5,169 research outputs found
A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains
The numerical analysis of elastic wave propagation in unbounded media may be
difficult due to spurious waves reflected at the model artificial boundaries.
This point is critical for the analysis of wave propagation in heterogeneous or
layered solids. Various techniques such as Absorbing Boundary Conditions,
infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers)
lead to an important reduction of such spurious reflections. In this paper, a
simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey
damping formulation which is often already available in existing Finite Element
softwares. The principle of the Caughey Absorbing Layer Method is first
presented (including a rheological interpretation). The efficiency of the
method is then shown through 1D Finite Element simulations considering
homogeneous and heterogeneous damping in the absorbing layer. 2D models are
considered afterwards to assess the efficiency of the absorbing layer method
for various wave types and incidences. A comparison with the PML method is
first performed for pure P-waves and the method is shown to be reliable in a
more complex 2D case involving various wave types and incidences. It may thus
be used for various types of problems involving elastic waves (e.g. machine
vibrations, seismic waves, etc)
Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media
To analyze seismic wave propagation in geological structures, it is possible
to consider various numerical approaches: the finite difference method, the
spectral element method, the boundary element method, the finite element
method, the finite volume method, etc. All these methods have various
advantages and drawbacks. The amplification of seismic waves in surface soil
layers is mainly due to the velocity contrast between these layers and,
possibly, to topographic effects around crests and hills. The influence of the
geometry of alluvial basins on the amplification process is also know to be
large. Nevertheless, strong heterogeneities and complex geometries are not easy
to take into account with all numerical methods. 2D/3D models are needed in
many situations and the efficiency/accuracy of the numerical methods in such
cases is in question. Furthermore, the radiation conditions at infinity are not
easy to handle with finite differences or finite/spectral elements whereas it
is explicitely accounted in the Boundary Element Method. Various absorbing
layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the
spurious wave reflections especially in some difficult cases such as shallow
numerical models or grazing incidences. Finally, strong earthquakes involve
nonlinear effects in surficial soil layers. To model strong ground motion, it
is thus necessary to consider the nonlinear dynamic behaviour of soils and
simultaneously investigate seismic wave propagation in complex 2D/3D geological
structures! Recent advances in numerical formulations and constitutive models
in such complex situations are presented and discussed in this paper. A crucial
issue is the availability of the field/laboratory data to feed and validate
such models.Comment: of International Journal Geomechanics (2010) 1-1
A hybrid PML formulation for the 2D three-field dynamic poroelastic equations
Simulation of wave propagation in poroelastic half-spaces presents a common
challenge in fields like geomechanics and biomechanics, requiring Absorbing
Boundary Conditions (ABCs) at the semi-infinite space boundaries. Perfectly
Matched Layers (PML) are a popular choice due to their excellent wave
absorption properties. However, PML implementation can lead to problems with
unknown stresses or strains, time convolutions, or PDE systems with Auxiliary
Differential Equations (ADEs), which increases computational complexity and
resource consumption.
This article presents two new PML formulations for arbitrary poroelastic
domains. The first formulation is a fully-mixed form that employs time-history
variables instead of ADEs, reducing the number of unknowns and mathematical
operations. The second formulation is a hybrid form that restricts the
fully-mixed formulation to the PML domain, resulting in smaller matrices for
the solver while preserving governing equations in the interior domain. The
fully-mixed formulation introduces three scalar variables over the whole
domain, whereas the hybrid form confines them to the PML domain.
The proposed formulations were tested in three numerical experiments in
geophysics using realistic parameters for soft sites with free surfaces. The
results were compared with numerical solutions from extended domains and
simpler ABCs, such as paraxial approximation, demonstrating the accuracy,
efficiency, and precision of the proposed methods. The article also discusses
the applicability of these methods to complex media and their extension to the
Multiaxial PML formulation.
The codes for the simulations are available for download from
\url{https://github.com/hmella/POROUS-HYBRID-PML}
Filtering random layering effects in imaging
Objects that are buried deep in heterogeneous media produce faint echoes which are difficult to distinguish from the backscattered field. Sensor array imaging in such media cannot work unless we filter out the backscattered echoes and enhance the coherent arrivals that carry information about the objects that we wish to image. We study such filters for imaging in strongly backscattering, finely layered media. The filters are based on a travel time transformation of the array data, the normal move-out, used frequently in connection with differential semblance velocity estimation in seismic imaging. In a previous paper [10] we showed that the filters can be used to remove coherent signals from strong plane reflectors. In this paper we show theoretically and with extensive numerical simulations that these filters, based on the normal move-out, can also remove the incoherent arrivals in the array data that are due to fine random layering in the medium. Key words. array imaging, randomly layered media, filtering
An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics
The numerical simulation of acoustic waves in complex 3D media is a key topic
in many branches of science, from exploration geophysics to non-destructive
testing and medical imaging. With the drastic increase in computing
capabilities this field has dramatically grown in the last twenty years.
However many 3D computations, especially at high frequency and/or long range,
are still far beyond current reach and force researchers to resort to
approximations, for example by working in 2D (plane strain) or by using a
paraxial approximation. This article presents and validates a numerical
technique based on an axisymmetric formulation of a spectral finite-element
method in the time domain for heterogeneous fluid-solid media. Taking advantage
of axisymmetry enables the study of relevant 3D configurations at a very
moderate computational cost. The axisymmetric spectral-element formulation is
first introduced, and validation tests are then performed. A typical
application of interest in ocean acoustics showing upslope propagation above a
dipping viscoelastic ocean bottom is then presented. The method correctly
models backscattered waves and explains the transmission losses discrepancies
pointed out in Jensen et al. (2007). Finally, a realistic application to a
double seamount problem is considered.Comment: Added a reference, and fixed a typo (cylindrical versus spherical
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Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments
We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.Civil, Architectural, and Environmental Engineerin
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