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.

Finite difference forward modelling across the Tyrrhenian basin

2021 ◽  
Author(s):  
Chiara Nardoni ◽  
Luca De Siena ◽  
Fabio Cammarano ◽  
Elisabetta Mattei ◽  
Fabrizio Magrini
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Wave Attenuation ◽  
Software Tool ◽  
Seismic Wave Propagation ◽  
Tyrrhenian Sea ◽  
Forward Modelling ◽  
Crustal Thinning ◽  
Energy Leakage ◽  
Radiative Transfer Equations

<p>Strong lateral variations in medium properties affect the response of seismic wavefields. The Tyrrhenian Sea is ideally suited to explore these effects in a mixed continental-oceanic crust that comprises magmatic systems. The study aims at investigating the effects of crustal thinning and sedimentary layers on wave propagation, especially the reverberating (e.g., Lg) phases, across the oceanic basin. We model regional seismograms (600-800 km) using the software tool OpenSWPC (Maeda et al., 2017, EPS) based on the finite difference simulation of the wave equation. The code simulates the seismic wave propagation in heterogeneous viscoelastic media including the statistical velocity fluctuations as well as heterogeneous topography, typical of mixed settings. This approach allows to evaluate the role of interfaces and layer thicknesses on phase arrivals and direct and coda attenuation measurements. The results are compared with previous simulations of the radiative-transfer equations. They provide an improved understanding of the complex wave attenuation and energy leakage in the mantle characterizing the southern part of the Tyrrhenian Sea and the Italian peninsula. The forward modelling is to be embedded in future applications of attenuation, absorption and scattering tomography performed with MuRAT (the Multi-Resolution Attenuation Tomography code – De Siena et al. 2014, JVGR) available at https://github.com/LucaDeSiena/MuRAT.</p>

scholarly journals Thin-layer solutions of the Helmholtz equation

2020 ◽  
pp. 1-15
Author(s):  
J. R. OCKENDON ◽  
R. H. TEW
Keyword(s):  
Wave Propagation ◽  
Thin Layer ◽  
Helmholtz Equation ◽  
Open Problem ◽  
High Frequency ◽  
Mathematical Structure ◽  
Mathematical Physics ◽  
Thin Layers ◽  
Frequency Wave ◽  
High Frequency Wave

This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

Monitoring the width of hydraulic fractures with acoustic waves

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 139-148 ◽  
Author(s):  
Jeroen Groenenboom ◽  
Jacob T. Fokkema
Keyword(s):  
Hydraulic Fracture ◽  
Acoustic Waves ◽  
Direct Determination ◽  
Time Lapse ◽  
Ultrasonic Waves ◽  
Hydraulic Fractures ◽  
Slip Model ◽  
Layer Model ◽  
Incident Wavelength ◽  
Linear Slip Model

During scaled hydraulic fracturing experiments in our laboratory, the fracture growth process is monitored in a time‐lapse experiment with ultrasonic waves. We observe dispersion of compressional waves that have propagated across the hydraulic fracture. This dispersion appears to be related to the width of the hydraulic fracture. This means that we can apply the dispersion measurements to monitor the width of the hydraulic fracture in an indirect manner. For a direct determination of the width, the resolution of the signal is required to distinguish the reflections that are related with two distinct fluid/solid interfaces delimiting the hydraulic fracture from its solid embedding. To make this distinction, the solid/fluid interfaces must be separated at least one eighth of a wavelength and represent sufficient impedance contrast. The applicability of the indirect dispersion measurement method however, extends to a fracture width that is in the order of 1% of the incident wavelength. The time‐lapse ultrasonic measurements allow us to relate the small difference in arrival time and amplitude between two measurements solely to the small changes in the width of the fracture. Additional experimental data show that shear waves are completely shadowed by hydraulic fractures, indicating that there is no acoustic contact mechanism at the fracture interface. Therefore we think it is appropriate to use a thin fluid‐filled layer model for these hydraulic fractures instead of the standard empirically oriented linear slip model. Nevertheless, the thin layer model is consistent with the linear‐slip model, if interpreted correctly. A comparison of width measurements inside the wellbore and width estimates by means of dispersion measurements close to the wellbore shows that the method can be successfully applied, at least under laboratory conditions, and that small changes in the width of the fracture are directly expressed in the dispersion of the transmitted signal. This opens the way for the important new application of width monitoring of hydraulic fractures.

On: “Wave Propagation in heterogeneous, porous media: A velocity‐stress, finite difference method,” by N. Dai, A. Vafidis, and E. R. Kanasewich (March‐April 1995 GEOPHYSICS, p. 327–340).

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 1230-1231 ◽  
Author(s):  
Boris Gurevich
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Seismic Wave Propagation ◽  
Heterogeneous Porous Media ◽  
Two Dimensions ◽  
Seismic Modeling ◽  
Modeling Technology ◽  
Interesting Paper

In their interesting paper the authors present a new advanced approach to the simulation of seismic wave propagation in media described by Biot’s theory of dynamic poroelasticity in two dimensions. The algorithm developed can be used to accurately simulate the effect of dynamic poroelasticity on seismic wavefields over hydrocarbon reservoirs. In cases where this effect proves significant this algorithm can be incorporated in the seismic modeling technology.

An adaptive node-distribution method for radial-basis-function finite-difference modeling with optimal shape parameter

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. T1-T18
Author(s):  
Peiran Duan ◽  
Bingluo Gu ◽  
Zhenchun Li ◽  
Zhiming Ren ◽  
Qingyang Li
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Finite Difference ◽  
Stability Condition ◽  
Seismic Wave Propagation ◽  
Optimal Shape ◽  
Shape Parameters ◽  
Seismic Modeling ◽  
Distribution Method ◽  
Node Distribution

The radial-basis-function finite-difference (RBF-FD) method has been proven successful in modeling seismic-wave propagation. Node distribution is typically the first and most critical step in RBF-FD. Regarding the difficulties in seismic modeling, such as node distribution of complex geologic structures, we have designed an adaptive node-distribution method that can generate nodes automatically and flexibly as the computation proceeds with the adaptive grain-radius satisfied dispersion relation and stability condition of seismic-wave propagation. Our method consists of two novel points. The first one is that we adopt an adaptive grain-radius generation method, which can automatically provide a wider scope of grain radius in seismic modeling while satisfying the dispersion relation and stability condition; the second one is that the node-generation algorithm is built by a smoothed model, which significantly improves the modeling stability at a reduced computational cost. Excessive or undesirable shape parameters will create a very ill-conditioned problem. A set of optimal shape parameters for different numbers of neighbor nodes is found quantitatively by minimizing root-mean-square error functions. This optimization method enables us to achieve an improved meshfree modeling process with higher accuracy and practicability and fewer spurious diffractions caused by the transition of different sampling areas. Several numerical results verify the feasibility of our adaptive node-distribution method and the optimal shape parameters.

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