The Random Distribution of the Loading and Unloading Response Ratio Under the Assumptions of Poisson Models

This paper discussed the random distribution of the loading and unloading response ratio(LURR) of different definitions(Y_1～Y_5)using the assumptions that the earthquakes occurfollowing the Poisson process and their magnitudes obey the Gutenberg-Richter law.Theresults show that Y_1～Y_5 are quite stable or concentrated when the expected number of eventsin the calculation time window is relatively large(>40);but when this occurrence ratebecomes very small,Y_2～Y_5 become quite variable or unstable.That is to say,a high value ofthe LURR can be produced not only from seismicity before a large earthquake,but also from arandom sequence of earthquakes that obeys a Poisson process when the expected number ofevents in the window is too small.To check the influence of randomness in the catalogue tothe LURR,the random distribution of the LURR under Poisson models has been calculated bysimulation.90%,95% and 99% confidence ranges of Y_1 and Y_3 are given in this paper,which is helpful to quantify the random influe     

地震临界区域尺度与地震预测

地震临界区域尺度的界定对于地震前兆研究有着重要意义。通过加卸载响应比(LURR)及震前矩张量加速释放(AMR)两种模型对地震临界区域尺度进行了分析。采用不同半径区域内地震事件的Benioff应变分别计算LURR和AMR时间序列,震前引起时间序列异常变化最明显的半径尺度所定义的区域就是最佳地震临界区域。华北地区M>5震例研究结果显示两种模型所得到的最佳地震临界区域具有明显的一致性,最佳临界区域半径与主震震级之间统计的线性关系斜率约为0.34～0.36。研究结果表明通过不同预测模型可以较为定量的评价地震临界区域尺度,从而为地震预测研究提供依据。     

地磁加卸载响应比方法最佳阈值研究

地磁加卸载响应比方法(LURR)是从测震学中移植过来的、用于地震中期分析预测的一种地磁学方法。笔者应用红山地震台地磁数字化观测数据进行了地磁加卸载响应比的计算分析,经过统计得出在阈值选择为3.0时对地震进行预测的效果比较好,其与地震的对应概率为42%。同时,笔者还认为可能受限于方法本身及外界因素,地磁加卸载响应比方法在进行地震预测时,其虚报率及漏报率较高。     

Comparison Between LURR and State Vector Analysis Before Strong Earthquakes in Southern California Since 1980

There are seven strong earthquakes with M ≥ 6.5 that occurred in southern California during the period from 1980 to 2005. In this paper, these earthquakes were studied by the LURR (Load/Unload Response Ratio) method and the State Vector method to detect if there are anomalies before them. The results show that LURR anomalies appeared before 6 earthquakes out of 7 and State Vector anomalies appeared before all 7 earthquakes. For the LURR method, the interval between maximum LURR value and the forthcoming earthquake is 1 to 19 months, and the dominant mean interval is about 10.7 months. For the State Vector method, the interval between the maximum modulus of increment State Vector and the forthcoming earthquake is from 3 to 27 months, but the dominant mean interval between the occurrence time of the maximum State Vector anomaly and the forthcoming earthquake is about 4.7 months. The results also show that the minimum valid space window scale for the LURR and the State Vector is a circle with a radius of 100 km and a square of 3°×3°, respectively. These results imply that the State Vector method is more effective for short-term earthquake prediction than the LURR method, however the LURR method is more effective for location prediction than the State Vector method.     

An Independent Assessment of the Load/Unload Response Ratio (LURR) Proposed Method of Earthquake Prediction

The Load/Unload Response Ratio (LURR) method is a proposed technique to predict earthquakes that was first put forward by Yin (1987). LURR is based on the idea that when an area enters the damage regime, the rate of seismic activity during loading of the tidal cycle increases relative to the rate of seismic activity during unloading in the months to one year preceding a large earthquake. Since earth tides generally contribute the largest temporal variations in crustal stress, it seems plausible that earth tides would trigger earthquakes in areas that are close to failure (e.g., Vidale et al., 1998). However, the vast majority of studies have shown that earth tides do not trigger earthquakes (e.g., Vidale et al., 1998; Heaton, 1982; Rydelek et al., 1992). In this study, we conduct an independent test of the LURR method, since there would be important scientific and social implications if it were proven to be a robust method of earthquake prediction. Smith and Sammis (2004) undertook a similar study and found no evidence that there was predictive significance to the LURR method. We have repeated calculations of LURR for the Northridge earthquake in California, following both the parameters of X.C. Yin (personal communication) and the somewhat different ones of Smith and Sammis (2004). Though we have followed both sets of parameters closely, we have been unable to reproduce either set of results. Our examinations have shown that the LURR method is very sensitive to certain parameters. Thus it seems likely that the discrepancies between our results and those of previous studies are due to unaccounted for differences in the calculation parameters. A general agreement was made at the 2004 ACES Workshop in China between research groups studying LURR to work cooperatively to resolve the differences in methods and results, and thus permit more definitive conclusions on the potential usefulness of the LURR method in earthquake prediction.     

量纲分析应用于地震预测的探索

加卸载响应比(LURR)的基本思路是希望能够通过刻画震源区介质的损伤程度,反映地震孕育的进程,从而预测地震.近30年来,很多人对加卸载响应比做了大量基础研究,取得了一系列新的进展.加卸载响应比在地震预测实践中也取得了一定的效果,异常区与地震发生的位置有较好的对应性,但是预测效果仍不够理想.究其原因主要是:在实际预测中对当地的地球物理情况考虑的不够.本文采用量纲分析与加卸载响应比结合的方法,综合考虑当地的地球物理情况,例如剪应变率和平均地震波能量等因素的影响.文中选取1970年以来发生在中国大陆的34个震例资料,通过分析得到了与发震震级和时间相关的无量纲量π₁和π₃,根据对实际数据的拟合,π₁和π₃均与震级成指数关系.在应用于地震预测实践时,首先根据LURR空间扫描结果选取异常区,然后确定异常区的地球物理参数,通过π₁确定震级M,再由π₃确定发震时间T.     

2019年6月17日长宁MS6.0地震前地震活动和水位的加卸载响应比异常研究

加卸载响应比（LURR）方法是通过固体潮加卸载过程中的某一物理参数的响应差异探查区域应力场演化。本文将这一方法应用于2019年6月17日四川长宁M_S6.0地震,根据LURR时序演化探查震源区介质的应力状态变化,提取可能的震前异常信息。首先采用贝尼奥夫应变作为响应量计算LURR,通过固体潮在地震断层面的最优滑动方向上引起的库仑破坏应力变化来判断加载还是卸载,结果显示LURR值自2018年年初开始快速增加并在2018年年中达到峰值,此后异常持续至地震。在此基础上对该地区的大地形变和地下井水位资料进行了LURR分析,发现水富水平摆倾斜仪的东西和南北分量在LURR出现异常的同期发生明显偏转,而地震周边的地下井水位高值变化过程与长宁地震也有较好的对应关系。研究表明在长宁地震发生前,存在地震活动和地下水位的LURR异常,且异常时间与水富倾斜同步,暗示震源区介质存在明显的应力积累过程。     

加卸载响应比(LURR)响应量的研究

加卸载响应比(LuRR)理论以响应比值Y来刻画孕震区介质的损伤演化进程。在计算Y值时可选择能量(Benioff应变)、模量(应变)等多种物理量做响应。本通过理论和实验方法对使用不同响应量时Y值演化趋势的异同进行了研究，结果表明在Y达到峰值之前具有相似地演化过程。     

The Newest Developments of Load-Unload Response Ratio (LURR)

The Load Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It is inspiring that its predictions using LURR have been improving. Since 2004 we have made a major breakthrough in intermediate-term earthquake forecasting of the strong earthquakes on the Chinese mainland using LURR and successfully predicted the Pakistan earthquake with magnitude M 7.6 on October 8, 2005. The causes for improving the prediction in terms of LURR have been discussed in the present paper.     

美国西部地区加卸载响应比的时空扫描及其地震趋势研究

加卸载响应比理论是近年来提出的地震预报新方法, 在中国大陆地区的实际地震预测中取得了较好的效果。 为了研究加卸载响应比理论是否适用于不同地质条件的地震, 是否具有普适性, 选择了典型的美国圣安德烈斯断层带及其周围地区的地震作为研究对象, 计算分析了美国西部地区加卸载响应比的变化情况, 并对该地区未来的地震趋势进行了研究。     

九寨沟M_s7.0地震前地应变LURR异常演化特征

从岩石应力-应变的本构关系出发,以能够反映岩石应变变化的地应变观测数据作为"响应量",通过库伦应力触发模型的加卸载响应比计算方法,计算2017年8月8日九寨沟M_S7.0地震前震中及周边500km范围内应变观测的加卸载响应比结果。结果显示,基于应变观测的加卸载响应比方法能够较好地从潮汐频段提取地震前LURR异常,九寨沟地震前,300km范围内的多个应变观测台站出现LURR异常,其中相距96km的两水台EW分量Y值最大达到3.27;LURR空间演化特征显示,在震前约9个月内震中及周边地区陆续出现异常"集中—增强—减弱"过程,证明该地区在长期应力累积的背景下,应力的不断累积增强导致震中及附近区域的岩石出现不断损伤或弱化,最终位于树正断裂上的应变能积累超过了介质强度而引发了此次地震。     

郯庐断裂带南段加卸载响应比变化特征分析

本文对郯庐断裂带南段开展了分段加卸载响应比变化研究,总结了区域内显著地震前加卸载响应比时序曲线的变化特征。研究表明,加卸载响应比表征了地下介质的损伤程度,具有明确的物理意义,在实际应用中取得了较好的效果。在中小地震较为丰富的研究区域,加卸载响应比在显著地震前会出现短临高值异常; 而在中小地震活动水平不高的区域,加卸载响应比在震前更多地表现为长期的背景高值异常。     

关于加卸载响应比理论运用于地震预测的几点思考

加卸载响应比理论已在地震预测中得到广泛应用，但也面临挑战。本对加卸载响应比理论及方法进行了分析，并提出该理论几个可能的研究方面：(1)根据固体潮应力变化值给定每个小地震Benio盯应变在加卸载响应比计算中的权重；(2)考虑地震之前应力空间分布，确定加卸载响应比可能升高的区域形状，进而确定加卸载响应比计算中小震资料的选取范围；(3)将实测的小震震源机制与假定小震震源机制都相同时的加卸载响应比计算结果进行比较，研究测定的小震震源机制对加卸载响应比方法的改善情况；(4)研究加卸载响应比方法对不同震源机制类型地震的适用情况。     

Revisiting the Tidal Activation of Seismicity with a Damage Mechanics and Friction Point of View

— The Load Unload Response Ratio theory (LURR) puts forward the idea that the ratio of seismicity during times of increased tidal loading to times of decreased tidal loading takes on anomalously large values as the preparatory region of the earthquake approaches a critical state. We repeated the calculations of LURR for several earthquakes in California, for which results had been published, using estimates of the parameters which could be determined from the published work. We were unable to confirm any LURR ratio predictive significance. We test an alternative method of evaluating the influence of tidal stresses on earthquakes based on damage mechanics. As in rock mechanics experiments, it may be that anomalous activation of seismicity prior to large earthquakes occurs only during those time intervals when the applied stress exceeds values previously attained. We applied this approach to analyze the same data set used to test the LURR hypothesis, and it also failed to reveal any significant precursory indications. It may be that time-dependent failure processes such as self-driven nucleation occur on a time scale longer than the diurnal tide, thus destroying the expected synchronization.     

祁连山地震带两次中强地震前的加卸载响应比异常

研究了祁连山地震带两次中强地震前的加卸载响应比异常特征，讨论了基于天然地震序列的样本条件对加卸载响应比计算结果的影响，提出处理序列中4．0级以上地震的新方法。     

2020年6月26日于田MS6.4地震前Benioff应变和地电场加卸载响应比异常研究

加卸载响应比（Load/Unload Response Ratio,LURR）是根据岩石介质本构关系的动态演化特征提出的地震预测方法。2020年6月26日新疆于田县发生6.4级地震,震前以Benioff应变为响应量观测到明显的LURR高值异常,异常出现于2019年初,持续1年后发生地震,意味着震源区介质的应力状态在2019年发生了明显改变。进一步,以地电场为响应量,计算了距震中280km的和田地电场长、短极距共6个测向的LURR异常时序曲线,结果表明：和田地电场长、短极距的NS向和NW向共4个测向在震前1~3个月出现了LURR异常逐渐增大的同步变化,这种现象可能反映了孕震区介质因微裂隙的产生和扩展导致流体在裂隙中的运移引起的动电效应。综合分析2种不同响应量的LURR异常演化特征,有助于更深入地认知地震孕育过程,更准确地评估地震活动趋势。     

Failure Potential Evaluation in Engineering Experiments Using Load/Unload Response Ratio Method

The Load/Unload Response Ratio (LURR) method is proposed for prediction of the failure of brittle heterogeneous materials. Application of the method typically involves evaluating the external load on materials or structures, differentiating between loading and unloading periods, determining the failure response during both periods from data input, and calculating the ratio between the two response rates. According to the method, the LURR time series usually climbs to an anomalously high peak prior to the macro-fracture. To show the validity of the approach in engineering practice, we applied it to the loading and unloading experimental data associated with a two-floor concrete-brick structure. Results show that the LURR time series of the two floors consists of the damage evolution of the structure: they are at low level for most of the time, and reach the maxima prior to the final fracture. We then attempt to combine the LURR values with damage variable (D) to provide the health assessment of the structure. The relationship between LURR and D, defined as a function of Weibull stochastic distribution, is set up to provide more detailed underlying physical means to study damage evolution of the structure. The fact that the damage evolution of the structure correlates well with the variation of LURR time series may suggest that the LURR approach can be severed as a useful tool to provide the health assessment to big scale structures or ancient buildings.     

山西数字地下水位固体潮加卸载响应比与中强地震关系分析

运用加卸载响应比方法,计算和分析了山西省2008年以来数字化地下水位固体潮观测数据,并选取大于2倍加卸载响应比值作为异常判定指标,将山西及周边地区发生的ML≥4．0地震的参数与井水位固体潮响应比异常变化对比分析。结果表明,山西地区9口数字水位观测井的地下水位固体潮加卸载响应比异常变化与附近的地震活动存在不同程度的对应关系。从而说明,利用井水位固体潮观测的加卸载响应比是一种能有效识别和提取地震前兆的方法。     

Statistical Tests of Load-Unload Response Ratio Signals by Lattice Solid Model: Implication to Tidal Triggering and Earthquake Prediction

— Statistical tests of Load-Unload Response Ratio (LURR) signals are carried in order to verify statistical robustness of the previous studies using the Lattice Solid Model (Mora et al., 2002b). In each case 24 groups of samples with the same macroscopic parameters (tidal perturbation amplitude A, period T and tectonic loading rate k) but different particle arrangements are employed. Results of uni-axial compression experiments show that before the normalized time of catastrophic failure, the ensemble average LURR value rises significantly, in agreement with the observations of high LURR prior to the large earthquakes. In shearing tests, two parameters are found to control the correlation between earthquake occurrence and tidal stress. One is, A/(k T) controlling the phase shift between the peak seismicity rate and the peak amplitude of the perturbation stress. With an increase of this parameter, the phase shift is found to decrease. Another parameter, A T/k, controls the height of the probability density function (Pdf) of modeled seismicity. As this parameter increases, the Pdf becomes sharper and narrower, indicating a strong triggering. Statistical studies of LURR signals in shearing tests also suggest that except in strong triggering cases, where LURR cannot be calculated due to poor data in unloading cycles, the larger events are more likely to occur in higher LURR periods than the smaller ones, supporting the LURR hypothesis.     

赣粤闽交界及邻区近年中强地震加卸载响应比特征研究

以地震应变能作为响应因子,研究了1997至2007年赣粤闽交界及邻区4．0级（ML≥4．0）以上中强地震临震前的加卸载响应比（Y值）的基本变化特征,研究结果表明,80％以上的地震在临震前Y值呈现出高值异常形态。因而它可以作为此地区地震预测的一种手段。