Propagation of seismic waves in a viscoelastic medium and the effect of topography

In this paper we have simulated the propagation of seismic waves in viscoelastic medium and calculated the effect of irregular surface topography by using finite element method. Several types of elastic and viscoelastic medium models, such as block structure, vidges and/or valley with and without a soft layer underneath have been studied. The distribution of maximum amplitude of displacement and acceleration on surface has been calculated in the case of vertically incident SH and P waves from the basement. The possible application in earthquake engineering is also discussed. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 442–449, 1991.     

The 1990 Zaisang earthquake of magnitude 7.3 in Kazakstan

The Zaisang earthquake (M _s=7.3) on June 14, 1990 occurred in the boundary between China and Kazakstan. During the great shock, 3 persons lost their lives, 30 people had been hurt and 340 houses collapsed. The intensity of the epicentre is VIII Degree. The economic losses equals to about 320 000 000 Yuan. This large earthquake was occurred on a new born fault, it belongs to main shock-aftershock type earthquake. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 360–365, 1993.     

Transitions to broad cells in a nonlinear thermal convection system

Abstract

This paper explores the properties of a two-dimensional, Boussinesq convection model with an ad hoc term in the buoyancy tendency equation that represents a positive external feedback process acting on the buoyancy fluctuations. Linear stability analyses and nonlinear integrations are presented for the case of constant heat flux boundary conditions. Although the large wavenumber modes grow the fastest from a state of rest, the nonlinear solutions progressively evolve to cells of small wavenumber. Applications to mesoscale cellular convection in the atmosphere are discussed.     

Investigations of nonlinear performances of implicit pseudodynamic algorithms

Although it has been shown that the implementation of the HHT-α method can result in improved error propagation properties in pseudodynamic testing if the equation of motion is used instead of the difference equation to evaluate the next step acceleration, this paper proves that this method might lead to instability when used to solve a nonlinear system. Its unconditional stability is verified only for linear elastic systems, while for nonlinear systems, instability occurs as the step degree of convergence is less than 1. It is worth noting that the step degree of convergence can frequently be less than 1 in pseudodynamic testing, since a convergent solution is achieved only when the step degree of convergence is close to 1 regardless of whether its value is greater or less than 1. Therefore, the application of this scheme to pseudodynamic testing should be prohibited, since the possibility of instability might incorrectly destroy a specimen. Consequently, the implementation of the HHT-α method by using the difference equation to determine the next step acceleration is recommended for use in pseudodynamic testing.     

A three-dimensional,iterative mapping procedure for the implementation of an ionosphere-magnetosphere anisotropic Ohm’s law boundary condition in global magnetohydrodynamic simulations

The mathematical formulation of an iterative procedure for the numerical implementation of an ionosphere-magnetosphere (IM) anisotropic Ohm’s law boundary condition is presented. The procedure may be used in global magnetohydrodynamic (MHD) simulations of the magnetosphere. The basic form of the boundary condition is well known, but a well-defined, simple, explicit method for implementing it in an MHD code has not been presented previously. The boundary condition relates the ionospheric electric field to the magnetic field-aligned current density driven through the ionosphere by the magnetospheric convection electric field, which is orthogonal to the magnetic field B, and maps down into the ionosphere along equipotential magnetic field lines. The source of this electric field is the flow of the solar wind orthogonal to B. The electric field and current density in the ionosphere are connected through an anisotropic conductivity tensor which involves the Hall, Pedersen, and parallel conductivities. Only the height-integrated Hall and Pedersen conductivities (conductances) appear in the final form of the boundary condition, and are assumed to be known functions of position on the spherical surface R=R₁ representing the boundary between the ionosphere and magnetosphere. The implementation presented consists of an iterative mapping of the electrostatic potential , the gradient of which gives the electric field, and the field-aligned current density between the IM boundary at R=R₁ and the inner boundary of an MHD code which is taken to be at R₂>R₁. Given the field-aligned current density on R=R₂, as computed by the MHD simulation, it is mapped down to R=R₁ where it is used to compute by solving the equation that is the IM Ohm’s law boundary condition. Then is mapped out to R=R₂, where it is used to update the electric field and the component of velocity perpendicular to B. The updated electric field and perpendicular velocity serve as new boundary conditions for the MHD simulation which is then used to compute a new field-aligned current density. This process is iterated at each time step. The required Hall and Pedersen conductances may be determined by any method of choice, and may be specified anew at each time step. In this sense the coupling between the ionosphere and magnetosphere may be taken into account in a self-consistent manner.     

Determination of Q S, spreading factor and S-wave acceleration by inversion of seismic intensity data

In this paper, on the basis of intensity data from 85 earthquakes occurred in China, the method of resolving overdetermined equations by using the damped least squares method is applied to inversing for the mean value of 1 s. S wave quality factor, the spreading factor and the S-wave acceleration at the foci of earthquakes in 7 regions of China. The relation between S-wave acceleration at the foci of earthquakes and magnitude is discussed. As an example, 2-DQ _S distribution in Taiwan Province is obtained by inversion. It is found that there exists some corresponding relation between this distribution and Bouguer gravitational anomaly and seismicity. Preliminary analysis and discussion on results of the inversion, and estimation of error inQ _S are made. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 202–211, 1991. The English version of this paper is improved by Professor Yushou Xie.     

Tangential discontinuities and the optical analogy for stationary fields. v. formal integration of the force-free field equations

Abstract

This paper demonstrates the appearance of tangential discontinuities in deformed force-free fields by direct integration of the field equation ? x B = αB. To keep the mathematics tractable the initial field is chosen to be a layer of linear force-free field B_x = + B ₀cosqz, B_y = — B ₀sinqz, B_z = 0, anchored at the distant cylindrical surface ? = (x ² + y ²)^1/2 = R and deformed by application of a local pressure maximum of scale l centered on the origin x = y = 0. In the limit of large R/l the deformed field remains linear, with α = q[1 + O(l ²/R ²)]. The field equations can be integrated over ? = R showing a discontinuity extending along the lines of force crossing the pessure maximum. On the other hand, examination of the continuous solutions to the field equations shows that specification of the normal component on the enclosing boundary ? = R completely determines the connectivity throughout the region, in a form unlike the straight across connections of the initial field. The field can escape this restriction only by developing internal discontinuities.

Casting the field equation in a form that the connectivity can be specified explicitly, reduces the field equation to the eikonal equation, describing the optical analogy, treated in papers II and III of this series. This demonstrates the ubiquitous nature of the tangential discontinuity in a force-free field subject to any local deformation.     

Numerical analysis model of horizontal displacement of active faults

In this paper, a numerical model was presented for interpreting the movement feature of an active fault zone. This model was based on the analytic solution, given by Crouch (Crouch, 1976), for the problem of displacement discontinuity in an infinite elastic solid, making full use of geodetic and geological data and it was constructed by the boundary element method. A numerous test computation shows that if you want to catch the possible seismic precursor from the displacement’s vector, you have to associate the computation with geological survey in a deep going way, otherwise you would fail in your propose. This method is valid for analysing the zone of strike-slip fault and it has some values for dealing with other analogous problems. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 153–158, 1993.     

Earthquake prediction decision and risk matrix

The issuance of an earthquake prediction must cause widespread social responses. It is suggested and discussed in this paper that the comprehensive decision issue for earthquake prediction considering the factors of the social and economic cost. The method of matrix decision for earthquake prediction (MDEP) is proposed in this paper and it is based on the risk matrix. The goal of decision is that search the best manner issuing earthquake prediction so that minimize the total losses of economy. The establishment and calculation of the risk matrix is discussed, and the decision results taking account of economic factors and not considering the economic factors are compared by examples in this paper. The Chinese version of this paper appeared in the Chinese edition ofActa Seismological Sinica,15, 232–238, 1993.     

Reply

Abstract

This paper develops a new analytical solution for the aquifer system, which comprises an unconfined aquifer on the top, a semi-confined aquifer at the bottom and an aquitard between them. This new solution is derived from the Boussinesq equation for the unconfined aquifer and one-dimensional leaky confined flow equation for the lower aquifer using the perturbation method, considering the water table over-height at the remote boundary. The head fluctuation predicted from this solution is generally greater than the one solved from the linearized Boussinesq equation when the ratio of the tidal amplitude to the thickness of unconfined aquifer is large. It is found that both submarine groundwater discharges from upper and lower aquifers increase with tidal amplitude–aquifer thickness ratio and may be underestimated if the discharge is calculated based on the average head fluctuation. The effects of the aquifer parameters and linearization of the Boussinesq equation on the normalized head fluctuation are also investigated.

Editor D. Koutsoyiannis; Associate editor J. Simunek

Citation Chuang, M.-H., Mahdi, A.-A. and Yeh, H.-D., 2012. A perturbation solution for head fluctuations in a coastal leaky aquifer system considering water table over-height. Hydrological Sciences Journal, 57 (1), 162–172.     

The research of a comprehensive program for earthquake prediction with seismological methods

In this paper, the MYCIN inexact inference method in Expert System is applied to comprehensive earthquake prediction. And it is proposed that the methods of determining various certainty factors, correcting correlation between anomalous evidences and computing comprehensive certainty factor of occurrence of some moderate or strong earthquake. By use of these methods, 18 earthquake cases since 1966 in North China is tested with seismological anomalies in different seismogenic stage, and the comprehensive certainty factors of occurrence of some moderate or strong earthquake are computed. At last some problems in application are discussed. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 328–337, 1991.     

Spatiotemporal distribution of seismic activity in East Asia and its relation to regional stress field

Tectonic forces from the relative movements between plates are transmitted into the continental crust, and then they create the earthquake generating stress field there. The space-time distribution of the seismic activity including the small earthquakes in a region reflects the variation of the stress field in the region. According to this idea, the characteristics of the stress fields in the various regions of East Asia have been analyzed in detail in this paper based on a lot of solutions of focal mechanisms and data of seismic activity during the last 500 years. The results indicate that the tectonic forces from the subduction of the Pacific Ocean plate underneath the Eurasian plate control the stress field in the region from North China to the northern part of the North-South Seismic Belt. The variation of the regional stress field shown by the variation of seismic activity in some regions of Japan has also been discussed based on characteristics of variation of the seimicity of small earthquakes. Synchronous variations of seismicity in the past 100 years or so in West China and in the boundary region between the Indo-Australian and Eurasian plates implicate that there is the transmission of tectonic forces into West China through the collision between the Indo-Australian and Eurasian plates. The active seismic activity in the boundary region between the Indo-Australian and the Eurasian plates and in West China is continuing consistently. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 287–294, 1991.     

The application of wave field continuation for seismic refraction

Based on wave equation a fundamental formula for plane wave propagaton is derived, the theoretical method of inverting wave volocity structure of earth interior through the observational wave field is discussed in this paper. The observational wave field can be decomposed into the surface plane wave field by using τ −p transform. The maximum amplitude curve in the plane wave field can show stably the change tendency of wave velocity with depth in the Earth. This property can be used to restrict the solution space. By using the wave field continuation method more useful information from the observational wave field can be extracted and the inverion solution not only can be obtained simply and quickly, but also is stable and less influenced by the subjective factor. The wave field continuation is a fine inversion method. Theoretical analysis and numerical modelling are carried out in the study of wave field continuation. By applying homomorphic decovolution the signal — to — noese ratio is improved. Finaly a sonar refraction profile in the northern part of the South China Sea is interpreted and computed. It is found as a result that there is a velocity interface from 1.76 km/s to 2.21 km/s at the depth of 1.4 km. The velocity gradients in the upper and lower layers are 0.54 km · s⁻¹/km and 0.63 km · s⁻¹/km respectively. A discussion of the characteristics of shallow sea structure in the view of tectonic movements is geven. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13. 41–52, 1991.     

Temporal and spacial analysis of regional composite nodal plane solutions for small earthquakes

A method is proposed in this paper for the analysis of temporal and spatial characteristics of composite nodal plane solutions for small earthquakes. With this method, the interested region is devided into small areas according to the geological features of the region. As an example, 107 composite nodal plane solutions are calculated for the adjoining region of Shaxi, Hebei and Neimenggu. The temporal and spatial characteristics of the variations of the solution parameters before and after the great Tangshan main earthquake in 1976 have been analysed and some interesting results are obtained. The Chinese version of this paper appeared in the Chinese edition ofActa Seismlogica Sinica,13, 9–20, 1991.     

A hydrodynamic curiosity: The salt oscillator

Abstract

This paper is concerned with the derivation of the dispersion relation of a static fully ionized hydrogen plasma, at a temperature much smaller than 10¹⁰°K, interacting with radiation through electron scattering. The Fokker-Planck form of the transfer equation is first considered and the derivation of the dispersion relation is reduced to the resolution of a v-differential eigenvalue problem, which could be realized by numerical integration. In the second part, the dispersion relation is explicitly derived in the frame of an algebraic approximation of the transfer equation. This shows that the branches of this relation, which are obtained in the optically thick and in the optically thin limits, are continuously connected to each other in a somehow remarkable way.     

Lateral density anomaly distribution in the lower mantle obtained from satellite low order geopotential coefficients

In this paper, we attempt to use satellite gravity data and a new inversion method to study the lateral density anomaly distribution in the mantle. First, density difference Δρ(τ,θ,φ) is expanded in terms of a three—dimensional orthogonal function system, the coefficients of the expansion are to be determined. Then, a set of observation equations is established from the relationship between density anomaly and disturbing geopotential. In the equations the unknown vector contains the coefficients of density anomaly expansion, the observational vector is obtained by computing geopotential perturbations using the potential coefficients of GEM10B, and a filtering process is done for the observational values by properly selecting the harmonic degrees of geopotentical. Finally, the lateral density variations in the lower mantle (670 km toCM boundary) are investigated. In this case, the degrees of disturbing geopotential are selected as 2–11, the truncated degrees of density anomaly expansion are taken asL=6 andK=4, and the damping least squares method is used to solve the observation equations. The resulting model shows the high level of density perturbations at 670 km discontinuity and core — mantle boundary, a high — density zone circumscribing the Pacific and a lower—density region under the center of Pacific. These features are in agreement with the three—dimensional seismic velocity variation features by Dziewonski (1984). In the Antarctic region and some parts of Atlantic and Indian Ocean, however, the resulting density anomalies are negatively correlated with the seismic velocity anomalies, the cause resulting in these phenomena is preliminarily analysed in this paper. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 53–65, 1991. The principle and method represented in this paper can also be suitable to study the lateral density anomaly distribution in the earth’s crust and the upper mantle.     

Wave hierarchies in alluvial river flows

Abstract

The long wave equations governing the flow in alluvial rivers and channels are considered. The linearized equations are re-cast in the form of a single equation of wave hierarchy type as discussed by Whitham (1974). The dynamic and kinematic waves are of third and second order respectively. Behaviour at the wave fronts is considered and a roll-wave type instability is revealed.

For stable flow, the theory is used to make both qualitative and quantitative predictions in the areas of short and long term floods, tidal waves and channel dredging.

The non-uniformity in the quasi-steady theory on bedform development [see, for example, Reynolds (1985)] as the Froude number, F, approaches unity is also discussed, and appropriate scalings are obtained to derive a theory which remains valid when F ～ 1.     

The Yecheng, Xinjiang, China, earthquake of February 14, 1980 —A destructive intermediate earthquake

In this study, we have checked the location and focal depth of the Yecheng earthquake (m _b = 6.0, maximum intensity VII) of February 14, 1980. The result shows that this is an intermediate event with a focal depth of 90 km. The microepicenter is located at 36. 4°N, 76, 9°E, while the macroepicenter is at 37.3°N, 76.9°E, 90 km to the north of the microepicenter. This is the first destructive intermediate event in China which led to a damage as severe as of intensity VII. The focal mechanism of the event is determined to be of thrust type. Combined with the analysis of seismological and geological data in surrounding area, the possible relation between the event and plate movement has been discussed. The result in this paper indicates that in some particular place, the destructive effect of intermediate event should be considered in seismic hazard assessment. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 137–143, 1992.     

Successive formula method for numerical analysis of vibrating response

The algorithm of successive formulas for computing numerical vibrating response of unequal time interval for a single-degree of freedom oscillator in linear cases are more systematically introduced in the paper. Some numerical analysis characteristics of the algorithm are discussed. It is proved that the algorithm is unconditionally stable and convergent. A computer program for simultaneous calculation of the relative displacement, the relative velocity and the absolute acceleration response spectra is edited in the paper. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 236–242, 1992.