A rectangular-grid lattice spring model for modeling elastic waves in Poisson’s solids

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. T69-T86 ◽  
Author(s):  
Muming Xia ◽  
Hui Zhou ◽  
Hanming Chen ◽  
Qingchen Zhang ◽  
Qingqing Li
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Heterogeneous Media ◽  
Elastic Wave Propagation ◽  
P Wave ◽  
Numerical Dispersion ◽  
Spring Model ◽  
Rectangular Grid ◽  
Lattice Spring Model

The lattice spring model (LSM) combined with the velocity Verlet algorithm is a newly developed scheme for modeling elastic wave propagation in solid media. Unlike conventional wave equations, LSM is established on the basis of micromechanics of the subsurface media, which enjoys better dynamic characteristics of elastic systems. We develop a rectangular-grid LSM scheme for elastic waves simulation in Poisson’s solids, and the direction-dependent elastic constants are deduced to keep the isotropy of the discrete grid. The stability condition and numerical dispersion properties of LSM are discussed and compared with other numerical methods. The 2D and 3D numerical simulations are carried out using the rectangular-grid LSM, as well as the second- and fourth-order accuracy staggered finite-difference method (FDM). Wavefields obtained by LSM are fairly similar with those by analytical solution and FDM, which demonstrates the correctness of the proposed scheme and its capability of modeling elastic wave propagation in heterogeneous media. Moreover, we perform plane P-wave simulation through a semi-infinite cavity model via LSM and FDM, the recorded wavefield snapshots indicate that our proposed rectangular-grid LSM obtains more reasonable wavefield details compared with those of FDM, especially in media with high compliance and structure complexity. Our main contribution lies in offering an alternative simulation scheme for modeling elastic wave propagation in media with some kinds of complexities, which conventional FDM may fail to simulate.

Elastic Wave Propagation in Heterogeneous Media

2003 ◽  
Vol 2003.78 (0) ◽  
pp. _5-51_-_5-52_
Author(s):  
Masatoshi YAMASHITA ◽  
Akihiro NAKATANI ◽  
Yoshikazu HIGA ◽  
Hiroshi KITAGAWA
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Heterogeneous Media ◽  
Elastic Wave Propagation

Anisotropic finite-difference algorithm for modeling elastic wave propagation in fractured coalbeds

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. C13-C26 ◽  
Author(s):  
Zhenglin Pei ◽  
Li-Yun Fu ◽  
Weijia Sun ◽  
Tao Jiang ◽  
Binzhong Zhou
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Taylor Series Expansion ◽  
Real Data ◽  
Elastic Wave Propagation ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
S Wave ◽  
Data Set

The simulation of wave propagations in coalbeds is challenged by two major issues: (1) strong anisotropy resulting from high-density cracks/fractures in coalbeds and (2) numerical dispersion resulting from high-frequency content (the dominant frequency can be higher than 100 Hz). We present a staggered-grid high-order finite-difference (FD) method with arbitrary even-order ([Formula: see text]) accuracy to overcome the two difficulties stated above. First, we derive the formulae based on the standard Taylor series expansion but given in a neat and explicit form. We also provide an alternative way to calculate the FD coefficients. The detailed implementations are shown and the stability condition for anisotropic FD modeling is examined by the eigenvalue analysis method. Then, we apply the staggered-grid FD method to 2D and 3D coalbed models with dry and water-saturated fractures to study the characteristics of the 2D/3C elastic wave propagation in anisotropic media. Several factors, like density and direction of vertical cracks, are investigated. Several phenomena, like S-wave splitting and waveguides, are observed and are consistent with those observed in a real data set. Numerical results show that our formulae can correlate the amplitude and traveltime anisotropies with the coal seam fractures.

scholarly journals Simulation of Dynamic Processes in Deformable Medium with the Grid-Characteristic Approach

2021 ◽  
pp. 74-81
Author(s):  
И.Б. Петров
Keyword(s):  
Neural Networks ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Elastic Wave Propagation ◽  
Seismic Survey ◽  
The Arctic ◽  
Dynamic Processes ◽  
Deformable Media ◽  
Direct Problems

Существует значительное количество прикладных задач, для решения которых применяется математическое моделирование динамических процессов в деформируемых средах. К таким задачам относят моделирование распространения упругих волн в геологических средах, в том числе с учетом ледовых образований, их рассеяния на зонах трещиноватости. Актуальность этих постановок обусловлена важностью решения обратных задач сейсмической разведки, обработки данных сейсмической разведки с целью уточнения запасов углеводородов и определения расположения углеводородов и других полезных ископаемых. Поэтому приобретает важность разработка высокоточных численных методов, позволяющих моделировать упругие волны в деформируемых средах. Одним из этих методов является сеточно-характеристический численный метод, примененный в данной работе. Этот численный метод применяется для решения прямых задач, то есть для расчета распространения упругих волн при известных параметрах рассматриваемой среды. А для решения обратной задачи по восстановлению параметров геологической среды по данным сейсмической разведки можно применять нейронные сети, для обучения которых можно использовать многократное решение прямых задач сеточно-характеристическим методом. В данной работе приведены примеры решения разнообразных прямых задач по распространению упругих волн в неоднородных геологических средах, в том числе в зоне Арктики, а также представлена постановка задачи по обучению нейронных сетей и графики, показывающие эффективность их обучения с использованием двух различных подходов. Many problems can be solved with the simulation of dynamic processes in deformable media. They are the simulation of elastic wave propagation in rocks including ice formations, and wave scattering on rock-fracture zones. Such studies are important for solving inverse problems of seismic exploration and seismic data processing to get a better estimation of hydrocarbon reserves, locate hydrocarbons and other minerals. Therefore, it is necessary to develop high-precision numerical methods used to simulate elastic waves in deformable media. One of such methods is the grid-characteristic approach used in this work. It is suitable for solving direct problems, i.e., to analyze the propagation of elastic waves in a medium with known properties. Neural networks can be applied to solve the inverse problem: reconstructing the geology from seismic survey data. Multiple solving of direct problems by the gridcharacteristic approach is used for network training. This paper contains some examples of solving a range of direct problems on the elastic wave propagation in heterogeneous rocks, also in the Arctic zone, and the problem statement for training neural networks and graphs is proposed to demonstrate the efficiency of training with two approaches.

A first‐order k‐space model for elastic wave propagation in heterogeneous media.

2011 ◽  
Vol 129 (4) ◽  
pp. 2611-2611 ◽  
Author(s):  
Kamyar Firouzi ◽  
Benjamin Cox ◽  
Bradley Treeby ◽  
Nader Saffari
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Heterogeneous Media ◽  
Elastic Wave Propagation ◽  
Space Model ◽  
First Order

scholarly journals Elastic Wave Propagation for Condition Assessment of Steel Bar Embedded in Mortar

2015 ◽  
Vol 20 (1) ◽  
pp. 159-170 ◽  
Author(s):  
M. Rucka ◽  
B. Zima
Keyword(s):  
Wave Propagation ◽  
Finite Elements ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Condition Assessment ◽  
Elastic Wave Propagation ◽  
Longitudinal Waves ◽  
Numerical Investigations ◽  
Steel Bar ◽  
Steel Bars

Abstract This study deals with experimental and numerical investigations of elastic wave propagation in steel bars partially embedded in mortar. The bars with different bonding lengths were tested. Two types of damage were considered: damage of the steel bar and damage of the mortar. Longitudinal waves were excited by a piezoelectric actuator and a vibrometer was used to non-contact measurements of velocity signals. Numerical calculations were performed using the finite elements method. As a result, this paper discusses the possibility of condition assessment in bars embedded in mortar by means of elastic waves.

Interface conditions for acoustic and elastic wave propagation

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 168-181 ◽  
Author(s):  
J. S. Sochacki ◽  
J. H. George ◽  
R. E. Ewing ◽  
S. B. Smithson
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Heterogeneous Media ◽  
Elastic Wave Propagation ◽  
Integration Scheme ◽  
Acoustic Wave Equation ◽  
Sh Wave ◽  
Numerical Schemes ◽  
Tangential Stresses

The divergence theorem is used to handle the physics required at interfaces for acoustic and elastic wave propagation in heterogeneous media. The physics required at regular and irregular interfaces is incorporated into numerical schemes by integrating across the interface. The technique, which can be used with many numerical schemes, is applied to finite differences. A derivation of the acoustic wave equation, which is readily handled by this integration scheme, is outlined. Since this form of the equation is equivalent to the scalar SH wave equation, the scheme can be applied to this equation also. Each component of the elastic P‐SV equation is presented in divergence form to apply this integration scheme, naturally incorporating the continuity of the normal and tangential stresses required at regular and irregular interfaces.

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