waveform Inversion (FWI) represents a seismic imaging method able to improve Earth structural models up to spatial resolutions beyond the limits of standard Travel Time Tomography (TTT), and more adequate for seismic imaging. TTT only inverts the time residuals of (mostly) P-wave phases picked on the recorded field traces, requiring human interaction.On the other hand, FWI processes the whole waveforms achieving a finer resolution. Nevertheless, given our surface to surface acquisition limitations, noise effects and initial models with poor Geophysics 3 low frequency content, convergence to the true model cannot be guaranteed. Among the strongest concerns when using FWI is the matching of synthetic and data phases when they are apart more than half a cycle in time, an effect known as cycle skipping (Luo and Schuster, 1991;Warner and Guasch, 2014; Metivier et al., 2016). Some functional have been developed over the last decades to cope with this issue: e.g the cross-correlation (CC) traveltime functional (Luo and Schuster, 1991), the adaptive FWI from Warner and Guasch (2014), or the optimal transport distance (Métivier et al., 2016). Although less sophisticated, the CC is able to provide good background models as reported by, e.g., Jimenez-Tejero et al. (2015), but lack in resolution. On
Height falls in construction work cause fatal or serious accidents every year. Safety devices used to avoid this are supposed to stop the falling worker by developing forces that are low enough to prevent serious injury being caused during the retention process.In this paper three safety systems are analysed: collective protection such as safety nets (V-type) or provisory edge protection (C-class guardrails) and personal fall arrest systems (with a harness).There are many biological and mechanical variables involved in the retention process. Maximum or minimum values are needed for kinetic energy to be absorbed; the forces against a retained worker or system deflection, respectively, are required by certain codes governing the safety systems. Other codes only establish limits for some of these variables. Code criteria about cited requirements are not homogeneous and sometimes they are even inadequate due to a lack of knowledge about the relationships and implications concerning the mechanical variables. The corresponding interaction is difficult to evaluate and requires expensive experimental studies to be carried out on instrumented real size samples.Nevertheless, in the last decade, research on safety systems has been done on refined finite element models that can perform dynamic simulations of the impact. This paper contains important conclusions drawn from the original contributions of authors that suggest making relevant improvements to some of the corresponding codes. Comparisons of cheaper numerical predictions and real size experiments have proved that finite element models can be reliably used to analyse and design these safety devices.
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