The single-station microtremor horizontal-to-vertical spectral ratio (MHVSR) method was initially proposed to retrieve the site amplification function and its resonance frequencies produced by ...unconsolidated sediments overlying high-velocity bedrock. Presently, MHVSR measurements are predominantly conducted to obtain an estimate of the fundamental site frequency at sites where a strong subsurface impedance contrast exists. Of the earthquake site characterization methods presented in this special issue, the MHVSR method is the furthest behind in terms of consensus towards standardized guidelines and commercial use. The greatest challenges to an international standardization of MHVSR acquisition and analysis are (1) the
what
— the underlying composition of the microtremor wavefield is site-dependent, and thus, the appropriate theoretical (forward) model for inversion is still debated; and (2) the
how
— many factors and options are involved in the data acquisition, processing, and interpretation stages. This paper reviews briefly a historical development of the MHVSR technique and the physical basis of an MHVSR (the
what
). We then summarize recommendations for MHVSR acquisition and analysis (the
how
). Specific sections address MHVSR interpretation and uncertainty assessment.
We introduce a novel scheme, DGCrack, to simulate dynamic rupture of earthquakes in three dimensions based on an hp‐adaptive discontinuous Galerkin method. We solve the velocity‐stress weak ...formulation of elastodynamic equations on an unstructured tetrahedral mesh with arbitrary mesh refinements (h‐adaptivity) and local approximation orders (p‐adaptivity). Our scheme considers second‐order fault elements (P2) where dynamic‐rupture boundary conditions are enforced throughad hocfluxes across the fault. To model the Coulomb slip‐dependent friction law, we introduce a predictor‐corrector scheme for estimating shear fault tractions, in addition to a special treatment of the normal tractions that guarantees the continuity of fault normal velocities. We verify the DGCrack by comparison with several methods for two spontaneous rupture tests and find excellent agreement (i.e., rupture times RMS errors smaller than 1.0%) provided that one or more fault elements resolve the fault cohesive zone. For a quantitative comparison, we introduce a methodology based on cross‐correlation measurements that provide a simple way to quantify the similarity between solutions. Our verification tests include a 60° dipping normal fault reaching the free surface. The DGCrack method reveals convergence rates close to those of well‐established methods and a numerical efficiency significantly higher than that of similar discontinuous Galerkin approaches. We apply the method to the 1992 Landers‐earthquake fault system in a layered medium, considering heterogeneous initial stress conditions and mesh adaptivities. Our results show that previously proposed dynamic models for the Landers earthquake require a reevaluation in terms of the initial stress conditions that take account of the intricate fault geometry.
Key Points
A 3D dynamic rupture modeling
The hp‐adaptive discontinuous Galerkin method
The 1992 Landers earthquake modeling with an unstructured mesh
Nakamura (Q Rep Railway Tech Res Inst 30:25–33,
1989
) popularized the application of the horizontal-to-vertical spectral ratio (HVSR) analysis of microtremor (seismic noise or ambient vibration) ...recordings to estimate the predominant frequency and amplification factor of earthquake shaking. During the following quarter century, popularity in the microtremor HVSR (MHVSR) method grew; studies have verified the stability of a site’s MHVSR response over time and validated the MHVSR response with that of earthquake HVSR response. Today, MHVSR analysis is a popular reconnaissance tool used worldwide for seismic microzonation and earthquake site characterization in numerous regions, specifically, in the mapping of site period or fundamental frequency and inverted for shear-wave velocity depth profiles, respectively. However, the ubiquity of MHVSR analysis is predominantly a consequence of its ease in application rather than our full understanding of its theory. We present the state of the art in MHVSR analyses in terms of the development of its theoretical basis, current state of practice, and we comment on its future for applications in earthquake site characterization.
ABSTRACT
Random field cross‐correlation is a new promising technique for seismic exploration, as it bypasses shortcomings of usual active methods. Seismic noise can be considered as a reproducible, ...stationary in time, natural source. In the present paper we show why and how cross‐correlation of noise records can be used for geophysical imaging. We discuss the theoretical conditions required to observe the emergence of the Green's functions between two receivers from the cross‐correlation of noise records. We present examples of seismic imaging using reconstructed surface waves from regional to local scales. We also show an application using body waves extracted from records of a small‐scale network. We then introduce a new way to achieve surface wave seismic experiments using cross‐correlation of unsynchronized sources. At a laboratory scale, we demonstrate that body wave extraction may also be used to image buried scatterers. These works show the feasibility of passive imaging from noise cross‐correlation at different scales.
Recently, the possibility of gathering relevant information from correlations of movements due to seismic noise has been demonstrated. Such is the case of the Green's function that is widely known as ...one mathematical solution of the wave equation and commonly used to represent particle displacements given an excitation source. That is the reason of its importance in the field of geophysics and seismology. From seismic noise correlations, it is also possible to obtain not only the Green's function, but the energy contributions of the wave types that are propagating in an elastic medium. For instance, in a two-dimensional (2D) medium, only the movement of compressional (P-) and shear (S-) waves takes place, each one providing fixed amounts of energy. A formulation that allows both, recovering of the Green's function from seismic noise correlations also called GFSNC binary-operator and, the gathering of related energy contributions of P- and S-waves for several representations of materials and models, is applied in this paper. As consequence of this study, it has been shown that the number of sources and their relative distribution with respect the observation points, are essential parameters for an accurate recovery of the exact Green's function. It is also proved that in all cases, P-waves have less energy in proportion to S-waves and even more, the P-wave energy contribution vanishes for Poisson's ratios close to 0.5. Having Poisson's ratios of ν={0.1,0.2,0.3,0.4}, P-waves contribute with approximately 30, 27, 22 and 14% of the total energy, while S-waves with 69, 72, 77 and 85%, respectively. These results agree with theoretical data and might be of much help to understand the origin of wave amplifications, seismic acquisition designs with artificial sources and modeling of the seismic response by potential earthquakes.
•A new study on the recovery of P- and S-waves with the use of Green's function seismic noise correlations.•We studied the energy contributions for those relative positions.•Error analysis in the recovery of both, the energy and the Green's function is provided.
A Triangular Spectral Element Method (TSEM) is presented to simulate elastic wave propagation using an unstructured triangulation of the physical domain. TSEM makes use of a variational formulation ...of elastodynamics based on unstructured straight-sided triangles that allow enhanced flexibility when dealing with complex geometries and velocity structures. The displacement field is expanded into a high-order polynomial spectral approximation over each triangular subdomain. Continuity between the subdomains of the triangulation is enforced using a multidimensional Lagrangian interpolation built on a set of Fekete points of the triangle. High-order accuracy is achieved by resorting to an analytical computation of the associated internal product and bilinear forms leading to a non-diagonal mass matrix formulation. Therefore, the time stepping involves the solution of a sparse linear algebraic system even in the explicit case. In this paper the accuracy and the geometrical flexibility of the TSEM is explored. Comparison with classical spectral elements on quadrangular grids shows similar results in terms of accuracy and stability even for long simulations. Surface and interface waves are shown to be accurately modelled even in the case of complex topography with the TSEM. Numerical results are presented for 2-D canonical examples as well as more specific problems, such as 2-D elastic wave scattering by a cylinder embedded in an homogeneous half-space. They all illustrate the enhanced geometrical flexibility of the TSEM. This clearly suggests the need of further investigations in computational seismology specifically targeted towards efficient implementations of the TSEM both in the time and the frequency domain.
The initiation of frictional instability is investigated for simple models of fault zone using a linearized perturbation analysis. The fault interface is assumed to obey a linear slip‐weakening law. ...The fault is initially prestressed uniformly at the sliding threshold. In the case of antiplane shear between two homogeneous linearly elastic media, space‐time and spectral solutions are obtained and shown to be consistent. The nucleation is characterized by (1) a long‐wavelength unstable spectrum bounded by a critical wave number; (2) an exponential growth of the unstable modes; and (3) an induced off‐fault deformation that remains trapped within a bounded zone in the vicinity of the fault. These phenomena are characterized in terms of the elastic parameters of the surrounding medium and a nucleation length that results from the coupling between the frictional interface and the bulk elasticity. These results are extended to other geometries within the same formalism and implications for three‐dimensional rupture are discussed. Finally, internal fault structures are investigated in terms of a fault‐parallel damaged zone. Spectral solutions are obtained for both a smooth and a layered distribution of damage. For natural faults the nucleation is shown to depend strongly on the existence of a internal damaged layer. This nucleation can be described in terms of an effective homogeneous model. In all cases, frictional trapping of the deformation out of the fault can lead to the property that arbitrarily long wavelengths remain sensitive to the existence of a fault zone.
Effect of Irregular Seabed on Seismic Motions Martínez-Calzada, V; Rodríguez-Castellanos, A; Samayoa-Ochoa, D ...
Journal of earthquake engineering : JEE,
02/2019, Letnik:
23, Številka:
2
Journal Article
Recenzirano
Several studies indicate that marine seismic activity is vast. Actually, about 90% of all natural earthquakes have epicenters in o_shore areas and may cause damage to subsea and floating structures. ...In this numerical study the indirect boundary element method is used to analyze the influence that some parameters, involved in this kind of problems, have on the dynamic response of marine waters under the incidence of theoretical seismic events. According with the results, the seismic amplifications depend on the seabed configuration and produce displacements which can be a serious concern.
In this paper scattering of elastic waves in fluid–solid interfaces is investigated. We use the Indirect Boundary Element Method to study this wave propagation phenomenon in 2D models. Three models ...are analyzed: a first one with an interface between two half-spaces, one fluid on the top part and the other solid in the bottom; a second model including a fluid half-space above a layered solid; and finally, a third model with a fluid layer bounded by two solid half-spaces. The source, represented by Hankel's function of the second kind, is always applied in the fluid. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with an analytical solution known as Discrete Wave Number. A near interface pulse generates scattered waves that can be registered by receivers located in the fluid and it is possible to infer wave velocities of solids. Results are presented in both time and frequency domain, where several aspects related to the different wave types that emerge from this kind of problems are pointed out.
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