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Many geophysical inverse problems are known to be ill-posed and, thus, requiring some kind of regularization in order to provide a unique and stable solution. A possible approach to overcome the inversion ill-posedness consists in constraining the position of the model interfaces. For a grid-based parameterization, such a structurally constrained inversion can be implemented by adopting the usual smooth regularization scheme in which the local weight of the regularization is reduced where an interface is expected. By doing so, sharp contrasts are promoted at interface locations while standard smoothness constraints keep affecting the other regions of the model. In this work, we present a structurally constrained approach and test it on the inversion of frequency-domain electromagnetic induction (FD-EMI) data using a regularization approach based on the Minimum Gradient Support stabilizer, which is capable to promote sharp transitions everywhere in the model, i.e., also in areas where no structural a prioriinformation is available. Using 1D and 2D synthetic data examples, we compare the proposed approach to a structurally constrained smooth inversion as well as to more standard (i.e., not structurally constrained) smooth and sharp inversions. Our results demonstrate that the proposed approach helps in finding a better and more reliable reconstruction of the subsurface electrical conductivity distribution, including its structural characteristics. Furthermore, we demonstrate that it allows to promote sharp parameter variations in areas where no structural information are available. Lastly, we apply our structurally constrained scheme to FD-EMI field data collected at a field site in Eastern Germany to image the thickness of peat deposits along two selected profiles. In this field example, we use collocated constant offset ground-penetrating radar (GPR) data to derive structural a priori information to constrain the inversion of the FD-EMI data. The results of this case study demonstrate the effectiveness and flexibility of the proposed approach.
The main scope of the InterPACIFIC (Intercomparison of methods for site parameter and velocity profile characterization) project is to assess the reliability of in-hole and surface-wave methods, used for estimating shear wave velocity. Three test-sites with different subsurface conditions were chosen: a soft soil, a stiff soil and a rock outcrop. This paper reports the surface-wave methods results. Specifically 14 teams of expert users analysed the same experimental surface-wave datasets, consisting of both passive and active data. Each team adopted their own strategy to retrieve the dispersion curve and the shear-wave velocity profile at each site. Despite different approaches, the dispersion curves are quite in agreement with each other. Conversely, the shear-wave velocity profiles show a certain variability that increases in correspondence of major stratigraphic interfaces. This larger variability is mainly due to non-uniqueness of the solution and lateral variability. As expected, the observed variability in V-s,V-30 estimatesis small, as solution non-uniqueness plays a limited role. (C) 2015 Elsevier Ltd. All rights reserved.
We present an integrated approach for deriving the 1D shear wave velocity (Vs) information at few tens to hundreds of meters down to the first strong impedance contrast in typical sedimentary environments. We use multiple small aperture seismic arrays in 1D and 2D configuration to record active and passive seismic surface wave data at two selected geotechnical sites in Germany (Horstwalde & Lobnitz). Standard methods for data processing include the Multichannel Analysis of Surface Waves (MASW) method that exploits the high frequency content in the active data and the sliding window frequency-wavenumber (f-k) as well as the spatial autocorrelation (SPAC) methods that exploit the low frequency content in passive seismic data. Applied individually, each of the passive methods might be influenced by any source directivity in the noise wavefield. The advantages of active shot data (known source location) and passive microtremor (low frequency content) recording may be combined using a correlation based approach applied to the passive data in the so called Interferometric Multichannel Analysis of Surface Waves (IMASW). In this study, we apply those methods to jointly determine and interpret the dispersion characteristics of surface waves recorded at Horstwalde and Lobnitz. The reliability of the dispersion curves is controlled by applying strict limits on the interpretable range of wavelengths in the analysis and further avoiding potentially biased phase velocity estimates from the passive f-k method by comparing to those derived from the SPatial AutoCorrelation method (SPAC). From our investigation at these two sites, the joint analysis as proposed allows mode extraction in a wide frequency range (similar to 0.6-35 Hz at Horstwalde and similar to 1.5-25 Hz at Lobnitz) and consequently improves the Vs profile inversion. To obtain the shear wave velocity profiles, we make use of a global inversion approach based on the neighborhood algorithm to invert the interpreted branches of the dispersion curves. Within the uncertainty given by the apparent spread of forward models we find that besides a well defined sediment velocity range also a reasonable minimum estimate of bedrock depth and bedrock velocity can be achieved. The Vs estimate for the best model in Horstwalde ranges from similar to 190 m/s at the surface up to similar to 390 m/s in the bottom of the soft sediment column. The bedrock starts earliest around 200 m depth and bedrock velocities are higher than 1000 m/s. In Lobnitz, we observe slightly lower velocities for the sediments (similar to 165-375 m/s for the best model) and a minimum thickness of 75 m. (C) 2016 Elsevier B.V. All rights reserved.
Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy
(2015)
To analyse and invert refraction seismic travel time data, different approaches and techniques have been proposed. One common approach is to invert first-break travel times employing local optimization approaches. However, these approaches result in a single velocity model, and it is difficult to assess the quality and to quantify uncertainties and non-uniqueness of the found solution. To address these problems, we propose an inversion strategy relying on a global optimization approach known as particle swarm optimization. With this approach we generate an ensemble of acceptable velocity models, i.e., models explaining our data equally well. We test and evaluate our approach using synthetic seismic travel times and field data collected across a creeping hillslope in the Austrian Alps. Our synthetic study mimics a layered near-surface environment, including a sharp velocity increase with depth and complex refractor topography. Analysing the generated ensemble of acceptable solutions using different statistical measures demonstrates that our inversion strategy is able to reconstruct the input velocity model, including reasonable, quantitative estimates of uncertainty. Our field data set is inverted, employing the same strategy, and we further compare our results with the velocity model obtained by a standard local optimization approach and the information from a nearby borehole. This comparison shows that both inversion strategies result in geologically reasonable models (in agreement with the borehole information). However, analysing the model variability of the ensemble generated using our global approach indicates that the result of the local optimization approach is part of this model ensemble. Our results show the benefit of employing a global inversion strategy to generate near-surface velocity models from refraction seismic data sets, especially in cases where no detailed a priori information regarding subsurface structures and velocity variations is available.
We study systematically the estimation of Earth's core angular momentum (CAM) variation between 1962.0 and 2008.0 by using core surface flow models derived from the recent geomagnetic field model C(3)FM2. Various flow models are derived by changing four parameters that control the least squares flow inversion. The parameters include the spherical harmonic (SH) truncation degree of the flow models and two Lagrange multipliers that control the weights of two additional constraints. The first constraint forces the energy spectrum of the flow solution to follow a power law l-p, where l is the SH degree and p is the fourth parameter. The second allows to modulate the solution continuously between the dynamical states of tangential geostrophy (TG) and tangential magnetostrophy (TM). The calculated CAM variations are examined in reference to two features of the observed length-of-day (LOD) variation, namely, its secular trend and 6year oscillation. We find flow models in either TG or TM state for which the estimated CAM trends agree with the LOD trend. It is necessary for TM models to have their flows dominate at planetary scales, whereas TG models should not be of this scale; otherwise, their CAM trends are too steep. These two distinct types of flow model appear to correspond to the separate regimes of previous numerical dynamos that are thought to be applicable to the Earth's core. The phase of the subdecadal CAM variation is coherently determined from flow models obtained with extensively varying inversion settings. Multiple sources of model ambiguity need to be allowed for in discussing whether these phase estimates properly represent that of Earth's CAM as an origin of the observed 6year LOD oscillation.
Characterizing the local site response in large cities is an important step towards seismic hazard assessment. To this regard, single station seismic noise measurements were carried out at 146 sites in the northern part of Santiago de Chile. This extensive survey allowed the fundamental resonance frequency of the sedimentary cover, derived from horizontal-to-vertical (H/V) spectral ratios, to be mapped. By inverting the spectral ratios under the constraint of the thickness of the sedimentary cover, known from previous gravimetric measurements, local S-wave velocity profiles have been retrieved. After interpolation between the individual profiles, the resulting high resolution 3D S-wave velocity model allows the entire area, as well as deeper parts of the basin, to be represented in great detail. Since one lithology shows a great scatter in the velocity values only a very general correlation between S-wave velocity in the uppermost 30 m (v(s)(30)) and local geology is found. Local S-wave velocity profiles can serve as a key factor in seismic hazard assessment, since they allow an estimate of the amplification potential of the sedimentary cover. Mapping the intensity distribution of the 27 February 2010 Maule, Chile, event (Mw = 8.8) the results indicate that local amplification of the ground motion might partially explain the damage distribution and encourage the use of the low cost seismic noise techniques for the study of seismic site effects.