Xiaofei Chen

An Efficient Numerical Method for Computing Synthetic Seismograms for a Layered Half-space with Sources and Receivers at Close or Same Depths

Abstract — It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (Kennett, 1983; Luco and Apsel, 1983; Yao and Harkrider, 1983; Chen, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (Apsel and Luco, 1983; Hisada, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (Dahlquist and Björck, 1974; Chang, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.

Wave Propagation in Irregularly Layered Elastic Models: A Boundary Element Approach with a Global Reflection/Transmission Matrix Propagator

A direct boundary element method that uses the full-space Green’s function is proposed for calculating elastic wave propagation in two-dimensional irregularly stratified models. The global matrix equation becomes larger as the number of layers increases. These equations are usually solved by improved block Gaussian elimination, conjugate gradient algorithms, or other approaches based on different approximations. In this article, we adopt the global generalized reflection/transmission matrix method (Chen, 1990, 1995, 1996) to solve this problem. This method can prevent excessive requirement of both computer memory and CPU time. The method is validated by comparing its results with those obtained using the finite- difference method.

The localized boundary integral equation-discrete wavenumber method for simulating P-SV wave scattering by an irregular topography

In this study, we present a new method, the local boundary integral equation-discrete wavenumber method (loBIE-DWM), for simulating the scattered P-SV waves by a 2D irregular surface topography. This method is rigorously derived from the basic formulation of Bouchon and Campillos BIE-DWM, which can provide accurate enough solutions for most problems, while the expensive computation cost, especially for the high-frequency problem, restricted its application. In this new algo- rithm we propose, the dimension of the inverse matrix involved is only proportional to the sampling number within the corrugated part of the surface. Therefore, its com- putation efficiency is increased dramatically while keeping the same accuracy as BIE-DWM, particularly for the problem in which the corrugated part of the topography is highly localized. Comparisons with previously existing validated results demon- strated the validity of the loBIE-DWM and further showed that its computational efficiency is much superior to the BIE-DWM. Finally, with this new method, we investigated the influences of the topography on the propagation of Rayleigh wave.

An Efficient Approach for Simulating Wave Propagation with the Boundary Element Method in Multilayered Media with Irregular Interfaces

The boundary element method (BEM) is a useful method for seismic-wave simulation in a stratified medium with irregular interfaces. However, the central processing unit (CPU) time required for the traditional BEM method increases exponentially as the number of layers increases. Ge and Chen (2007) presented a BEM with global reflection/transmission matrix propagators that can prevent excessive requirement of both computer memory and CPU time. In this article, we present a more efficient approach for this method. In the new approach, the global matrix propagators can be calculated directly, which can further increase the efficiency by about 40%.

Seismogram synthesis for radially layered media using the generalized reflection/transmission coefficients method: Theory and applications to acoustic logging

A new method based on generalized reflection and transmission coefficients is proposed to calculate the synthetic seismograms in radially multilayered media. This method can be used to efficiently simulate full waveform acoustic logs and crosswell seismic profiles in situations where we need to consider borehole effects. The new formulation is tested by comparing our numerical results with previous available work and shows excellent agreement. Because of the use of the normalized Hankel functions and the normalization factors, this new algorithm for computing seismograms is stable numerically even for high-frequency problems. To show the applicability of this new approach to full waveform sonic logging, we apply it to investigate the effects of complex invaded zones on the geometrical spreading and attenuation estimation for P-waves. We find that a damaged zone (its velocity is slower than the unperturbed formation velocity) exhibits a convergence effect on the P-waves, and a flushed zone (velocity is faster than the unperturbed formation velocity) exhibits a divergence effect on the P-waves.

An Efficient Method for Computing Green's Functions for a Layered Half-Space at Large Epicentral Distances

Nowadays, with the dramatic increase in computational ability, the dis- crete wavenumber integration method (DWIM) (see, e.g., Bouchon and Aki, 1977; Bouchon, 1979, 1981) has been one of the most favorable techniques of computing the synthetic seismograms for a layered half-space because of its simplicity, accuracy, and fair efficiency for some cases, particularly for the case of the near field. However, it becomes less efficient for the case of far field, that is, at large epicentral distances, and the larger the epicentral distance is, the less efficient DWIM will be. In this study, we propose an efficient numerical wavenumber integration method, the self-adaptive Filons integration method (SAFIM), to compute efficiently the dynamic Greens functions for a layered half-space at large epicentral distances. This new integration technique is build upon the particular fifth-order Filons integration scheme (Apsel, 1979; Apsel and Luco, 1983) and the principle of the self-adaptive Simpson inte- gration technique. By using numerical examples, we demonstrate that SAFIM is not only accurate but also very efficient for large epicentral distances. According to our study, we find that at a relatively short epicentral distance (r � 500 km), the classical DWIM is more efficient than SAFIM; at a medium range of epicentral distance (500 kmr � 1200 km), both methods have similar efficiency; at large epicentral dis- tance (r � 1200 km), however, SAFIM is significantly more efficient than DWIM, and the larger the epicentral distance is, the more efficient SAFIM will be. For in- stance, when r 2000 km, SAFIM only needs about 1/3 of the computation time of DWIM. Therefore, this new integration method is expected to be very useful in com- puting synthetic seismograms at large epicentral distances.

Localized Boundary Integral Equation–Discrete Wavenumber Method for Simulating Wave Propagation in Irregular Multiple Layers, Part I: Theory

Abstract We present a new method of synthesizing seismograms for irregular multilayered problems. It is an extension of the local ( lo ) boundary integral equation (BIE) discrete wavenumber method (DWM) topography problem. Following similar procedures as those developed in solving the P - SV waves of topography problems, we first provide the formulation of Bouchon and Campillo’s BIE–DWM (Bouchon, 1985; Campillo and Bouchon, 1985) for the multilayered problem. By orthogonally decomposing the forces on irregular and flat parts of each interface and applying a discrete Fourier transform (DFT) we derive their relation. Finally, considering the continuity of displacement and traction on each interface, we get a linear equation only involving the unknown forces on irregular parts of interfaces and discuss its solution. In this algorithm the dimension of the lineal equation is decided by the sampling number on irregular parts of interfaces. Therefore, its computation efficiency increases dramatically, particularly for the problem in which the corrugated part of the layer is highly localized.

Localized Boundary Integral Equation–Discrete Wavenumber Method for Simulating Wave Propagation in Irregular Multiple Layers, Part II: Validation and Application

In the present study, the localized boundary integral equation–discrete wavenumber method ( lo BIE–DWM) obtained in a companion article (Zhou and Chen, 2009) is validated. For SH waves our results are tested by comparing them with Cao’s (Cao, 2003), while for P - SV waves they are compared with Kawase’s (Kawase and Aki, 1989). The good agreement demonstrated that the method has the same accuracy as other methods. We subsequently used this method to synthesize wave propagation in two examples and discuss the effects of irregular interfaces. Finally, we synthesized the velocity records at the Baijiatuan station due to the Zhangbei earthquake to demonstrate the ability of the lo BIE–DWM to handle the problem with the long epicenter distance. In order to help understand the formulation of the lo BIE–DWM, the numerical implementation and efficiency analysis for a simple example are given.

Acoustic Attenuation Logging Using Centroid Frequency Shift And Amplitude Ratio Methods: A Numerical Study

The centroid frequency shift method is proposed to estimate seismic attenuation from full waveform acoustic logs. This approach along with the amplitude ratio method is applied to investigate the attenuation properties of the P head wave in fluid-filled boreholes. The generalized reflection and transmission coefficients method is used to perform forward modeling. The authors suggest an empirical formula to describe the frequency-dependent geometrical spreading of the P-wave in a borehole. They simulate a more realistic borehole by including a mudcake and an invaded zone which are modeled by a large number of radially symmetric thin layers. The numerical tests show that this invaded zone exhibits very strong influence on the attenuation measurement.

An Effective Approach to Determine the Dynamic Source Parameters

In this study, we present a new and effective method to determine the dynamic source parameters (i.e., stress drop and strength distribution). We first assume that the kinematic source parameters, i.e., the slip and rupture time distributions on the fault plane, are known from the previous source inversion studies. Then, using the seismic source representation theorem we determine the dynamic stress field on a fault plane from known kinematic parameters. Finally, we determine the strength of the fault defined as the peak stress just before the rupture. We have tested the validity of this method by using an illustrative two-dimensional analytical example. To assess the applicability of this method, we have applied it to study the 1979 Imperial Valley earthquake, and obtained consistent results with those ofMiyatakes (1992) andQuins (1990). Compared with previous methods, this new method is simple, straightforward and accurate, and needs much less calculation. Therefore, it is expected to be useful in exploring the seismic source process.