scholarly journals Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling

Solid Earth ◽  
2017 ◽  
Vol 8 (5) ◽  
pp. 969-986 ◽  
Author(s):  
Shaolin Liu ◽  
Dinghui Yang ◽  
Xingpeng Dong ◽  
Qiancheng Liu ◽  
Yongchang Zheng
Keyword(s):  
Boundary Condition ◽  
Wave Field ◽  
Scattered Wave ◽  
Spectral Element ◽  
Perfectly Matched Layers ◽  
Time Step ◽  
Absorbing Boundary ◽  
Field Modeling ◽  
Adjoint Tomography ◽  
Gradient Calculation

Abstract. The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency–wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

scholarly journals Element-by-element parallel spectral-element methods for 3-D acoustic-wave-equation-based teleseismic wave modeling

2017 ◽  
Author(s):  
Shaolin Liu ◽  
Dinghui Yang ◽  
Xingpeng Dong ◽  
Qiancheng Liu ◽  
Yongchang Zheng
Keyword(s):  
Boundary Condition ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Computational Effort ◽  
Model Parameters ◽  
Perfectly Matched Layers ◽  
Time Step ◽  
Absorbing Boundary ◽  
Adjoint Tomography ◽  
Increasing Demand

Abstract. The increasing demand for the high-resolution imaging of deep lithosphere structures requires the utilization of a teleseismic dataset for waveform inversion. The construction of an efficient algorithm for the teleseismic wavefield modeling is valuable for the calculation of misfit kernels or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wavefield propagation in a localized geology model. Under the assumption of the plane wave, the frequency-wavenumber (FK) technique is implemented to compute the boundary wavefield used for constructing the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wavefield for the incidence boundary condition, an economical strategy is introduced to store the boundary wavefield on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated by the EBE-SEM to absorb the scattered wavefield from the model interior. The misfit kernel (derivatives of the waveform misfit with respect to model parameters) can be easily constructed without extra computational effort for the calculation of the element stiffness matrix per time step during the calculation of the adjoint wavefield. Three synthetic examples demonstrate the validity of EBE-SEM for use in teleseismic wavefield modeling and the misfit kernel calculation.

scholarly journals Well-Designed Termination Wall of Perfectly Matched Layers for ATS-FDTD Method

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Ju Ge ◽  
Liping Gao ◽  
Rengang Shi
Keyword(s):  
Boundary Condition ◽  
Numerical Experiments ◽  
Fdtd Method ◽  
Difference Schemes ◽  
Absorbing Boundary Condition ◽  
Perfectly Matched Layers ◽  
Absorbing Boundary ◽  
Matched Layers ◽  
Special Difference

This paper presents a well-designed termination wall for the perfectly matched layers (PML). This termination wall is derived from Mur’s absorbing boundary condition (ABC) with special difference schemes. Numerical experiments illustrate that PML and the termination wall works well with ATS-FDTD(Shi et al. 2015). With the help of termination wall, perfectly matched layers can be decreased to two layers only; meanwhile, the reflection error still reaches -60[dB] when complex waveguide is simulated by ATS-FDTD.

PERFECTLY MATCHED LAYERS FOR ELASTODYNAMICS: A NEW ABSORBING BOUNDARY CONDITION

1996 ◽  
Vol 04 (04) ◽  
pp. 341-359 ◽  
Author(s):  
W.C. CHEW ◽  
Q.H. LIU
Keyword(s):  
Boundary Condition ◽  
Half Space ◽  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Absorbing Boundary Condition ◽  
Perfectly Matched Layers ◽  
Absorbing Boundary ◽  
Multiple Data ◽  
Open Region ◽  
Matched Layers

The use of perfectly matched layers (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, we will first prove that a fictitious elastodynamic material half-space exists that will absorb an incident wave for all angles and all frequencies. Moreover, the wave is attenuative in the second half-space. As a consequence, layers of such material could be designed at the edge of a computer simulation region to absorb outgoing waves. Since this is a material ABC, only one set of computer codes is needed to simulate an open region. Hence, it is easy to parallelize such codes on multiprocessor computers. For instance, it is easy to program massively parallel computers on the SIMD (single instruction multiple data) mode for such codes. We will show two- and three-dimensional computer simulations of the PML for the linearized equations of elastodynamics. Comparison with Liao’s ABC will be given.

The Auxiliary Differential Equations Perfectly Matched Layers Based on the Hybrid SETD and PSTD Algorithms for Acoustic Waves

2018 ◽  
Vol 26 (01) ◽  
pp. 1750031 ◽  
Author(s):  
Chunhua Deng ◽  
Ma Luo ◽  
Mengqing Yuan ◽  
Bo Zhao ◽  
Mingwei Zhuang ◽  
...  
Keyword(s):  
Differential Equations ◽  
Time Domain ◽  
Acoustic Waves ◽  
Wave Equations ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Spectral Element ◽  
Body Waves ◽  
Perfectly Matched Layers ◽  
Absorbing Boundary

The perfectly matched layer (PML) absorbing boundary condition has been proven to absorb body waves and surface waves very efficiently at non-grazing incidence. However, the traditional PML would generate large spurious reflections at grazing incidence, for example, when the sources are located near the truncating boundary and the receivers are at a large offset. In this paper, a new PML implementation is presented for the boundary truncation in three-dimensional spectral element time domain (SETD) for solving acoustic wave equations. This method utilizes pseudospectral time-domain (PSTD) method to solve first-order auxiliary differential equations (ADEs), which is more straightforward than that in the classical FEM framework.

Application of Symplectic Partitioned Runge-Kutta Method and Total-Field Scattered-Field Formulation to Simulation of GPR Data

2014 ◽  
Vol 926-930 ◽  
pp. 2777-2780
Author(s):  
Hong Yuan Fang ◽  
Jian Li ◽  
Jia Li
Keyword(s):  
Scattered Field ◽  
Measured Signal ◽  
Total Field ◽  
Time Step ◽  
Absorbing Boundary ◽  
Runge Kutta Method ◽  
Actual Field ◽  
Ground Penetrating ◽  
Radar Wave ◽  
Difference Time

The second-order Lobatto IIIA-IIIB symplectic partitioned RungeKutta (SPRK) method, combining with the first-order Mur absorbing boundary condition, is developed for the simulation of ground penetrating radar wave propagation in layered pavement structure. For 2-dimetional case, a significant advantage of this method is that only two functions need to be calculated at each time step. The total-field/scattered-field technique is used for plane wave excitation. Numerical examples are presented to verify the accuracy and efficiency of the proposed algorithm. The results illustrate that the reflected signal calculated by the SPRK method is in good agreement with that obtained using the finite difference time domain (FDTD) scheme, but the CPU time consumed by proposed algorithm is reduce about 20% of the FDTD scheme. In addition, an actual field test is conducted to evaluate the further performance of the SPRK method. It is found that the simulated waveform fits well with the measured signal in many aspects, especially in the peak amplitude and time delay.

Interaction of High Frequency Lamb Waves with Surface-Mount Sensor Adhesives

2013 ◽  
Vol 558 ◽  
pp. 489-500 ◽  
Author(s):  
Patrick Norman ◽  
Claire Davis ◽  
Cédric Rosalie ◽  
Nik Rajic
Keyword(s):  
Wave Field ◽  
Lamb Waves ◽  
Base Material ◽  
Adhesive Layer ◽  
Scattered Wave ◽  
Phase Lag ◽  
Wave Fields ◽  
Surface Mount ◽  
Frequency Regime ◽  
Fibre Bragg Gratings

The application of Lamb waves to damage and/or defect detection in structures is typicallyconfined to lower frequencies in regimes where only the lower order modes propagate in order to simplifyinterpretation of the scattered wave-fields. Operation at higher frequencies offers the potentialto extend the sensitivity and diagnostic capability of this technique, however there are technical challengesassociated with the measurement and interpretation of this data. Recent work by the authorshas demonstrated the ability of fibre Bragg gratings (FBGs) to measure wave-fields at frequencies inexcess of 2 MHz [1]. However, when this work was extended to other thinner plate specimens it wasfound that at these higher frequencies, the cyanoacrylate adhesive (M-Bond 200) used to attach theFBG sensors to the plate was significantly affecting the propagation of the waves. Laser vibrometrywas used to characterise the wave-field in the region surrounding the adhesive and it was found that theself-adhesive retro-reflective tape applied to aid with this measurement was also affecting the wavefieldin the higher frequency regime. This paper reports on an experimental study into the influence ofboth of these materials on the propagating wave-field. Three different lengths of retro-reflective tapewere placed in the path of Lamb waves propagating in an aluminium plate and laser vibrometry wasused to measure the wave-field upstream and downstream of the tape for a range of different excitationfrequencies. The same experiment was conducted using small footprint cyanoacrylate film samplesof different thickness. The results show that both of these surface-mount materials attenuate, diffractand scatter the incoming waves as well as introducing a phase lag. The degree of influence of thesurface layer appears to be a function of its material properties, the frequency of the incoming waveand the thickness and footprint of the surface layer relative to the base material thickness. Althoughfurther work is required to characterise the relative influence of each of these variables, investigationsto date show that for the measurement of Lamb Waves on thin structures, careful considerationshould be given to the thickness and footprint of the adhesive layer and sensor, particularly in the highfrequency regime, so as to minimise their effect on the measurement.

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