2,739 research outputs found
Sensitivity of Rayleigh wave ellipticity and implications for surface wave inversion
No full textThe use of Rayleigh wave ellipticity has gained increasing popularity in recent years for investigating earth structures, especially for near-surface soil characterization. In spite of its widespread application, the sensitivity of the ellipticity function to the soil structure has been rarely explored in a comprehensive and systematic manner. To this end, a new analytical method is presented for computing the sensitivity of Rayleigh wave ellipticity with respect to the structural parameters of a layered elastic half-space. This method takes advantage of the minor decomposition of the surface wave eigenproblem and is numerically stable at high frequency. This numerical procedure allowed to retrieve the sensitivity for typical near surface and crustal geological scenarios, pointing out the key parameters for ellipticity interpretation under different circumstances. On this basis, a thorough analysis is performed to assess how ellipticity data can efficiently complement surface wave dispersion information in a joint inversion algorithm. The results of synthetic and real-world examples are illustrated to analyse quantitatively the diagnostic potential of the ellipticity data with respect to the soil structure, focusing on the possible sources of misinterpretation in data inversion
Global surface wave inversion with model constraints
No full textPractical applications of surface wave inversion demand reliable inverted shear-wave profiles and a rigorous assessment of the uncertainty associated to the inverted parameters. As a matter of fact, the surface wave inverse problem is severely affected by solution non-uniqueness: the degree of non-uniqueness is closely related to the complexity of the observed dispersion pattern and to the experimental inaccuracies in dispersion measurements. Moreover, inversion pitfalls may be connected to specific problems such as inadequate model parametrization and incorrect identification of the surface wave modes. Consequently, it is essential to tune the inversion problem to the specific dataset under examination to avoid unnecessary computations and possible misinterpretations. In the heuristic inversion algorithm presented in this paper, different types of model constraints can be easily introduced to bias constructively the solution towards realistic estimates of the 1D shear-wave profile. This approach merges the advantages of global inversion, like the extended exploration of the parameter space and a theoretically rigorous assessment of the uncertainties on the inverted parameters, with the practical approach of Lagrange multipliers, which is often used in deterministic inversion, which helps inversion to converge towards models with desired properties (e.g., 'smooth' or 'minimum norm' models). In addition, two different forward kernels can be alternatively selected for direct-problem computations: either the conventional modal inversion or, instead, the direct minimization of the secular function, which allows the interpreter to avoid mode identification. A rigorous uncertainty assessment of the model parameters is performed by posterior covariance analysis on the accepted solutions and the modal superposition associated to the inverted models is investigated by full-waveform modelling. This way, the interpreter has several tools to address the more probable sources of inversion pitfalls within the framework of a rigorous and well-tested global inversion algorithm. The effectiveness and the versatility of this approach, as well as the impact of the interpreter's choices on the final solution and on its posterior uncertainty, are illustrated using both synthetic and real data. In the latter case, the inverted shear velocity profiles are blind compared with borehole data. © 2010 European Association of Geoscientists & Engineers
Computation of partial derivatives of Rayleigh-wave phase velocity using second-order subdeterminants
No full textRayleigh-wave propagation in a layered, elastic earth model is frequency-dependent (dispersive) and also function of the S-wave velocity, the P-wave velocity, the density and the thickness of the layers. Inversion of observed surface wave dispersion curves is used in many fields, from seismology to earthquake and environmental engineering. When normal-mode dispersion curves are clearly identified from recorded seismograms, they can be used as input for a so-called surface wave 'modal' inversion, mainly to assess the 1-D profile of S-wave velocity. When using 'local' inversion schemes for surface wave modal inversion, calculation of partial derivatives of dispersion curves with respect to layer parameters is an essential and time-consuming step to update and improve the earth model estimate. Accurate and high-speed computation of partial derivatives is recommended to achieve practical inversion algorithms. Analytical methods exist to calculate the partial derivatives of phase-velocity dispersion curves. In the case of Rayleigh waves, they have been rarely compared in terms of accuracy and computational speed. In order to perform such comparison, we hereby derive a new implementation to calculate analytically the partial derivatives of Rayleigh-mode dispersion curves with respect to the layer parameters of a 1-D layered elastic half-space. This method is based on the Implicit Function Theorem and on the Dunkin restatement of the Haskell recursion for the calculation of the Rayleigh-wave dispersion function. The Implicit Function Theorem permits calculation of the partial derivatives of modal phase velocities by partial differentiation of the dispersion function. Using a recursive scheme, the partial derivatives of the dispersion function are derived by a layer stacking procedure, which involves the determination of the analytical partial derivatives of layer matrix subdeterminants of order two. The resulting algorithm is compared with methods based on the more widely used variational theory in terms of accuracy and computational speed
Very Fast Simulated Annealing Surface Wave Inversion with Model Constraints
No full textGeophysical Inversion is an ill-posed problem that is inherently affected by the non-uniqueness of the solution. Moreover, several peculiar aspects characterize the surface wave inverse problem as the associated forward problem is implicit, modal identification is often difficult and higher mode solutions may not even exist for certain frequency ranges. To this end, the use of a priori information is of great help in reducing the solution ambiguities. In the heuristic inversion algorithm presented in this note, mathematical measures of the desired nature of the inverted models (e.g. smooth or minimum norm solutions) are introduced into the objective function to bias constructively the solution towards realistic estimates of the ID shear wave profile. In the inversion algorithm, two different forward kernels can be alternatively selected for the direct problem computation: the conventional modal inversion based on modal identification, or the direct minimization of the secular function, to avoid possible pitfalls associated with an ambiguous mode identification of the observed dispersion pattern. The versatility of the inversion algorithm is illustrated using both synthetic and real data. In the latter case, the inverted shear velocity profiles are blind compared with crosshole results. Copyright 2009, European Association of Geoscientists and Engineers
Effectiveness of group velocity analysis of surface waves for near surface characterization
No full textIn earthquake seismology, group velocity of surface waves is widely used to infer the interior structure of the Earth. Robust techniques exist to compute the group velocity spectrum, also for single trace data. This feature, when applied to shallow shear-wave characterization, seems to be very appealing to practitioners for reducing field operations. The main problem concerning the application of group velocity measurements to active seismograms for shallow targets is the interference between the modes, especially at short offsets. The main objective of this work is to analyse the potential of group velocity dispersion for near surface characterization, with particular focus on signal discrimination, sensitivity with respect to the soil structure and possible sources of interpretation pitfalls. Our analysis demonstrate that the sensitivities and the depth of penetration of group velocity data are almost similar to phase velocity ones. Consequently, when the dispersion analysis is based on active multichannel arrays, group velocity does not add much information to the inversion process. On the other hand, the possibility of using single station measurements has a great value in all those situations when data are fundamental-mode dominated or the deployment of large arrays is not feasible, such as in urban areas
Sensitivity analysis of rayleigh-wave ellipticity with application to near surface characterization
No full textThe joint inversion of surface-wave measurements and Rayleigh-wave ellipticity has gained popularity in recent years for near-surface soil characterization. The common approach is to use low-frequency, singlestation ellipticity data in conjunction with high-frequency dispersion measurements obtained employing small aperture arrays. A complete understanding of the diagnostic potential of ellipticity in such conditions can be assessed only with a complete sensitivity analysis. To this end, a new analytical method is presented for computing the sensitivity of Rayleigh-wave ellipticity with respect to the structural parameters of a layered elastic halfspace. This method employs a layer stacking procedure based on the subdeterminant formulation of the surface-wave forward problem and is numerically stable at high frequencies. The sensitivity of the ellipticity curve is then evaluated quantitatively with specific focus on near-surface examples and compared to the dispersion patterns and sensitivity of modal phase velocity. © (2015) by the European Association of Geoscientists & Engineers (EAGE)
Linearized inversion of MASW data using inequality constraints
No full textInequality constraint formulation of least squares inversion is a flexible method to insert physical constraints (as well as a priori information) into the inversion process. In MASW (Multichannel Analysis of Surface Waves) inversion this has proved to be useful to stabilize convergence when applied to fundamental-mode dominated data as well as to data containing higher modes of propagation. A reliable S-wave velocity profile can be obtained from inversion of surface wave data if all available information is inserted into the inversion algorithm
Addressing non-uniqueness in linearized multichannel surface wave inversion
No full textThe multichannel analysis of the surface waves method is based on the inversion of observed Rayleigh-wave phase-velocity dispersion curves to estimate the shear-wave velocity profile of the site under investigation. This inverse problem is nonlinear and it is often solved using 'local' or linearized inversion strategies. Among linearized inversion algorithms, least-squares methods are widely used in research and prevailing in commercial software; the main drawback of this class of methods is their limited capability to explore the model parameter space. The possibility for the estimated solution to be trapped in local minima of the objective function strongly depends on the degree of nonuniqueness of the problem, which can be reduced by an adequate model parameterization and/or imposing constraints on the solution. In this article, a linearized algorithm based on inequality constraints is introduced for the inversion of observed dispersion curves; this provides a flexible way to insert a priori information as well as physical constraints into the inversion process. As linearized inversion methods are strongly dependent on the choice of the initial model and on the accuracy of partial derivative calculations, these factors are carefully reviewed. Attention is also focused on the appraisal of the inverted solution, using resolution analysis and uncertainty estimation together with a posteriori effective-velocity modelling. Efficiency and stability of the proposed approach are demonstrated using both synthetic and real data; in the latter case, cross-hole S-wave velocity measurements are blind-compared with the results of the inversion process
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