Spectral element simulation of elastic wave propagation through fractures using linear slip model: microfracture detection for CO2 storage

2020 ◽  
Vol 223 (3) ◽  
pp. 1794-1804
Author(s):  
R Ponomarenko ◽  
D Sabitov ◽  
M Charara
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Co2 Storage ◽  
Carbon Capture And Storage ◽  
Spectral Element ◽  
Slip Model ◽  
Theoretical Formulation ◽  
Small Aperture ◽  
Wide Range ◽  
Linear Slip Model

SUMMARY Simulation of seismic wave propagation through fracture has a wide range of applications in environmental sciences. In this paper, we propose an efficient tool to compute accurate seismic response from a fracture within a reasonable time frame. Its theoretical formulation is based on the spectral element method (SEM) and extended to Schoenberg’s linear slip model (LSM). SEM is very effective in terms of accuracy and stability criteria. LSM is treated as a boundary condition and perfectly fits for modelling fractures with a small aperture. The method is implemented for 3-D heterogeneous media on GPU, which allows calculating the tasks with large and complex geometries. The validation of the numerical method shows good agreement with the theory. Finally, we applied the method to the task that illustrates the possibility of the proposed solution to handle real problems. We model sonic logging for a well with a microfracture in a cement sheath. Based on synthetic seismograms, strong connections between wave mode parameters and the fracture parameters were established. This task is of high importance for carbon capture and storage, as microfractures provide the path for long-term CO2 migration.

WAVE PROPAGATION MODELING IN HIGHLY HETEROGENEOUS MEDIA BY A POLY-GRID CHEBYSHEV SPECTRAL ELEMENT METHOD

2012 ◽  
Vol 20 (02) ◽  
pp. 1240004 ◽  
Author(s):  
GÉZA SERIANI ◽  
CHANG SU
Keyword(s):  
Wave Propagation ◽  
Computational Efficiency ◽  
Spectral Element Method ◽  
Heterogeneous Media ◽  
Spectral Element ◽  
Small Scale ◽  
Computational Domain ◽  
Problem Size ◽  
Wide Range ◽  
Element Method

A wide range of applications requires the modeling of wave propagation phenomena in media with variable physical properties in the domain of interest, while highly accurate algorithms are needed to avoid unphysical effects. Spectral element methods (SEM), based on either a Chebyshev or a Legendre polynomial basis, have excellent properties of accuracy and flexibility in describing complex models, outperforming other techniques. In the standard SEM approach the computational domain is discretized by using very coarse meshes and constant-property elements, but in some cases the accuracy and the computational efficiency may be seriously reduced. For instance, a finely heterogeneous medium requires grid resolution down to the finest scales, leading to an extremely large problem dimension. In such problems the wavelength scale of interest is much larger but cannot be exploited in order to reduce the problem size. A poly-grid Chebyshev spectral element method (PG-CSEM) can overcome this limitation. In order to accurately deal with continuous variation in the properties, or even with small scale fluctuations, temporary auxiliary grids are introduced which avoid the need of using any finer global grid, and at the macroscopic level the wave field propagation is solved maintaining the SEM accuracy and computational efficiency.

Two-dimensional finite-difference seismic modeling of an open fluid-filled fracture: Comparison of thin-layer and linear-slip models

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. T57-T62 ◽  
Author(s):  
Chunling Wu ◽  
Jerry M. Harris ◽  
Kurt T. Nihei ◽  
Seiji Nakagawa
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Thin Layer ◽  
Computational Cost ◽  
Seismic Wave Propagation ◽  
Thin Layers ◽  
Single Fracture ◽  
Slip Model ◽  
Layer Model ◽  
Linear Slip Model

Within the context of seismic wave propagation, fractures can be described as thin layers or linear-slip interfaces. In this paper, numerical simulations of elastic wave propagation in a medium with a single fracture represented by these two models are performed by 2D finite-difference codes: a variable-grid isotropic code for the thin-layer model and a regular-grid anisotropic code for the linear-slip model. Numerical results show excellent agreement between the two models for wavefields away from the fracture; the only discrepancy between the two is the presence of a slow wave traveling primarily within the fracture fluid of the thin-layer model. The comparison of the computational cost shows that modeling of the linear-slip model is more efficient than that of the thin-layer model. This study demonstrates that the linear-slip model is an efficient and accurate modeling approach for the remote seismic characterization of fractures.

Simulation of borehole acoustic wavefields in fractured media by combining the spectral element method and linear-slip model

Geophysics ◽  
2021 ◽  
pp. 1-69
Author(s):  
Jiaqi Xu ◽  
Qing Huo Liu ◽  
Hengshan Hu ◽  
Yang Zhong
Keyword(s):  
Finite Difference ◽  
Tilt Angle ◽  
Spectral Element Method ◽  
Numerical Solutions ◽  
Spectral Element ◽  
Fractured Media ◽  
Dipole Source ◽  
Slip Model ◽  
Linear Slip Model ◽  
Element Method

We use the spectral element method (SEM) to simulate 3D acoustic wavefields in the fluid-filled borehole embedded in the fractured media. The fractures are characterized by the linear-slip model (LSM), which is incorporated into the surface integral of the SEM weak form, avoiding meshing individual fractures, thus reducing the degrees of freedom of the fractures comparing with meshing each fracture directly. For the fracture-free case, we validate SEM through the comparison with the real-axis integration (RAI) method for both monopole and dipole sources. For the case with a fracture, we compare the SEM-LSM solutions with the reference numerical solutions of a thin layer model using finite-difference method. Good agreement is achieved between the results from the proposed method and the reference finite-difference solutions. We find that the acoustic wavefields excited by a dipole source are more sensitive to the fractures than those by a monopole source. To show the ability of the approach to handle complex problems, we simulate the cases with a tilted fracture and multiple fractures. Based on the simulated results, we investigate the influence of the fracture parameters (e.g., stiffness, tilt angle, azimuth, thickness, number and spatial intervals of fractures) on the scattered wavefields. We find that the tilt angle has an obvious influence on the scattered waveforms and amplitudes. The results also demonstrate that the wavefields are quite sensitive to the number of fractures. The magnitudes of the horizontal-components transmitted wavefields decrease linearly with the number of the fractures. Through analyzing the synthetic data in time and frequency domains, we discuss how to evaluate the properties of fractures intersected by a borehole.

Two efficient modeling schemes for fractional Laplacian viscoacoustic wave equation

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. T233-T249 ◽  
Author(s):  
Hanming Chen ◽  
Hui Zhou ◽  
Qingqing Li ◽  
Yufeng Wang
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Computational Efficiency ◽  
Fractional Laplacian ◽  
Heterogeneous Media ◽  
Spatial Variable ◽  
Variable Order ◽  
Wide Range ◽  
Seismic Quality Factor ◽  
Efficient Modeling

Recently, a decoupled fractional Laplacian viscoacoustic wave equation has been developed based on the constant-[Formula: see text] model to describe wave propagation in heterogeneous media. We have developed two efficient modeling schemes to solve the decoupled fractional Laplacian viscoacoustic wave equation. Both schemes can cope with spatial variable-order fractional Laplacians conveniently, and thus are applicable for modeling viscoacoustic wave propagation in heterogeneous media. Both schemes are based on fast Fourier transform, and have a spectral accuracy in space. The first scheme solves a modified wave equation with constant-order fractional Laplacians instead of spatial variable-order fractional Laplacians. Due to separate discretization of space and time, the first scheme has only first-order accuracy in time. Differently, the second scheme is based on an analytical wave propagator, and has a higher accuracy in time. To increase computational efficiency of the second modeling scheme, we have adopted the low-rank decomposition in heterogeneous media. We also evaluated the feasibility of applying an empirical approximation to approximate the fractional Laplacian that controls amplitude loss during wave propagation. When the empirical approximation is applied, our two modeling schemes become more efficient. With the help of numerical examples, we have verified the accuracy of our two modeling schemes with and without applying the empirical approximation, for a wide range of seismic quality factor ([Formula: see text]). We also compared computational efficiency of our two modeling schemes using numerical tests.

scholarly journals A coupled finite and boundary spectral element method for linear water-wave propagation problems

2017 ◽  
Vol 48 ◽  
pp. 1-20 ◽  
Author(s):  
Antonio Cerrato ◽  
Luis Rodríguez-Tembleque ◽  
José A. González ◽  
M.H. Ferri Aliabadi
Keyword(s):  
Wave Propagation ◽  
Water Wave ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method

scholarly journals Wave Propagation Analysis in Composite Laminates Containing a Delamination Using a Three-Dimensional Spectral Element Method

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Fucai Li ◽  
Haikuo Peng ◽  
Xuewei Sun ◽  
Jinfu Wang ◽  
Guang Meng
Keyword(s):  
Wave Propagation ◽  
Lamb Wave ◽  
Composite Laminates ◽  
Composite Structures ◽  
Spectral Element Method ◽  
Three Dimensional ◽  
Spectral Element ◽  
Wave Mode ◽  
Diagonal Form ◽  
Element Method

A three-dimensional spectral element method (SEM) was developed for analysis of Lamb wave propagation in composite laminates containing a delamination. SEM is more efficient in simulating wave propagation in structures than conventional finite element method (FEM) because of its unique diagonal form of the mass matrix. Three types of composite laminates, namely, unidirectional-ply laminates, cross-ply laminates, and angle-ply laminates are modeled using three-dimensional spectral finite elements. Wave propagation characteristics in intact composite laminates are investigated, and the effectiveness of the method is validated by comparison of the simulation results with analytical solutions based on transfer matrix method. Different Lamb wave mode interactions with delamination are evaluated, and it is demonstrated that symmetric Lamb wave mode may be insensitive to delamination at certain interfaces of laminates while the antisymmetric mode is more suited for identification of delamination in composite structures.

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