Analysis of Remote Sensing Images of Ground Ruptures Resulting from the Kunlun Mountain Pass Earthquake in 2001

On November 14, 2001, an earthquake measuring a magnitude of 8.1 occurred to the west of the Kunlun Mountain Pass which is near the border between Xinjiang and Qinghai of China. Since its epicenter is located in an area at an elevation of 4900 m where the environment is extremely adverse, field investigation to this event seems very difficult. We have performed interpretation and analysis of the satellite images of ETM, SPOT, Ikonos, and ERS-1/2SAR to reveal the spatial distribution and deformation features of surface ruptures caused by this large earthquake. Our results show that the rupture zone on the ground is 426 km long, and strikes N90-110°E with evident left-lateral thrusting. In spatial extension, it has two distinct sections. One extends from the Bukadaban peak to the Kunlun Mountain Pass, with a total length of 350 km, and trending N95-110°E. Its fracture plane is almost vertical, with clear linear rupture traces and a single structure, and the maximum left-lateral offset is 7.8 m. This section is the main rupture zone caused by the earthquake, which is a re-fracturing along an old fault. The other is the section from Kushuihuan to the Taiyang Lake. It is 26 km long, trending N90-105°E, with the maximum strike-slip displacement being 3 m, and is a newly-generated seismic rupture. In a 50 km-long section between the Taiyang Lake and the Bukadaban peak, no rupture is found on the ground. The eastern and western rupture zones may have resulted from two earthquakes. The macroscopic epicenter is situated at 65 km east of the Hoh Sai Lake. The largest coseismic horizontal offset in the macroscopic epicenter ranges from 7 m to 8 m. Based on the dislocation partition of the whole rupture zone, it is suggested that this rupture zone has experienced a process of many times of intensification and fluctuation, exhibiting a remarkable feature of segmentation.

A discussion on Corioli force effect and aftershock activity tendency of the M=8.1 Kunlun Mountain Pass earthquake on Nov. 14, 2001

Following the theory and definition of the Corioli force in physics, the Corioli force at the site of the M=8.1 Kunlun Mountain Pass earthquake on November 14, 2001, is examined in this paper on the basis of a statistical research on relationship between the Corioli force effect and the maximum aftershock magnitude of 20 earthquakes with M7.5 in Chinese mainland, and then the variation tendency of aftershock activity of the M=8.1 earthquake is discussed. The result shows: a) Analyzing the Corioli force effect is an effective method to predict maximum aftershock magnitude of large earthquakes in Chinese mainland. For the sinistral slip fault and the reverse fault with its hanging wall moving toward the right side of the cross-focus meridian plane, their Corioli force pulls the two fault walls apart, decreasing frictional resistance on fault plane during the fault movement and releasing elastic energy of the mainshock fully, so the maximum magnitude of aftershocks would be low. For the dextral slip fault, its Corioli force presses the two walls against each other and increases the frictional resistance on fault plane, prohibiting energy release of the mainshock, so the maximum magnitude of aftershocks would be high. b) The fault of the M=8.1 Kunlun Mountain earthquake on Nov. 14, 2001 is essentially a sinistral strike-slip fault, and the Corioli force pulled the two fault walls apart. Magnitude of the induced stress is about 0.06 MPa. After a comparison analysis, we suggest that the aftershock activity level will not be high in the late period of this earthquake sequence, and the maximum magnitude of the whole aftershocks sequence is estimated to be about 6.0.

Estimation of the stress levels in the focal region before and after the 2001 M=8.1 Western Kunlun Mountain Pass earth-quake

A method estimating the stress level in the focal region of an earthquake is proposed here. Taking the 2001 M=8.1 Western Kunlun Mountain Pass earthquake as an example, we estimate its stress level in the focal region before and after it by this method. The results show that the stress level in the focal region just prior to the initiation of this event is approximately 6.3-8 MPa, and about 5-6.7 MPa remained in the focal region after its occurrence. The stress in the focal region decreased by roughly twenty percent after this event.

求Duffing方程周期解的Mountain Pass方法

研究一类超线性Duffing方程周期解的存在性及其数值求解方法.利用山路引理证明了超线性Duffing方程周期解的存在性,并给出一种求Duffing方程周期解的Mountain Pass算法及其具体算例.

Effect of phase transition during roasting of Mountain Pass rare earth concentrate on leaching efficiency of rare earths

To find a greener and more economical approach for treating the Mountain Pass rare earth concentrate(MPREC),a novel "Combination Method",including the processes of oxidizing roasting,HCI leaching and sulfuric acid roasting,is proposed in this research.In this paper,the effect of phase transition behavior in hydrochloric acid leaching during oxidative roasting at 450-600℃ was studied.During roasting,the bastnasite in MPREC is decomposed into CeLa_(2)O_(3)F_(3) and(Ce_(0.33),La_(0.33),Ca_(0.33))O_(1.5).As the CeLa_(2)O_(3)F_(3) phase has the fluorine-fixation effect,the generated CeLa_(2)O_(3)F_(3) phase can not be dissolved by HCI after roasting at 500 and 550℃,but it can be decomposed by HCI after roasting at over 600℃,resulting in the improvement of the leaching rate of total F element.The maximum leaching efficiency of rare earth elements(REEs) can reach 70.32 wt% at the roasting temperature of 550℃.After roasting at over 600℃,some F^-ions in the solution combined with RE^(3+) to form REF_(3) precipitate and enter the leaching residue,and the others are in the form of [CeF_(3)]^+ in the leaching solution during leaching,therefore,the leaching efficiency of non-ce rium REEs decreases while that of cerium element increases.This work provides basic research for optimizing the actual production process of MPREC.

An Application of a Mountain Pass Theorem

We are concerned with the following Dirichlet problem: -△u(x) = f(x, u), x ∈ Ω. u ∈ H_0~1(Ω). (P) where f(x, t) ∈ C(Ω×R), f(x, t)/t is nondecreasing in t ∈ R and tends to an L~∝-function q(x) uniformly in x ∈ Ω as t→+∝ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case. an Ambrosetti-Rabinowitz-type condition, that is. for some θ>2. M>0, 0<θF(x. s)≤ f(x, s)s, for all |s|≥M and x ∈ Ω, (AR) is no longer true, where F(x, s) = integral from n=0 to s f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming (AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable, conditions on f(x, t) and q(x). Our methods also work for the case where f(x, f) is superlinear in t at infinity. i.e., q(x) ≡∞.

带有不同Hardy项的椭圆方程组的Mountain-Pass解

研究了一类带有不同Hardy项和线性扰动项的临界椭圆方程组,解决了由不同Hardy项带来的困难,分析了相关最佳Sobolev常数达到函数的渐近性质.首次利用变分方法成功地证明了这类奇异椭圆方程组Mountain-Pass解的存在性.

Ekeland’s Variational Principle and the Mountain Pass Lemma

Ekeland’s variational principle is a fundamental theorem in nonconves analysis. Its general statement is as the following:Ekeland’s Variational Principle"’a:. Let V be a complete metric space, and F: F—*-RU{ + °°} a lower semicontinuous function, not identically +00 and bounded from, below. Let s>0 be given, and a point u^V such thatF(u)<infF+e.vThen there exists some point v ￡ V such that

Mountain pass solutions to a generalized Frenkel-Kontorova model

We study a generalized Frenkel-Kontorova model and obtain periodic and heteroclinic mountain pass solutions.The heteroclinic mountain pass solution in the second laminations is new to the generalized Frenkel-Kontorova model.Our proof follows that of Bolotin and Rabinowitz(2005)for an Allen-Cahn equation,which is different from the heat flow method of finding the critical point of the Frenkel-Kontorova model in the literature.The proofs depend on suitable choices of functionals and working spaces.We also study the multiplicity of these mountain pass solutions.

Characteristics of Collapses Caused by the M8.1 Earthquake West of the Kunlun Mountains Pass

An M 8.1 earthquake that occurred west of the Kunlun Mountains Pass has caused more than 20 collapse bodies or zones, which are mainly distributed near the surface seismic rupture zone, west of Hoh Sai Lake. The collapses are of four types, bedrock, soil mass and ice mass collapses and avalanches. The spatial distribution and the characteristics of development of the collapses are analyzed in the paper. Comparised with those caused by other earthquakes, the collapses are smaller in scale. In addition to the lithological characteristics of the crustal media, topographic, geomorphic and climatic factors, weaker seismic ground motion is an important cause for formation of the smaller-scale collapses. The long surface rupture zone and weaker ground motion are important features of the seismic rupture, which may be related to the structure of the preexisting fault.

New Insight into the Surface Rupture Parameters of the Kunlun Mountains Pass M_S8.1 Earthquake

Field observation shows that the surface rupture of the Kunlun Mountains Pass M_S 8.1 earthquake is about 426km long, and the maximum sinistral displacement is about 6m. Distribution of horizontal displacement along the surface ruptures is markedly controlled by fault structure. The rupture length of this earthquake is significantly longer than statistic value. In this paper, using the method of “ultimate linear strain", we discussed the independency and integrality of the whole rupture zone and rupture segments of the Kunlun Mountains Pass earthquake by comparing with some large earthquakes on strike-slip faults on the Chinese continent. The conclusion is that the Kunlun Mountains Pass earthquake consists of successively triggered multiple earthquake events, other than a single earthquake event.

Characteristics of Far-field Precursory Anomalies Before the M_S8.1 Earthquake in the West of Kunlun Mountains Pass

In this study, a number of typical precursory anomalies recorded by stations in Qinghai, Gansu, Sichuan, Xinjiang, Ningxia, Hebei and Shaanxi provinces and autonomous regions before the Ms8.1 earthquake in the west of Kunlun Mountains Pass are collected and checked. According to the standards of earthquake cases in China, the criteria of the precursory anomalies are determined, and 53 distinguished. The characteristics of these anomalies before the Ms S. 1 earthquake are analyzed, with results showing a very large earthquake affected area. The precursory anomalies recorded by instruments were 2900 km away from the epicenter, and according to the study in this paper, reached 2100 km away. The results also show that the anomalies present characteristics of long duration, multi-measurement items and large-amplitude variation. The authors believe that in large earthquake monitoring, attention should be paid to the variation of data over a large area, ranging up to thousands kilometers, with much denser earthquake observation networks.

The Frozen Soils and Devastating Characteristics of West Kunlun Mountains Pass M_S 8.1 Earthquake Area in 2001

The investigation on damages to frozen soil sites during the West Kunlun Mountains Pass earthquake with M S 8.1 in 2001 shows that the frozen soil in the seismic area is composed mainly of moraine, alluvial deposit, diluvial deposit and lacustrine deposit with the depth varying greatly along the earthquake rupture zone. The deformation and rupture of frozen soil sites are mainly in the form of coseismic fracture zones caused by tectonic motion and fissures, liquefaction, seismic subsidence and collapse resulting from ground motion. The earthquake fracture zones on the surface are main brittle deformations, which, under the effect of sinistral strike-slip movement, are represented by shear fissures, tensional cracks and compressive bulges. The distribution and configuration patterns of deformation and rupture such as fissures, liquefaction, seismic subsidence and landslides are all related to the ambient rock and soil conditions of the earthquake area. The distribution of earthquake damage is characterized by large-scale rupture zones, rapid intensity attenuation along the Qinghai-Xizang (Tibet) Highway, where buildings distribute and predominant effect of rock and soil conditions.

R^(3)上具有一般凹凸非线性项的Klein-Gordon-Born-Infeld方程无穷多解的存在性

该文运用临界点理论中的Z_(2)-山路定理得到了R^(3)上具有凹凸非线性项的Klein-Gordon方程和Born-Infeld理论耦合系统无穷多解的存在性.

Existence of a Sigh-Changing Solution Result for Logarithmic Schrödinger Equations with Weight Function

This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).

一类拟线性薛定谔方程解的存在性

在R^(N)上探究形式为-Δu+V(x)u-Δ(u^(2))u=h(u)的拟线性薛定谔方程解的存在性,其中N≥3,V:R^(N)→R,h:R→R。运用变分法和山路引理,证明了当函数V和非线性项h分别满足一些适当条件时,该拟线性薛定谔方程存在一个非平凡正解。

一类带扰动项的拟线性薛定谔方程的多解性

该文研究了强制位势下非齐次拟线性薛定谔方程的多解性问题.通过山路定理和Ekeland变分原理,得到了该方程两个不同的解.所得结论是对此类拟线性方程已有结果的补充和推广.

具有周期系数的Kirchhoff-型差分方程同宿解的存在性

运用临界点理论研究一类具有周期系数的Kirchhoff-型差分方程同宿解问题。首先,构造了差分方程所对应的能量泛函。在文中的假设条件下,保证了能量泛函具有山路几何结构,从而得到了一个Palais-Smale序列。然后,利用一个可变号的全局性条件证明了该Palais-Smale序列的有界性。进一步,借助于l^(2)空间的紧支撑子集的性质和系数的周期性得到了该差分方程的一个非平凡同宿解。最后,给出两个例子说明了主要结论的正确性。

一类具有扰动非线性项和奇异项的Schrödinger-Poisson系统的多重正解

本文考虑一类具有扰动非线性项和奇异项的Schrödinger-Poisson系统的多重正解的存在性.通过扰动方法解决奇异项在零点不可微的问题,利用Ekeland变分原理和山路引理,得到两个正解的存在性.

一类具梯度项的分数阶椭圆方程解的存在性

运用山路定理与迭代的技巧证明下面分数阶椭圆方程:{(-Δ)_(p)^(s)u+V(x)u^(p-2)u=f(u,|▽u|^(p-2)▽u),u∈X^(s)(R^(N)),u(x)>0,x∈R^(N).正解的存在性,其中1<p<N,N≥2,0<s<1,(-Δ)_(p)^(s)是分数阶p-拉普拉斯算子,非线性项f:R×R^(N)→R是依赖于解的梯度项的连续函数,V(x)是正的连续函数.