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Reply to comment on Shear wave profile from surface wave inversion: the impact of uncertainty on seismic site response analysis
No full textSocco et al (2012 J. Geophys. Eng. 9 241) comment on our study about the effect of non-uniqueness of surface wave solutions on seismic site response analysis. In particular, they refer to the approach we adopted for the selection of equivalent shear wave velocity profiles and argue that it leads to overestimation of the uncertainty due to the inherent ill-posedness of the problem. Moreover, for one of the synthetic cases of our original paper, they calculate a different set of equivalent velocity profiles, retrieving the corresponding amplification spectra. From these results, Socco et al claim that their general conclusion that the impact of solution non-uniqueness on seismic response simulations is negligible. In this reply we demonstrate that (a) the uncertainty bounds used by Socco et al in their prediction analysis, as a consequence of their surface wave inversion procedure, are unreasonably narrow; (b) consequently, their shaking predictions appear to suffer no impact from their underestimated uncertainty; and (c) their presented case shows an amplification spectrum that is only the result of assuming the existence of a bedrock at 150 m that causes resonance of the overlying layerpractically independent of the details of the S-wave velocity distribution
Sharp boundary inversion in crosswell travel-time tomography
No full textThe reconstruction of seismic images of the medium from crosswell travel-time data is a typical example of the ill-posed inverse problem. In order to obtain a stable solution and to replace an ill-posed problem by a well-posed one, a stabilizing functional (stabilizer) has to be introduced. The role of this functional is to select the desired stable solution from a class of solutions with specific physical and/or geometrical properties. One of these properties is the existence of sharp boundaries separating rocks with different petrophysical parameters, e.g., oil- and water-saturated reservoirs. In this paper, we develop a new tomographic method based on application of a minimum support stabilizer to the crosswell travel-time inverse problem. This stabilizer makes it possible to produce clear and focused images of geological targets with sharp boundaries. We demonstrate that the minimum support stabilizer allows a correct recovery of not only the shape but also the velocity value of the target. We also point out that this stabilizer provides good results even with a low ray density, when the traditional minimum norm stabilizer fails
Focused inversion of vertical radar profile (VRP) traveltime data
No full textThe reconstruction of the GPR velocity vertical profile from vertical radar profile (VRP) traveltime data is a problem with a finite number of measurements and imprecise data, analogous to similar seismic techniques, such as the shallow down-hole test used for S-wave velocity profiling or the vertical seismic profiling (VSP) commonly used in deeper exploration. The uncertainty in data accuracy and the error amplification inherent in deriving velocity estimates from gradients of arrival times make this an example of an ill-posed inverse problem. In the framework of Tikhonov regularization theory, ill-posedness can be tackled by introducing a regularizing functional (stabilizer). The role of this functional is to stabilize the numerical solution by incorporating the appropriate a priori assumptions about the geometrical and/or physical properties of the solution. One of these assumptions could be the existence of sharp boundaries separating rocks with different physical properties. We apply a method based on the minimum support stabilizer to the VRP traveltime inverse problem. This stabilizer makes it possible to produce more accurate profiles of geological targets with compact structure. We compare more traditional inversion results with our proposed compact reconstructions. Using synthetic examples, we demonstrate that the minimum support stabilizer allows an improved recovery of the profile shape and velocity values of blocky targets. We also study the stabilizer behavior with respect to different noise levels and different choices of the reference model. The proposed approach is then applied to real cases where VPRs have been used to derive moisture content profiles as a function of depth. In these real cases, the derived sharper profiles are consistent with other evidence, such as GPR zero-offset profiles, GPR reflections and known locations of the water table
Identification of lateral discontinuities via multi-offset phase analysis of surface wave data
No full textSurface wave methods are based on the inversion of observed Rayleigh wave phase-velocity dispersion curves. The goal is to estimate mainly the shear-wave velocity profile of the investigated site. The model used for the interpretation is 1D, hence results obtained wherever lateral variations are present cannot be considered reliable.
In this paper, we study four synthetic models, all with a lateral heterogeneity. When we process the entire corresponding seismograms with traditional f-k approach, the resulting 1D profiles are representative of the subsurface properties averaged over the whole length of the receivers lines. These results show that classical analysis disregards evidences of sharp lateral velocity changes even when they show up in the raw seismograms.
In our research, we implement and test over the same synthetic models, a novel robust automated method to check the appropriateness of 1D model assumption and locate the discontinuities. This new approach is a development of the recent multi-offset phase analysis with the following further advantages: it does not need previous noise evaluation and more than one shot.
Only once the discontinuities are clearly identified, we confidently perform classical f-k dispersion curve extraction and inversion separately on both sides of the discontinuity. Thus the final results, obtained by putting side by side the 1D profiles, are correct 2D reconstructions of the discontinuous S-wave distributions obtained without any additional ad-hoc hypotheses
Reconstruction, with tunable sparsity levels, of shear wave velocity profiles from surface wave data
Full text linkThe analysis of surface wave dispersion curves is a way to infer the vertical distribution of shear wave velocity. The range of applicability is extremely wide: going, for example, from seismological studies to geotechnical characterizations and exploration geophysics. However, the inversion of the dispersion curves is severely ill-posed and only limited efforts have been put in the development of effective regularization strategies. In particular, relatively simple smoothing regularization terms are commonly used, even when this is in contrast with the expected features of the investigated targets. To tackle this problem, stochastic approaches can be utilized, but they are too computationally expensive to be practical, at least, in case of large surveys. Instead, within a deterministic framework, we evaluate the applicability of a regularizer capable of providing reconstructions characterized by tunable levels of sparsity. This adjustable stabilizer is based on the minimum support regularization, applied before on other kinds of geophysical measurements, but never on surface wave data. We demonstrate the effectiveness of this stabilizer on (i) two benchmark—publicly available—data sets at crustal and near-surface scales and (ii) an experimental data set collected on a well-characterized site. In addition, we discuss a possible strategy for the estimation of the depth of investigation. This strategy relies on the integrated sensitivity kernel used for the inversion and calculated for each individual propagation mode. Moreover, we discuss the reliability, and possible caveats, of the direct interpretation of this particular estimation of the depth of investigation, especially in the presence of sharp boundary reconstructions
An efficient hybrid scheme for fast and accurate inversion of airborne transient electromagnetic data
No full textAirborne transient electromagnetic (TEM) methods target a range of applications that all rely on analysis of extremely large datasets, but with widely varying requirements with regard to accuracy and computing time. Certain applications have larger intrinsic tolerances with regard to modelling inaccuracy, and there can be varying degrees of tolerance throughout different phases of interpretation. It is thus desirable to be able to tune a custom balance between accuracy and compute time when modelling of airborne datasets. This balance, however, is not necessarily easy to obtain in practice. Typically, a significant reduction in computational time can only be obtained by moving to a much simpler physical description of the system, e.g. by employing a simpler forward model. This will often lead to a significant loss of accuracy, without an indication of computational precision. We demonstrate a tuneable method for significantly speeding up inversion of airborne TEM data with little to no loss of modelling accuracy. Our approach introduces an approximation only in the calculation of the partial derivatives used for minimising the objective function, rather than in the evaluation of the objective function itself. This methodological difference is important, as it introduces no further approximation in the physical description of the system, but only in the process of iteratively guiding the inversion algorithm towards the solution. By means of a synthetic study, we demonstrate how our new hybrid approach provides inversion speed-up factors ranging from ∼3 to 7, depending on the degree of approximation. We conclude that the results are near identical in both model and data space. A field case confirms the conclusions from the synthetic examples: that there is very little difference between the full nonlinear solution and the hybrid versions, whereas an inversion with approximate derivatives and an approximate forward mapping differs significantly from the other results
Assessment of Distributed Acoustic Sensing (DAS) performance for geotechnical applications
Full text linkDistributed Acoustic Sensing (DAS) is a recent technology that acquires acoustic vibrations via fiber optics sensors. The utilization of such technique for near-surface geotechnical applications has great potential, especially for the characterization and verification of artificially stabilized ground. A popular procedure to stabilize the superficial ground (for example, for the preparation of infrastructure subgrade) is the blend of the natural shallower layer with a binder (lime and/or cement). Quality control is required when the binder hardens, and acoustic surveys are an option for non-invasive and non-destructive testing. Relevant parameters to validate the effectiveness of the stabilization procedure are the mechanical properties of the materials. The distribution of shear-wave velocities in the ground is a critical parameter for the geotechnical characterization, since it depends directly on the shear-modulus of the media. The present experiment verifies the applicability of DAS technology in such geotechnical contexts, which can be representative of a wide range of utilizations, spanning, for example, from road and pavement design to building constructions. The discussed test focuses on the spectral content of the acquired signal and on the estimation of the shear-wave distribution, and compares the DAS responses against signals measured during more traditional seismic surveys using standard geophones. Despite the inevitable differences between the datasets collected with the different techniques, all the reconstructed shear-wave velocity profiles effectively identify the stabilized soil layer. Also for this reason, one of the main conclusions is that, for geotechnical characterizations, DAS can be a convenient non-invasive alternative to more standard approaches
1D Stochastic Inversion of Airborne Time-Domain Electromagnetic Data with Realistic Prior and Accounting for the Forward Modeling Error
Full text linkAirborne electromagnetic surveys may consist of hundreds of thousands of soundings. In most cases, this makes 3D inversions unfeasible even when the subsurface is characterized by a high level of heterogeneity. Instead, approaches based on 1D forwards are routinely used because of their computational efficiency. However, it is relatively easy to fit 3D responses with 1D forward modelling and retrieve apparently well-resolved conductivity models. However, those detailed features may simply be caused by fitting the modelling error connected to the approximate forward. In addition, it is, in practice, difficult to identify this kind of artifacts as the modeling error is correlated. The present study demonstrates how to assess the modelling error introduced by the 1D approximation and how to include this additional piece of information into a probabilistic inversion. Not surprisingly, it turns out that this simple modification provides not only much better reconstructions of the targets but, maybe, more importantly, guarantees a correct estimation of the corresponding reliability
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