ALBERT

Description: We analyse the physics and geometry of trade-offs between Earth structure and noise sources in interstation noise correlations. Our approach is based on the computation of off-diagonal Hessian elements that describe the extent to which variations in noise sources can compensate for variations in Earth structure without changing the misfit beyond the measurement uncertainty. Despite the fact that all ambient noise inverse problems are special in terms of their receiver configuration and data, some general statements concerning source-structure trade-offs can be made: (i) While source-structure trade-offs may be reduced to some extent by clever measurement design, there are inherent trade-offs that can generally not be avoided. These inherent trade-offs may lead to a mispositioning of structural heterogeneities when the noise source distribution is unknown. (ii) When attenuation is weak, source-structure trade-offs in ambient noise correlations are a global phenomenon, meaning that there is no noise source perturbation that does not trade-off with some Earth structure, and vice versa. (iii) The most significant source-structure trade-offs occur within two elliptically shaped regions connecting a potential noise source perturbation to each one of the receivers. (iv) Far from these elliptical regions, only small-scale structure can trade off against changes in the noise source. (v) While source-structure trade-offs mostly decay with increasing attenuation, they are nearly unaffected by attenuation when the noise source perturbation is located near the receiver-receiver line. This work is intended to contribute to the development of joint source-structure inversions of ambient noise correlations, and in particular to an understanding of the extent to which source-structure trade-offs may be reduced. It furthermore establishes the foundation of future resolution analyses that properly quantify trade-offs between noise sources and Earth structure.

Description: We develop and apply a full waveform inversion method that incorporates seismic data on a wide range of spatio-temporal scales, thereby constraining the details of both crustal and upper-mantle structure. This is intended to further our understanding of crust–mantle interactions that shape the nature of plate tectonics, and to be a step towards improved tomographic models of strongly scale-dependent earth properties, such as attenuation and anisotropy. The inversion for detailed regional earth structure consistently embedded within a large-scale model requires locally refined numerical meshes that allow us to (1) model regional wave propagation at high frequencies, and (2) capture the inferred fine-scale heterogeneities. The smallest local grid spacing sets the upper bound of the largest possible time step used to iteratively advance the seismic wave field. This limitation leads to extreme computational costs in the presence of fine-scale structure, and it inhibits the construction of full waveform tomographic models that describe earth structure on multiple scales. To reduce computational requirements to a feasible level, we design a multigrid approach based on the decomposition of a multiscale earth model with widely varying grid spacings into a family of single-scale models where the grid spacing is approximately uniform. Each of the single-scale models contains a tractable number of grid points, which ensures computational efficiency. The multi-to-single-scale decomposition is the foundation of iterative, gradient-based optimization schemes that simultaneously and consistently invert data on all scales for one multi-scale model. We demonstrate the applicability of our method in a full waveform inversion for Eurasia, with a special focus on Anatolia where coverage is particularly dense. Continental-scale structure is constrained by complete seismic waveforms in the 30–200 s period range. In addition to the well-known structural elements of the Eurasian mantle, our model reveals a variety of subtle features, such as the Armorican Massif, the Rhine Graben and the Massif Central. Anatolia is covered by waveforms with 8–200 s period, meaning that the details of both crustal and mantle structure are resolved consistently. The final model contains numerous previously undiscovered structures, including the extension-related updoming of lower-crustal material beneath the Menderes Massif in western Anatolia. Furthermore, the final model for the Anatolian region confirms estimates of crustal depth from receiver function analysis, and it accurately explains cross-correlations of ambient seismic noise at 10 s period that have not been used in the tomographic inversion. This provides strong independent evidence that detailed 3-D structure is well resolved.

Description: Many studies have sought to seismically image plumes rising from the deep mantle in order to settle the debate about their presence and role in mantle dynamics, yet the predicted seismic signature of realistic plumes remains poorly understood. By combining numerical simulations of flow, mineral-physics constraints on the relationships between thermal anomalies and wave speeds, and spectral-element method based computations of seismograms, we estimate the delay times of teleseismic S and P waves caused by thermal plumes. Wave front healing is incomplete for seismic periods ranging from 10 s (relevant in traveltime tomography) to 40 s (relevant in waveform tomography). We estimate P -wave delays to be immeasurably small (〈0.3 s). S -wave delays are larger than 0.4 s even for S waves crossing the conduits of the thinnest thermal plumes in our geodynamic models. At longer periods (〉20 s), measurements of instantaneous phase misfit may be more useful in resolving narrow plume conduits. To detect S -wave delays of 0.4–0.8 s and the diagnostic frequency dependence imparted by plumes, it is key to minimize the influence of the heterogeneous crust and upper mantle. We argue that seismic imaging of plumes will advance significantly if data from wide-aperture ocean-bottom networks were available since, compared to continents, the oceanic crust and upper mantle are relatively simple.

Description: We develop and apply a novel technique to image ambient seismic noise sources. It is based on measurements of cross-correlation asymmetry defined as the logarithmic energy ratio of the causal and anticausal branches of the cross-correlation function. A possible application of this technique is to account for the distribution of noise sources, a problem which currently poses obstacles to noise-based surface wave dispersion analysis and waveform inversion. The particular asymmetry measurement used is independent of absolute noise correlation amplitudes. It is shown how it can be forward-modelled and related to the noise source power-spectral density using adjoint methods. Simplified sensitivity kernels allow us to rapidly image variations in the power-spectral density of noise sources. This imaging method correctly accounts for viscoelastic attenuation and is to first order insensitive to unmodelled Earth structure. Furthermore, it operates directly on noise correlation data sets. No additional processing is required, which makes the method fast and computationally inexpensive. We apply the method to three vertical-component cross-correlation data sets of different spatial and temporal scales. Processing is deliberately minimal so as to keep observations consistent with the imaging concept. In accord with previous studies, we image seasonally changing sources of the Earth's hum in the Atlantic, Pacific and the Southern Ocean. The sources of noise in the microseismic band recorded at stations in Switzerland are predominantly located in the Atlantic and show a clear dependence on both season and frequency. Our developments are intended as a step towards full 3-D inversions for the sources of ambient noise in various frequency bands, which may ultimately lead to improvements of noise-based structural imaging.

Description: 〈span〉〈div〉Abstract〈/div〉Our physical understanding of earthquakes, along with our ability to forecast them, is hampered by limited indications on the current and future state of stress on faults. Integrating indirect observations, laboratory experiments and physics-based numerical modeling to quantitatively estimate this evolution is crucial. However, quantitative integrations are tenuous in light of the scarcity and uncertainty of observations and the difficulty of modelling the physics governing earthquakes. We show that observations and prior physical knowledge, along with their errors, can be efficiently integrated through the statistical framework of ensemble data assimilation (EDA), which is adopted from weather forecasting. To evaluate whether fault stress estimation and forecasting is possible, we perform a perfect model test in a subduction zone setup that mimicks a scaled laboratory experiment. Synthetic noised data on velocities and stresses from one point near the surface are assimilated using an Ensemble Kalman Filter. These data update the velocity and stress states throughout 150 ensemble members, whose dynamics is governed by a seismic cycle model. This visco-elasto-plastic forward model forecasts the system’s evolution through solving Navier-Stokes equations with a strongly rate-dependent friction coefficient. The ensemble assimilation of data from a single location already provides probabilistic estimates of fault stress and dynamic strength evolution, which capture the true solution exceptionally well. This is possible, because the sampled error covariance matrix contains prior information from the physics that relates velocities, stresses and pressure at the surface to those at the fault. In the analysis step, this covariance allows stress and strength distributions to be reconstructed. In the subsequent forecast step the physical equations are solved to propagate the updated states forward in time. This provides probabilistic information on the likelihood of occurrence of the next earthquake in this synthetic laboratory setting. Throughout the ensemble simulations the forecasting ability for large, quasi-periodic events turns out to be significantly better than that of a periodic recurrence model. For example, it only requires an alarm to sound for 17% instead of 68% of the time to forecast 70% of 21 events. We show that combining our prior knowledge of physical laws with observations through a Bayesian framework provides distinct added value with respect to using observations or numerical models independently. This educational test thus shows vast potential for including physics-based information into probabilistic seismic hazard assessment using ensemble data assimilation. However, assumptions on an exact representation of the physics in a 2D simplified system remain to be explored to analyze its real world potential.〈/span〉

Description: Kunz M, Hess C, Raumonen P, Bienert A, Hackenberg J, Maas HG, Härdtle W, Fichtner A, von Oheimb G COMPARISON OF WOOD VOLUME ESTIMATES OF YOUNG TREES FROM TERRESTRIAL LASER SCAN DATA Abstract : Many analyses in ecology and forestry require wood volume estimates of trees. However, non-destructive measurements are not straightforward because trees are differing in their three-dimensional structures and shapes. In this paper we compared three methods (one voxel-based and two cylinder-based methods) for wood volume calculation of trees from point clouds obtained by terrestrial laser scanning. We analysed a total of 24 young trees, composed of four different species ranging between 1.79 m to 7.96 m in height, comparing the derived volume estimates from the point clouds with xylometric reference volumes for each tree. We found that both voxel- and cylinder-based approaches are able to compute wood volumes with an average accuracy above 90% when compared to reference volumes. The best results were achieved with the voxel-based method (r2 = 0.98). Cylinder-model based methods (r2 = 0.90 and 0.92 respectively) did perform slightly less well but offer valuable additional opportunities to analyse structural parameters for each tree. We found that the error of volume estimates from point clouds are strongly species-specific. Therefore, species-specific parameter sets for point-cloud based wood volume estimation methods are required for more robust estimates across a number of tree species. Keywords : Mixed Forests, Quantitative Structure Models, Voxel-based, Xylometry iForest 10 (2): 451-458 (2017) - doi: 10.3832/ifor2151-010 http://iforest.sisef.org/contents/?id=ifor2151-010

Description: 〈span〉〈div〉Summary〈/div〉We present the theory for and applications of Hamiltonian Monte Carlo (HMC) solutions of linear and nonlinear tomographic problems. HMC rests on the construction of an artificial Hamiltonian system where a model is treated as a high-dimensional particle moving along a trajectory in an extended model space. Using derivatives of the forward equations, HMC is able to make long-distance moves from the current towards a new independent model, thereby promoting model independence, while maintaining high acceptance rates. Following a brief introduction to HMC using common geophysical terminology, we study linear (tomographic) problems. Though these may not be the main target of Monte Carlo methods, they provide valuable insight into the geometry and the tuning of HMC, including the design of suitable mass matrices, and the length of Hamiltonian trajectories. This is complemented by a self-contained proof of the HMC algorithm in the Appendix. A series of tomographic/imaging examples is intended to illustrate (i) different variants of HMC, such as constrained and tempered sampling, (ii) the independence of samples produced by the HMC algorithm, and (iii) the effects of tuning on the number of samples required to achieve practically useful convergence. Most importantly, we demonstrate the combination of HMC with adjoint techniques. This allows us to solve a fully nonlinear, probabilistic traveltime tomography with several thousand unknowns on a standard laptop computer, without any need for supercomputing resources.〈/span〉

Description: 〈span〉〈div〉SUMMARY〈/div〉We propose a theory for rotational and strain ambient noise interferometry, motivated by the recent development of rotational ground motion sensors and distributed acoustic sensing (DAS) technology. In this context, we demonstrate that displacement, strain and rotation interferograms can be generically written in the form of a representation theorem, that is, as a solution to the seismic wave equation that we refer to as the interferometric wavefield. The physical quantity (displacement, strain or rotation) determines the distributed source of the interferometric wavefield, as well as an observational operator that extracts the correct type of noise correlation function. The proposed interferometric equations are free of assumptions on the distribution of noise sources or the equipartitioning of the ambient field, typically required for Green’s function retrieval. In addition to being valid for any kind of heterogeneous source and visco-elastic medium, they allow us to account for measurement details, such as the gauge length in DAS. We illustrate the practical feasibility of our approach with a series of numerical examples, based on regional-scale, spectral-element simulations of the interferometric wavefield. Specifically, we compare displacement and strain interferograms for homogeneous and heterogeneous Earth models, and for homogeneous and heterogeneous noise sources. Ultimately, our developments are intended to enable adjoint-based waveform inversion with emerging measurement technologies that provide spatial gradient information in addition to conventional seismic displacement recordings.〈/span〉

Description: We present a method for the computation of finite-frequency sensitivity kernels for two-station surface wave measurements. It is based on the combination of spectral-element modelling of seismic wave propagation, adjoint techniques and traveltime estimates from two-station cross-correlations of seismograms. The analysis of sensitivity kernels for a 1-D earth model resulted in two major conclusions: (1) The finite-frequency sensitivity is zero along the interstation ray path for group velocity measurements obtained by cross-correlations. It follows that interstation group velocity measurements should not be made by cross-correlation if a ray-based interpretation is used. (2) Although sensitivity along the interstation ray path is dominant for phase velocity measurements, sensitivity far from the ray path can be large, depending on the details of the source–receiver geometry. The complexities of finite-frequency two-station sensitivity kernels should be taken into account to avoid misinterpretations and to improve the quality of tomographic inversions.