FDM Simulation of Seismic Waves, Ocean Acoustic Waves, and Tsunamis Based on Tsunami-Coupled Equations of Motion

We have developed a new, unified modeling technique for the total simulation of seismic waves, ocean acoustic waves, and tsunamis resulting from earthquakes, based on a finite difference method simulation of the 3D equations of motion. Using the equilibrium between the pressure gradient and gravity in these equations, tsunami propagation is naturally incorporated in the simulation based on the equations of motion. The performance of the parallel computation for the newly developed tsunami-coupled equations using a domain partitioning procedure shows a high efficiency coefficient with a large number of CPU cores. The simulation results show how the near-field term associated with seismic waves produced by shallow earthquakes leads to a permanent coseismic deformation of the ground surface, which gives rise to the initial tsunami on the sea surface. Propagation of the tsunami along the sea surface as a gravity wave, and ocean acoustic waves in seawater with high-frequency multiple P-wave reflections between the free surface and sea bottom, are also clearly demonstrated by the present simulations. We find a good agreement in the tsunami waveform between our results and those obtained by other simulations based on an analytical model and the Navier–Stokes equations, demonstrating the effectiveness of the tsunami-coupling simulation model. Based on this simulation, we show that the ratio of the amplitude of ocean acoustic waves to the height of the tsunami, both of which are produced by the earthquake, strongly depends on the rise time of the earthquake rupture. This ratio can be used to obtain a more detailed understanding of the source rupture processes of subduction zone earthquakes, and for implementing an improved tsunami alert system for slow tsunami earthquakes.     

Waves, circulation and vertical dependence

Longuet-Higgins and Stewart (J Fluid Mech 13:481–504, 1962; Deep-Sea Res 11:529–562, 1964) and later Phillips (1977) introduced the problem of waves incident on a beach, from deep to shallow water. From the wave energy equation and the vertically integrated continuity equation, they inferred velocities to be Stokes drift plus a return current so that the vertical integral of the combined velocities was nil. As a consequence, it can be shown that velocities of the order of Stokes drift rendered the advective term in the momentum equation negligible resulting in a simple balance between the horizontal gradients of the vertically integrated elevation and wave radiation stress terms; the latter was first derived by Longuet-Higgins and Stewart. Mellor (J Phys Oceanogr 33:1978–1989, 2003a), noting that vertically integrated continuity and momentum equations were not able to deal with three-dimensional numerical or analytical ocean models, derived a vertically dependent theory of wave–circulation interaction. It has since been partially revised and the revisions are reviewed here. The theory is comprised of the conventional, three-dimensional, continuity and momentum equations plus a vertically distributed, wave radiation stress term. When applied to the problem of waves incident on a beach with essentially zero turbulence momentum mixing, velocities are very large and the simple balance between elevation and radiation stress gradients no longer prevails. However, when turbulence mixing is reinstated, the vertically dependent radiation stresses produce vertical velocity gradients which then produce turbulent mixing; as a consequence, velocities are reduced, but are still larger by an order of magnitude compared to Stokes drift. Nevertheless, the velocity reduction is sufficient so that elevation set-down obtained from a balance between elevation gradient and radiation stress gradients is nearly coincident with that obtained by the aforementioned papers. This paper includes four appendices. The first appendix demonstrates the numerical process by which Stokes drift is excluded from the turbulence stress parameterization in the momentum equation. A second appendix determines a bottom slope criterion for the application of linear wave relations to the derivation of the wave radiation stress. The third appendix explores the possibility of generalizing results by non-dimensionalization. The final appendix applies the basic theory to a problem introduced by Bennis and Ardhuin (J Phys Oceanogr 41:2008–2012, 2011).     

Automated Detection, Extraction, and Measurement of Regional Surface Waves

v--vOur goal is to develop and test an effective method to detect, identify, extract, and quantify surface wave signals for weak events observed at regional stations. We describe an automated surface wave detector and extractor designed to work on weak surface wave signals across Eurasia at intermediate periods (8 s-40 s). The method is based on phase-matched filters defined by the Rayleigh wave group travel-time predictions from the broadband group velocity maps presented by Ritzwoller and Levshin (1998) and Ritzwoller et al. (1998) and proceeds in three steps: Signal compression, signal extraction or cleaning, and measurement. First, the dispersed surface wave signals are compressed in time by applying an anti-dispersion or phase-matched filter defined from the group velocity maps. We refer to this as the `compressed signal.' Second, the surface wave is then extracted by filtering `noise' temporally isolated from the time-compressed signal. This filtered signal is then redispersed by applying the inverse of the phase-matched filter. Finally, we adaptively estimate spectral amplitude as well as group and phase velocity on the filtered signal. The method is naturally used as a detector by allowing origin time to slide along the time axis. We describe preliminary results of the application of this method to a set of nuclear explosions and earthquakes that occurred on or near the Chinese Lop Nor test site from 1992 through 1996 and one explosion on the Indian Rajasthan test site that occurred in May of 1998.     

Thunderstorms,Lightning, Sprites and Magnetospheric Whistler-Mode Radio Waves

Thunderstorms and the lightning that they produce are inherently interesting phenomena that have intrigued scientists and mankind in general for many years. The study of thunderstorms has rapidly advanced during the past century and many efforts have been made towards understanding lightning, thunderstorms and their consequences. Recent observations of optical phenomena above an active lightning discharge along with the availability of modern technology both for data collection and data analysis have renewed interest in the field of thunderstorms and their consequences in the biosphere. In this paper, we review the electrification processes of a thunderstorm, lightning processes and their association with global electric circuit and climate. The upward lightning discharge can cause sprites, elves, jets, etc. which are together called transient luminous events. Their morphological features and effects in the mesosphere are reviewed. The wide spectrum of electromagnetic waves generated during lightning discharges couple the lower atmosphere with the ionosphere/magnetosphere. Hence various features of these waves from ULF to VHF are reviewed with reference to recent results and their consequences are also briefly discussed.     

与地震波抢时间

１９９２年６月２８日,美国南加州一个宁静的星期天,一次强烈的地震于凌晨４时５７分把成千上万人从睡梦中惊醒。这次地震的震中位于洛杉矶以东大约３００ｋｍ的莫哈韦沙漠,震级７．３,使南加州１／４地区的电力供应中断。洛杉矶居民奈尔斯（ＫｅｎＮｉｌｅｓ）与许多邻居一样,打开电视机想从新闻节目中了解有关该震的详细情况。他说：“我正在看电视的时候,电视屏幕突然晃动起来,接着,新闻广播员播放了地震警报。尔后,外面就是一片混乱。”源于强余震的震动把电视机震得格格直响,但此时震动尚未到达位于该城西部的奈尔斯的家。他…     

On Motion of Wind Waves

Parameters of wind waves in a deep-water zone of a reservoir is studied in the context of wave influence on shore stability. Data from measurements of wave parameters in reservoirs of Czech Republic are used. The relationship between the period and phase velocity of wind waves is discussed.     

地震波研究://car

回顾了近4年来中国地球物理学家在地震波研究方面取得的主要进展. 分别简要地讨论了层状均匀介质、横向不均匀介质和多孔介质中的地震波传播，地震面波及波形反演，以及地震勘探、测井问题中的地震波研究方面取得的新成果. 指出当前地震波研究的重要课题是发展高效的数值方法，并利用该方法开展复杂介质中的地震波激发和传播，以及强地面运动的研究，为精细的地震危险分析与预测奠定基础.      

Attenuation of Coda Waves in the Saurashtra Region, Gujarat (India)

The attenuation characteristics based on coda waves of two areas—Jamnagar and Junagarh of Saurashtra, Gujarat (India)—have been investigated in the present study. The frequency dependent relationships have been developed for both the areas using single back scattering model. The broadband waveforms of the vertical components of 33 earthquakes (Mw 1.5–3.5) recorded at six stations of the Jamnagar area, and broadband waveforms of 68 earthquakes (Mw 1.6–5) recorded at five stations of the Junagarh area have been used for the analysis. The estimated relations for the Junagarh area are: Q _c?=?(158?±?5)f^(0.99±0.04) (lapse time : 20?s), Q _c?=?(170?±?4.4)f^(0.97±0.02) (lapse time : 30?s) and Q _c?=?(229?±?6.6)f^(0.94±0.03) (lapse time : 40?s) and for the Jamnagar area are: Q _c?=?(178?±?3)f^(0.95±0.05) (lapse time : 20?s), Q _c?=?(224?±?6)f^(0.98±0.06) (lapse time : 30?s) and Q _c?=?(282?±?7)f^(0.91±0.03) (lapse time : 40?s). These are the first estimates for the areas under consideration. The Junagarh area appears to be more attenuative as compared to the Jamnagar area. The increase in Q _c values with lapse time found here for both the areas show the depth dependence of Q _c as longer lapse time windows will sample larger area. The rate of decay of attenuation (Q ^?1) with frequency for the relations obtained here is found to be comparable with those of other regions of the world though the absolute values differ. A comparison of the coda-Q estimated for the Saurashtra region with those of the nearby Kachchh region shows that the Saurashtra region is less heterogeneous. The obtained relations are expected to be useful for the estimation of source parameters of the earthquakes in the Saurashtra region of Gujarat where no such relations were available earlier. These relations are also important for the simulation of earthquake strong ground motions in the region.     

Visco-Elastic Waves in Rock-Like Composites

The subject of this paper is the treatment of rocks - and, especially, fluid-saturated and partially saturated reservoir rocks, as composite visco-elastic media. By this we mean to study and partially answer the question of how the effective material (frequency-dependent and complex-valued stiffness/density) parameters can be estimated from a knowledge of the constituents of the rocks, their volume fractions, the statistical distribution of sizes, shapes, orientations and positions of the individual particles (minerals of quartz, clay, etc.) and cavities (pores, cracks, etc.); in addition to parameters related to the fluid and its ability to flow, at the scale of the microstructure as well as that of the wavelength (assumed to be long compared to the scale-size of the microstructure).Our approach is to develop and combine a theory of stochastic waves with established results for the micromechanics of defects in solids, as well as state-of-the-art models of wave-induced fluid flow. Specifically, we first derive an exact formal expression for the effective material parameters in terms of a dynamic T-matrix for the material, which satisfies a single integral equation of the Lippmann-Schwinger type (known from quantum scattering theory), but formulated in an abstract vector space, associated with the combination of the strain and velocity fields into a more general state vector . Inclusions-based models are developed on the basis of standard many-body techniques, known from the static T-matrix approach as well as nuclear collision theory. The t-matrix of a low-aspect-ratio spheroidal crack is expressed in terms of the familiar displacement discontinuity parameters of Hudson, via the so-called K-tensor, which is of interest in itself, for example, when connecting cracks to pores (in the presence of multiple solid constituents) on the basis of an expression for the t-matrix of a communicating cavity.The present theory can in principle be used beyond the Rayleigh limit, but explicit estimates of the effective material parameters have so far been derived only under the assumption that (scattering attenuation can be ignored) the wavelength is large compared to the scale-size of a representative volume element. Starting with the dynamic equations of motion, we show that the behaviour of the mean wave in the Rayleigh limit is indeed determined by the effective stiffness tensor associated with a static theory of composites, in conjunction with the spatially averaged density for the heterogeneous material as a whole. Thus, we have provided justification to the procedure we used in a series of related papers, where we started out with the static equilibrium condition and employed the elastic/visco-elastic correspondence principle. Numerical examples (dealing with the effects of randomly oriented cracks on the isotropic velocity and attenuation spectra of a dual porosity model of clay-sand mixtures, and the effects of spatial distribution on the anisotropic attenuation spectra of fully aligned cracks that are partially saturated with two different fluids) will be provided in order to complement those in our earlier papers.     

相对密实度对随机波与定次数波作用下土体变形关系的影响

通过砂土的一系列动三轴实验,研究不规则地震荷载作用下与定次数等幅荷载作用下土体变形间的关系,给出砂土相对密实度对二者间关系的影响规律。结果表明:真实地震荷载下土的变形发展与等幅正弦荷载明显不同,应变发展时程的形态主要受地震动的形态控制;应变比C与砂土相对密度间关系具有规律性,随相对密度增大而降低,若采用以20周作为标准作用次数、0.65倍地震波峰值为等幅荷载代替不规则的地震荷载,修正真实地震应力下的残余变形,其应变比C随砂土密实度的增大而减小。同时,冲击型荷载的应变比C`要远大于振动型荷载。     

Common-Reflection-Surface Stack for Converted Waves

The finite-offset (FO) common-reflection-surface (CRS) stack has been shown to be able to handle not only P-P or S-S but also arbitrarily converted reflections. It can provide different stack sections such as common-offset (CO), common-midpoint (CMP) and common-shot (CS) sections with significantly increased signal-to-noise ratio from the multi-coverage pre-stack seismic data in a data-driven way. It is our purpose in this paper to demonstrate the performance of the FO CRS stack on data involving converted waves in inhomogeneous layered media. In order to do this we apply the FO CRS stack for common-offset to a synthetic seismic data set involving P-P as well as P-S converted primary reflections. We show that the FO CRS stack yields convincing improvement of the image quality in the presence of noisy data and successfully extracts kinematic wavefield attributes useful for further analyses. The extracted emergence angle information is used to achieve a complete separation of the wavefield into its P-P and P-S wave components, given the FO CRS stacked horizontal and vertical component sections.     

粘弹性介质中的地震波

给出了三元件的标准线性粘弹性固体在半平面内传播的地震波的解析解，它是由已知的弹性半平面内的解析解迭粘滞性解而得，从而克服了视地壳为二元件粘弹性体的Voigt模型或Maxell模型的缺点。     

Spectrum Analysis of the Reflected Waves Observed in the Nikko Region, Central Japan

—The Nikko region, in northern Kanto, central Japan, which is a high seismicity region, is located near the volcanic front. Many seismic observations have been carried out around the Nikko region because the seismograms of the shallow earthquakes occurring in this region show an S-wave reflected phase (SxS) and an S-to-P mode-converted and reflected phase (SxP) from a mid-crustal seismic velocity discontinuity. The depth of the mid-crustal reflector was estimated to be about 9–16 km. From the amplitude analyses of SxS and SxP phases, the material of the mid-crustal layer just beneath the reflector was expected to be a low rigidity layer, which was interpreted as partially molten rocks. No evidence has been shown for the internal properties of the material of the reflector. The Vp/Vs ratio is a good measure to distinguish between the two candidates for seismic reflectors; i.e., partially molten rocks and rocks containing water. We investigate the Vp/Vs ratio of the reflector using the spectrum analyses of the data observed by a seismic array. From spectrum analysis of the data, we indicate that the Vp/Vs ratio of 2.5 is better than that of 1.8 to explain the observed data, which shows that the material beneath the reflector consists of partially molten rocks.     

Attenuation of High Frequency P and S Waves in the Gujarat Region,India

The local earthquake waveforms recorded on broadband seismograph network of Institute of Seismological Research in Gujarat, India have been analyzed to understand the attenuation of high frequency (2–25 Hz) P and S waves in the region. The frequency dependent relationships for quality factors for P (Q _P) and S (Q _S) waves have been obtained using the spectral ratio method for three regions namely, Kachchh, Saurashtra and Mainland Gujarat. The earthquakes recorded at nine stations of Kachchh, five stations of Saurashtra and one station in mainland Gujarat have been used for this analysis. The estimated relations for average Q _P and Q _S are: Q _P = (105 ± 2) f ^{0.82 ± 0.01}, Q _S = (74 ± 2) f ^{1.06 ± 0.01} for Kachchh region; Q _P = (148 ± 2) f ^{0.92 ± 0.01}, Q _S = (149 ± 14) f ^{1.43 ± 0.05} for Saurashtra region and Q _P = (163 ± 7) f ^{0.77 ± 0.03}, Q _S = (118 ± 34) f ^{0.65 ± 0.14} for mainland Gujarat region. The low Q (<200) and high exponent of f (>0.5) as obtained from present analysis indicate the predominant seismic activities in the region. The lowest Q values obtained for the Kachchh region implies that the area is relatively more attenuative and heterogeneous than other two regions. A comparison between Q _S estimated in this study and coda Q (Qc) previously reported by others for Kachchh region shows that Q _C > Q _S for the frequency range of interest showing the enrichment of coda waves and the importance of scattering attenuation to the attenuation of S waves in the Kachchh region infested with faults and fractures. The Q _S/Q _P ratio is found to be less than 1 for Kachchh and Mainland Gujarat regions and close to unity for Saurashtra region. This reflects the difference in the geological composition of rocks in the regions. The frequency dependent relations developed in this study could be used for the estimation of earthquake source parameters as well as for simulating the strong earthquake ground motions in the region.     

Nonlinear wave Packets of Equatorial Kelvin Waves

The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular perturbation theory applied to the shallow water wave equations. Within the limits of the perturbation theory, which is formally restricted to weak mean shear and weak nonlinearity, we derive a Nonlinear Schroedinger equation to describe the envelope of the wave packet. We find that nonlinearity has a defocusing effect so that coherent wave packets must owe their existence entirely to the generation mechanism rather than to nonlinear focusing of a broad initial disturbance.     

Frequency-Dependent Energy Dissipation of Irregular Breaking Waves

Results of field experiments and simulation are used to study the hypothesis that energy dissipation from irregular breaking waves can have a nonuniform distribution over the frequency. It was found that the wave energy dissipation in the outer surf zone is practically independent of the frequency and can be approximated by a constant. A quadratic or a selective (at the frequency band of second–third harmonics) dependence of energy dissipation on frequency was found to form in the inner part of the surf zone, where it is controlled by wave asymmetry and bed slope. The dissipation of the energy of breaking waves was shown to proceed in such a way as to compensate for the effect of processes of linear or nonlinear deformation of waves.     

Runup of Tsunami Waves in U-Shaped Bays

The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of 1D shallow water theory with the use of an assumption of the uniform current on the cross-section. The wave shoaling in bays, when the depth varies smoothly along the channel axis, is studied with the use of asymptotic approach. In this case a weak reflection provides significant shoaling effects. The existence of traveling (progressive) waves, propagating in bays, when the water depth changes significantly along the channel axis, is studied within rigorous solutions of the shallow water theory. It is shown that traveling waves do exist for certain bay bathymetry configurations and may propagate over large distances without reflection. The tsunami runup in such bays is significantly larger than for a plane beach.     

On the propagation of finite Love Waves

Summary The problem of the propagation of finite Love Waves in a heterogeneous elastic half space lying over a homogeneous elastic half space, using the quasilinear stress-strain relation due toS. Ferhst [4] is considered in detail. The variations of the parameter in the layer assumed to be of the form 1= 0e ^z, 0e ^z where is a constant andz is distance measured from the surface into the layer.