Simulation of the Rayleigh waves in the proximity of the scattering velocity heterogeneities. Exploring the capabilities of the microseismic sounding method

The interaction between the fundamental mode surface Rayleigh waves and the buried heterogeneities with various sizes and different velocity contrasts was studied on base numerical simulation. The field of surface oscillations in the proximity of the scattering heterogeneities was computed as a function of frequency. The synthetic seismograms were used for numerical simulation of the microseismic sounding technology proposed earlier, implying that the solution of the inverse problem for the structure of the medium containing inclusions can be derived from the information contained in the ambient microseismic field. It is assumed that the depth of the layer to be reconstructed is linked with the frequency of the microseisms by a simple relation with the help of a numerical coefficient equal to 0.4–0.5. The combined results of the simulation of a direct problem together with the simple inverse problem solution show that the microseismic sounding technique ensures adequate estimation of the medium structure. Previously, the technology was based on the experimental data only and was phenomenological in character. Some relations between the velocity parameters of the original model heterogeneities and their reconstructed images were also studied.     

SYNTHETIC SEISMOGRAMS AT NON-VERTICAL INCIDENCE*

Synthetic seismograms are usually computed for reflections from vertical incidence of P waves for a horizontally layered medium. In actual practice the angle of incidence departs from the vertical, as receivers are usually located at some distance from the source. At angles other than the vertical, the conversion of P- to S-wave energy and changes in the reflection coefficient affect the shape of the synthetic seismograms. The effect of non-vertical incidence on synthetic seismograms is examined in this paper. Seismograms at non-vertical incidence have been computed using the plane-wave approach of Haskell (1953) for a layered medium. The use of plane waves is an approximation to the actual case of spherical wavefronts from a surface source. Using plane-wave theory, the expected wave forms as a function of angle of incidence were computed numerically for several simple models. The results indicate that the synthetic seismograms do not change significantly for angles of incidence between o and 25 degrees. For larger angles the changes in the wave forms may be severe. The effect is more pronounced for high-velocity layers than for low-velocity layers.     

SEISMOGRAM SYNTHESIS AND RECOMPRESSION OF DISPERSIVE IN-SEAM SEISMIC MULTIMODE DATA USING A NORMAL-MODE SUPERPOSITION APPROACH

In spite of a geometrical rotation into radial and transverse parts, two- or three-component in-seam seismic data used for underground fault detection often suffer from the problem of overmoding ‘noise’. Special recompression filters are required to remove this multimode dispersion so that conventional reflection seismic data processing methods, e.g. CMP stacking techniques, can be applied afterwards. A normal-mode superposition approach is used to design such multimode recompression filters. Based on the determination of the Green's function in the far-field, the normal-mode superposition approach is usually used for the computation of synthetic single- and multi-mode (transmission) seismograms for vertically layered media. From the filter theory's point of view these Green's functions can be considered as dispersion filters which are convolved with a source wavelet to produce the synthetic seismograms. Thus, the design of multimode recompression filters can be reduced to a determination of the inverse of the Green's function. Two methods are introduced to derive these inverse filters. The first operates in the frequency domain and is based on the amplitude and phase spectrum of the Green's function. The second starts with the Green's function in the time domain and calculates two-sided recursive filters. To test the performance of the normal-mode superposition approach for in-seam seismic problems, it is first compared and applied to synthetic finite-difference seismograms of the Love-type which include a complete solution of the wave equation. It becomes obvious that in the case of one and two superposing normal modes, the synthetic Love seam-wave seismograms based on the normal-mode superposition approach agree exactly with the finite-difference data if the travel distance exceeds two dominant wavelengths. Similarly, the application of the one- and two-mode recompression filters to the finite-difference data results in an almost perfect reconstruction of the source wavelet already two dominant wavelengths away from the source. Subsequently, based on the dispersion analysis of an in-seam seismic transmission survey, the normal-mode superposition approach is used both to compute one- and multi-mode synthetic seismograms and to apply one- and multimode recompression filters to the field data. The comparison of the one- and two-mode synthetic seismograms with the in-seam seismic transmission data reveals that arrival times, duration and shape of the wavegroups and their relative excitation strengths could well be modelled by the normal-mode superposition approach. The one-mode recompressions of the transmission seismograms result in non-dispersive wavelets whose temporal resolution and signal-to-noise ratio could clearly be improved. The simultaneous two-mode recompressions of the underground transmission data show that, probably due to band-limitation, the dispersion characteristics of the single modes could not be evaluated sufficiently accurately from the field data in the high-frequency range. Additional techniques which overcome the problem of band-limitation by modelling all of the enclosed single-mode dispersion characteristics up to the Nyquist frequency will be mandatory for future multimode applications.     

Seismic Discrimination of the May 11, 1998 Indian Nuclear Test with Short-period Regional Data from Station NIL (Nilore, Pakistan)

v—vRegional seismic discriminants for the May 11, 1998 Indian underground nuclear test(s) and earthquakes recorded at station NIL (Nilore, Pakistan) provide new data to test strategies that can be used to monitor the Comprehensive Nuclear-Test-Ban Treaty (CTBT). Three categories of regional discriminants (ratios of P- and/or S-wave energy) were measured on short-period (0.5–6uHz) seismograms: P/S amplitude ratios (phase ratios) measured in the same frequency band, P- and S-wave spectral ratios (i.e., low frequency to high frequency for the same phase) and P/S cross-spectral ratios (i.e., low frequency S-wave to high frequency P-wave). The P/S amplitude ratios show good separation of the Indian nuclear test and regional earthquakes for Pn/Lg and Pn/Sn, however Pg/Lg does not discriminate as well. Pn/Lg and Pn/Sn discriminate well at frequencies as low as 0.5–2uHz, especially after accounting for path effects. This observation differs from previous studies that report poor separation of earthquakes and explosions at lower frequencies. The P/S amplitude ratios do not show any magnitude dependence, suggesting that forming the ratios in a fixed frequency band cancels the effects of source size-corner frequency scaling. Spatial variability of the observed discriminants arises from variations in crustal waveguide and/or attenuation structure (path propagation effects). Grouping amplitude ratios for earthquakes with paths similar to the Indian test greatly improves discrimination. Removing distance trends does not generally improve discrimination. Accounting for path effects with Bayesian kriging significantly improves discrimination. Spectral ratios (e.g., Pn [0.5–1uHz]/Pn [4–6uHz]) and cross-spectral ratios (e.g., Lg [1–2uHz]/Pn [4–6uHz]) show distance and magnitude dependence. We developed a technique for simultaneously removing the effects of distance and source size-corner frequency scaling on amplitude and spectral ratios. The technique uses a gridsearch to find several parameters that characterize the observed distance and magnitude dependence. Discrimination of the Indian test improved dramatically after the distance and magnitude trends were removed from the spectral and cross-spectral ratio data.     

Receiver function estimated by maximum entropy deconvolution

Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than I, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.     

频率域中的合成地震记录

波动理论的合成地震记录是地震资料处理和解释中的重要研究课题。 目前,制作波动理论的合成记录主要是用Trorey的克希霍夫方法,正在研究的有有限差分法和有限元素法。本文提出一种新的方法,在频率域中制作波动理论的合成记录,给出了与克希霍夫绕射波方程等价的频率域中的绕射波方程。在国产DJS-11型计算机上,应用两种绕射波方程实现了合成地震记录,并且进行了比较,认为频率域方法是有效的,可以用于波动方程偏移和地震资料解释,进一步工作有可能获得多层变速模型的波动理论记录。     

Determining the focal mechanisms and depths of relatively small earthquakes using a few stations by full‐waveform modelling

Determining the focal mechanism of earthquakes helps us to better define faults and understand the stress regime. This technique can be helpful in the oil and gas industry where it can be applied to microseismic events. The objective of this paper is to find double couple focal mechanisms, excluding scalar seismic moments, and the depths of small earthquakes using data from relatively few local stations. This objective is met by generating three‐component synthetic seismograms to match the observed normalized velocity seismograms. We first calculate Green's functions given an initial estimate of the earthquake's hypocentre, the locations of the seismic recording stations and a 1D velocity model of the region for a series of depths. Then, we calculate the moment tensor for different combinations of strikes, dips and rakes for each depth. These moment tensors are combined with the Green's functions and then convolved with a source time function to produce synthetic seismograms. We use a grid search to find the synthetic seismogram with the largest objective function that best fits all three components of the observed velocity seismogram. These parameters define the focal mechanism solution of an earthquake. We tested the method using three earthquakes in Southern California with moment magnitudes of 5.0, 5.1 and 4.4 using the frequency range 0.1–2.0 Hz. The source mechanisms of the events were determined independently using data from a multitude of stations. Our results obtained, from as few as three stations, generally match those obtained by the Southern California Earthquake Data Center. The main advantage of this method is that we use relatively high‐frequency full‐waveforms, including those from short‐period instruments, which makes it possible to find the focal mechanism and depth of earthquakes using as few as three stations when the velocity structure is known.     

“Repeating Events” as Estimator of Location Precision: The China National Seismograph Network

“Repeating earthquakes” identified by waveform cross-correlation, with inter-event separation of no more than 1 km, can be used for assessment of location precision. Assuming that the network-measured apparent inter-epicenter distance X of the “repeating doublets” indicates the location precision, we estimated the regionalized location quality of the China National Seismograph Network by comparing the “repeating events” in and around China by Schaff and Richards (Science 303: 1176–1178, 2004; J Geophys Res 116: B03309, 2011) and the monthly catalogue of the China Earthquake Networks Center. The comparison shows that the average X value of the China National Seismograph Network is approximately 10 km. The mis-location is larger for the Tibetan Plateau, west and north of Xinjiang, and east of Inner Mongolia, as indicated by larger X values. Mis-location is correlated with the completeness magnitude of the earthquake catalogue. Using the data from the Beijing Capital Circle Region, the dependence of the mis-location on the distribution of seismic stations can be further confirmed.     

Synthetic Seismograms and Wide-angle Seismic Attributes from the Gaussian Beam and Reflectivity Methods for Models with Interfaces and Velocity Gradients

— The effects of interfaces and velocity gradients on wide-angle seismic attributes are investigated using synthetic seismograms. The seismic attributes considered include envelope amplitude, pulse instantaneous frequency, and arrival time of selected phases. For models with interfaces and homogeneous layers, head waves can propagate which have lower amplitudes, as well as frequency content, compared to the direct arrivals. For media with interfaces and velocity gradients, higher amplitude diving waves and interference waves can also occur. The Gaussian beam and reflectivity methods are used to compute synthetic seismograms for simple models with interfaces and gradients. From the results of these methods, seismic attributes are obtained and compared. It was found that both methods were able to simulate wide-angle seismic attributes for the simple models considered. The advantage of using the Gaussian beam method for seismic modeling and inversion is that it is fast and also asymptotically valid for laterally varying media.     

Theoretical study on the influence of CMB topography on the core reflection ScS

Computing synthetic seismograms for media with localized heterogeneous regions can be performed using hybrid methods. Here, a combination of a finite-difference (FD) technique and a frequency-wavenumber (ω − k) filtering is applied to model wave reflection at different kinds of core-mantle boundary (CMB) topography. The FD method is only applied in the neighbourhood of the CMB, while the ω − k filter is used to continue the reflected wavefield to the Earth's surface. Synthetic SH-seismograms for ScS with a dominant frequency of 0.5 Hz are computed at epicentral distances from 44° to 69°. The topography varies in amplitude (maximum amplitude of 1.0–2.7 km) and in its wavenumber spectrum; it is either monochromatic (wavelengths from 55 to 270 km) or statistical (coloured noise). The seismograms for a CMB with topography are compared with those for a plane CMB. We observe that monochromatic topography with short wavelengths (less than 100 km) results in amplitude reduction and shorter travel times than in the case of a plane CMB, but no variations with epicentral distance appear, whereas greater wavelengths exhibit amplitude variations with distance as well as travel time residuals, which both correlate with the CMB topography. Statistical models show amplitude variations with epicentral distance, while the travel time residuals are very small (less than 0.1 s). All synthetics illustrate that wavefront healing occurs along the ray path from the CMB to the Earth's surface. While the seismograms at the CMB exhibit strong fluctuations, the fluctuations at the surface are smoothed and reduced. This demonstrates that it is necessary to use wave theoretical methods for computing synthetic seismograms for complicated structures at greater depth. It also follows that travel times are less sensitive to the structure than the amplitudes.     

On the Effects of Non-planar Geometry for Blind Thrust Faults on Strong Ground Motion

— We quantify the effects of complex fault geometry on low-frequency (<1 Hz) strong ground motion using numerical modeling of dynamic rupture. Our tests include the computation of synthetic seismograms for several simple rupture scenarios with planar and curved fault approximations of the 1994 Northridge earthquake. We use the boundary integral equation method (BIEM) to compute the dynamic rupture process, which includes the normal stress effects along the curved fault geometries. The wave propagation and computation of synthetic seismograms are modeled using a fourth-order finite-difference method (FDM). The near-field ground motion is significantly affected by the acceleration, deceleration and arrest of rupture due to the curvature of the faults, as well as the variation in directivity of the rupture. For example, a 6-km-long hanging-wall or footwall splay with a maximum offset of 1 km can change 1-Hz peak velocities by up to a factor of 2-3 near the fault. Our tests suggest that the differences in waveform are larger on the hanging wall compared to those on the footwall, although the differences in amplitude are larger in the forward rupture direction (footwall). The results imply that kinematic ground motion estimates may be biased by the omission of dynamic rupture effects and even relatively gentle variation in fault geometry, and even for long-period waves.     

基于谱元-简正振型耦合方法的核幔边界D″区地震波波形模拟方法研究

本文拓展了一种模拟地震波在地球核幔边界D″区各向异性介质中传播的数值方法:谱元-简正振型耦合方法(CSEM).该方法通过在球对称各向同性介质空间采用简正振型方法,在各向异性的D″区采用谱元方法,并在两种介质的边界采用"DtN"算子耦合的策略计算一维模型PREM(见文献[1])或修改后的D″区横向各向同性VTI-PREM模型的理论地震图.模拟所得数值解结果与采用简正振型方法得到的解析解结果进行对比以验证方法的精度.在中国科学院地球深部结构重点实验室高性能计算机上使用128个CPU计算得到的结果显示,在10^-5～0.125 Hz的频率范围内谱元简正振型法得到的波形与简正振型方法能很好拟合.此外,对于VTI介质结构模型,谱元简正振型法能够准确模拟S波分裂现象,从而验证了谱元简正振型耦合方法对各向异性介质中地震波传播数值模拟是一种有效的方法.     

On reproducibility of relative locations of recurrent earthquakes recovered from similarity of their waveforms at a single station

Relative locations of recurrent earthquakes can be recovered from values of cross-correlation coefficients between their waveforms at a single station, provided that an idea of Menke (1999) that the values depend inversely exponentially from separation between the sources is true. An algorithm developed in Gnyp (2013) based on this idea was applied here for recovering relative locations of the two groups of the 2005–2006 recurrent earthquakes in Mukacheve, Ukraine, from the sets of cross-correlation coefficients between their records at the four local network stations to find out whether the locations were in principle reproducible independently at each of the stations, at epicentral distances from about 6 to 64 km. The resulting sets of locations occurred in good agreement with each other, which may be considered as an experimental evidence for validity of the Menke’s dependence over the corresponding range of distances. The reproducibility of relative locations has been analyzed in terms of existence and uniqueness of the inverse problem’s solution, and in connection with data completeness and the influence of noise on it.     

Real-time envelope cross-correlation detector: application to induced seismicity in the Insheim and Landau deep geothermal reservoirs

We develop and test a real-time envelope cross-correlation detector for use in seismic response plans to mitigate hazard of induced seismicity. The incoming seismological data are cross-correlated in real-time with a set of previously recorded master events. For robustness against small changes in the earthquake source locations or in the focal mechanisms we cross-correlate the envelopes of the seismograms rather than the seismograms themselves. Two sequenced detection conditions are implemented: After passing a single trace cross-correlation condition, a network cross-correlation is calculated taking amplitude ratios between stations into account. Besides detecting the earthquake and assigning it to the respective reservoir, real-time magnitudes are important for seismic response plans. We estimate the magnitudes of induced microseismicity using the relative amplitudes between master event and detected event. The real-time detector is implemented as a SeisComP3 module. We carry out offline and online performance tests using seismic monitoring data of the Insheim and Landau geothermal power plants (Upper Rhine Graben, Germany), also including blasts from a nearby quarry. The comparison of the automatic real-time catalogue with a manually processed catalogue shows, that with the implemented parameters events are always correctly assigned to the respective reservoir (4 km distance between reservoirs) or the quarry (8 km and 10 km distance, respectively, from the reservoirs). The real-time catalogue achieves a magnitude of completeness around 0.0. Four per cent of the events assigned to the Insheim reservoir and zero per cent of the Landau events are misdetections. All wrong detections are local tectonic events, whereas none are caused by seismic noise.     

On the possibility of using the tidal modulation of seismic waves for forecasting earthquakes

The earthquake forecasting technique based on the effect of the modulation of high frequency seismic noise (HFSN) by the Earth’s tides is discussed and the experience of its practical application in Kamchatka is described based on the extensive measurement data for 1996–2013. The empirical development of the lower magnitude threshold on the epicentral distance is refined. The reliability and validity of the precursor are assessed. The efficiency of the precursor is estimated in two ways. It is shown that the results of applying the prognostic procedure statistically significantly differ from a random guess. The presented estimates are based on the catalog containing 68 earthquakes of 1996–2013 in the predicted magnitude interval M ≥ 5.0 at the epicentral distances that are linked to the magnitude by functional dependence.     

PHASE DISTORTION DUE TO ABSORPTION IN SEISMOGRAMS AND VSP*

Absorption of seismic energy in the earth reduces amplitudes and changes phases of the propagating seismic waves. Amplitudes are usually recovered according to an estimated exponential decay curve, while phase distortions are generally disregarded. Therefore, accurate processing of seismic data requires a careful investigation of the relationship between absorption and phases. In this paper a procedure is suggested to achieve this goal, and some related topics are worked out. A method is outlined for computing synthetic seismograms and vertical seismic profiles with phase distortion due to absorption. The algorithm works in the frequency domain, and it provides for absorption according to the usual model of exponential decay of amplitude with distance. The absorption coefficient is a linear function of frequency and is related to the quality factor Q of the rocks. Complex seismic velocities are introduced and minimum-phase delay due to absorption is assumed for all cases considered. Methods for estimating Q profiles from seismic well surveys and seismic data are described. Comparison between field and synthetic data shows the effectiveness and benefits of the procedure. Some applications of the method to phase distortion recovery and wavelet processing are presented.     

合成地震图的广义反射透射系数矩阵方法

简述了在均匀层状介质中，合成地震图的广义反射透射系数矩阵方法，并通过与有人的计算结果对比，检验了经过修改调试后的合成地震图的计算程序。计算与对比表明，经修改调试后的程序对于各种因素，包括震源类型、震源深度、震中、频率和慢度都有较好的普适性，适用于实际的地震波形研究。     

Computation of Synthetic Seismograms in 2-D and 3-D Media Using the Gaussian beam Method

The Gaussian beam method is applied to vertical seismic profiling in 2-D and 3-D models. A simple approach to the computation of Gaussian beam seismograms in the vicinity of structural interfaces is proposed. The effects of (a) the radiation pattern of a point source, (b) non-causal attenuation, (c) transverse inhomogeneities in synthetic seismograms are studied on numerical examples.     

EXPERIMENTAL EVIDENCE OF S*-WAVE*

During development of theoretical methods to compute synthetic seismograms, a new type of wave called S*-wave was discovered by Hron and Mikhailenko. This wave propagates with the shear-wave velocity and can be interpreted as a non-geometrical wave arrival with large amplitudes strongly depending on the depth of a pure P-point source. In this first experimental verification of the existence of S*-waves by means of two-dimensional model-seismics it is demonstrated that: 1. the S*-wave exists and depends on the source distance from the free surface; 2. the S*-wave is generated as an ordinary shear wave on the free surface at the point located directly above the P-source, as illustrated in the synthetic seismograms. The measured seismograms agree remarkably well with the computed ones.     

Matrix impedance in the problem of the calculation of synthetic seismograms for a layered-homogeneous isotropic elastic medium

A new method is proposed for calculating synthetic seismograms caused by a force in a plane-parallel medium consisting of homogeneous elastic isotropic layers. The matrix impedance, i.e., the matrix function of depth, by which motion vector must be multiplied in order to obtain the stress vector, is introduced for solving a system of ordinary differential equations with respect to the motion-stress vector, which appears during the separation of variables. An independent nonlinear equation is obtained for the impedance. The propagator for the motion vector is constructed with the aid of the impedance. The closed analytical formulas, which do not contain any exponents with positive indices, are obtained both for the impedance and for the motionvector propagator. The algorithm for the calculation of seismograms, free of limitations on the number and thickness of layers, as well as on the frequency range of interest, is constructed on the basis of these formulas. The algorithm is tested with the aid of an analytical solution.