Load-Unload Response Ratio Research Articles

Relationship between load/unload response ratio and damage variable and its application

AbstractThe physics‐based parameter: load/unload response ratio (LURR) was proposed to measure the proximity of a strong earthquake, which achieved good results in earthquake prediction. As LURR can be used to describe the damage degree of the focal media qualitatively, there must be a relationship between LURR and damage variable (D) which describes damaged materials quantitatively in damage mechanics. Hence, based on damage mechanics and LURR theory, taking Weibull distribution as the probability distribution function, the relationship between LURR and D is set up and analyzed. This relationship directs LURR applied in damage analysis of materials quantitatively from being qualitative earlier, which not only provides the LURR method with a more solid basis in physics, but may also give a new approach to the damage evaluation of big scale structures and prediction of engineering catastrophic failure. Copyright © 2009 John Wiley & Sons, Ltd.

A probabilistic approach for earthquake potential evaluation based on the load/unload response ratio method

AbstractPrevious studies indicate that the occurrence of a large earthquake might be predicted by anomalous temporal increase of the load/unload response ratio (LURR), which was often defined as the ratio of Benioff strain of small earthquakes released during loading and unloading time periods, corresponding to earth tide‐induced Coulomb failure stress change on optimally oriented faults. The conventional LURR anomalous evaluation usually sets a critical LURR value, above which an earthquake may occur. In this paper a probabilistic approach for the evaluation of earthquake potential based on the LURR method is developed. In the approach, the occurrence probability of a future earthquake is quantitatively evaluated by assessing the confidence level of LURR anomaly associated with its stochastic distribution. As retrospective studies, we apply the approach to investigate the time series of LURR prior to the 50M>6.3 earthquakes that occurred in the Chinese mainland and the 21M>6.0 earthquakes in southern California over the past 30 years, and find high correlation between the confidence level of the LURR anomalies and the occurrence of the large earthquakes. We then depict all the high peaks that appeared in the LURR time series, and evaluate the earthquake occurrence rate as a function of the confidence level. The research results show considerable promise that our probabilistic approach may provide a useful tool to evaluate quantitatively the occurrence possibilities of future earthquakes. Copyright © 2009 John Wiley & Sons, Ltd.

The peak point of LURR and its significance

AbstractThe Load/Unload Response Ratio (LURR) value fluctuates around one during the early stage of the seismogenic process and then rises and reaches its peak point before the occurrence of a strong earthquake; the strong earthquake however does not onset at that time, but after the peak point LURR decreases sharply at the eve of the main shock before the final event outbreak. Thus, the peak point of LURR is ahead of the occurrence of an earthquake. We denote the lead time as T2. The discovery of peak point for LURR and the relationship between T2 and magnitude M is of great significance as the peak point is usually easy to determine and then we can predict the occurrence time for the coming event according to Equation (3) so that we can enhance the precision of time for earthquake prediction in terms of LURR from ‘year’ scale to ‘month’ scale. The variation of LURR around the Wenchuan earthquake and its lesson to us are depicted in the paper. Copyright © 2009 John Wiley & Sons, Ltd.

Load-unload response ratio and its application to estimate future seismicity of Qiandao Lake region

LURR (Load-Unload Response Ratio) has been introduced briefly in this paper and future seismicity of Qiandao Lake region has been predicted in terms of LURR for the purpose of SFT (Submerged Floating Tunnel) project.

The dynamic parameter of rainfall: its importance in the prediction of colluvial landslides

The paper discusses rainfall as a dynamic parameter in terms of the load–unload response theory, using the Xintan landslide in China as a case study. The computational results show that an abrupt jump occurs in the curve of the load–unload response ratio just before the landslide takes place. This indicates the potential of the dynamic parameter of rainfall for the prediction of colluvial landslides.

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.

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.

Earthquake Trend Around Sumatra Indicated by a New Implementation of LURR Method

The current implementation of LURR (Load/Unload Response Ratio) theory has shown promise in intermediate to short-term earthquake forecasting through past practice, but has also met difficulties at the same time. In this paper a new implementation of LURR method is presented to address one of the problems. The major change in the new implementation is that LURR values will result from a calculated maximum faulting orientation (MFO) instead of any focal mechanism selected by users. After comparison with the world stress map, the calculated MFO has been found to be in good agreement with the observation from the regional tectonic stress regime. The MFO pattern in the Indonesia region has a special feature which may be related to the unique subduction complexity. The MFO pattern in the Sumatra region in general is different from that in the Java region after the 2004 M 9.0 Sumatra Andaman Islands earthquake. This phenomenon may be supported by the evidence of the recent observation that a section in the southern part of the Sumatran arc is locked. Furthermore, the MFO pattern before the 2004 main shock is different from that after the event. Retrospective examination of the Indonesia region by means of this implementation can produce significant LURR anomaly not only prior to the 2004 main shock but also before the 2006 M 7.7 South Java earthquake. Therefore future great earthquakes might favorably be forecasted if the LURR anomaly detected by MFO method could be considered a precursor.

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.

A Statistical Investigation of the Earthquake Predictions Using LURR

In terms of the spatial scanning of LURR (Load-Unload Response Ratio), we have been predicting the seismic tendency within the next year for the mainland of China from 1995 to 2003. In order to make the quantitative retrospective assessment of LURR method, we compare the results with Poisson null hypothesis. The results show that the prediction by LURR method is much better than Poisson hypothesis.

Acoustic Emission Experiments of Rock Failure Under Load Simulating the Hypocenter Condition

A series of acoustic emission (AE) experiments of rock failure have been conducted under cyclic load in tri-axial stress tests. To simulate the hypocenter condition the specimens are loaded by the combined action of a constant stress, intended to simulate the tectonic loading, and a small sinusoidal disturbance stress, analogous to the Earth tide induced by the Sun and the Moon. Each acoustic emission signal can indicate the occurrence time, location and relative magnitude of the damage (micro-crack) in the specimen. The experimental results verified some precursors such as LURR (Load/Unload Response Ratio) and AER (Accelerating Energy Release) before macro-fracture of the samples. A new parameter, the correlation between the AE and the load, has been proposed to describe the loading history. On the eve of some strong earthquakes the correlation between the Benioff strain and the Coulomb failure stress (CFS) decreases, similar to the variation of LURR prior to strong earthquakes.

Computational Earthquake Physics PART II: Introduction

Exciting developments in earthquake science have benefited from new observations, improved computational technologies, and improved modeling capabilities. Designing realistic supercomputer simulation models for the complete earthquake generation process is a grand scientific challenge due to the complexity of phenomena and range of scales involved from microscopic to global. The present volume - Part II - incorporates computational environment and algorithms, data assimilation and understanding, model applications and iSERVO. Topics covered range from iSERVO and QuakeSim: implementing the international solid earth research virtual observatory by integrating computational grid and geographical information web services; LURR (Load-Unload Response Ratio) described in six papers involving this promising earthquake forecasting model; pattern informatics and phase dynamics and their applications, which was also a highlight in the Workshop; computational algorithms, including continuum damage models and visualization and analysis of geophysical datasets; evolution of mantle material; the state vector approach; and assimilation of data such as geodetic data, GPS data, and seismicity and laboratory experimental data.

Increasing critical sensitivity of the Load/Unload Response Ratio before large earthquakes with identified stress accumulation pattern

The Load/Unload Response Ratio (LURR) method is proposed for short-to-intermediate-term earthquake prediction [Yin, X.C., Chen, X.Z., Song, Z.P., Yin, C., 1995. A New Approach to Earthquake Prediction — The Load/Unload Response Ratio (LURR) Theory, Pure Appl. Geophys., 145, 701–715]. This method is based on measuring the ratio between Benioff strains released during the time periods of loading and unloading, corresponding to the Coulomb Failure Stress change induced by Earth tides on optimally oriented faults. According to the method, the LURR time series usually climb to an anomalously high peak prior to occurrence of a large earthquake. Previous studies have indicated that the size of critical seismogenic region selected for LURR measurements has great influence on the evaluation of LURR. In this study, we replace the circular region usually adopted in LURR practice with an area within which the tectonic stress change would mostly affect the Coulomb stress on a potential seismogenic fault of a future event. The Coulomb stress change before a hypothetical earthquake is calculated based on a simple back-slip dislocation model of the event. This new algorithm, by combining the LURR method with our choice of identified area with increased Coulomb stress, is devised to improve the sensitivity of LURR to measure criticality of stress accumulation before a large earthquake. Retrospective tests of this algorithm on four large earthquakes occurred in California over the last two decades show remarkable enhancement of the LURR precursory anomalies. For some strong events of lesser magnitudes occurred in the same neighborhoods and during the same time periods, significant anomalies are found if circular areas are used, and are not found if increased Coulomb stress areas are used for LURR data selection. The unique feature of this algorithm may provide stronger constraints on forecasts of the size and location of future large events.

Computational Earthquake Physics PART I: Introduction

Large earthquakes are terrible natural disasters which usually cause massive casualties and huge property loss. In the beginning of the new century, large earthquakes violently struck the world, especially the Asia-Pacific region. Nearly 300,000 people were killed by the magnitude 9.0 Northern Sumatra earthquake and tsunami, and the magnitude 7.8 Pakistan earthquake of October 8th, 2005 resulted in 90,000 deaths. In the meantime, there has been great progress in computational earthquake physics. New understanding of earthquake processes, numerous ideas on earthquake dynamics and complexity, new numerical models and methods, higher performance super-computers, and new data and analysis methods are emerging. These include the LSM (Lattice Solid particle simulation Model) Australian Computational Earth Systems Simulator (ACcESS), Japan’s Earth Simulator, GeoFEM, GeoFEST, QuakeSim, SERVO grid, iSERVO, LURR (Load-Unload Response Ratio), PI (Pattern Informatics), Critical Sensitivity, earthquake Critical Point Hypothesis, the friction law and seismicity, tremor, the Virtual California model, interaction between faults and the conversation of earthquakes, ROC (Relative Operating Characteristic), MFEM (Multiscale Finite-Element Model), etc. Most of these are the outcome of ACES-related research and activities, and will be presented in this volume.

Load-Unload Response Ratio (LURR), Accelerating Moment/Energy Release (AM/ER) and State Vector Saltation as Precursors to Failure of Rock Specimens

In order to verify some precursors such as LURR (Load/Unload Response Ratio) and AER (Accelerating Energy Release) before large earthquakes or macro-fracture in heterogeneous brittle media, four acoustic emission experiments involving large rock specimens under tri-axial stress, have been conducted. The specimens were loaded in two ways: monotonous or cycling. The experimental results confirm that LURR and AER are precursors of macro-fracture in brittle media. A new measure called the state vector has been proposed to describe the damage evolution of loaded rock specimens.

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.

Spatio-temporal Scanning and Statistical Test of the Accelerating Moment Release (AMR) Model Using Australian Earthquake Data

— The Accelerating Moment Release (AMR) preceding earthquakes with magnitude above 5 in Australia that occurred during the last 20 years was analyzed to test the Critical Point Hypothesis. Twelve earthquakes in the catalog were chosen based on a criterion for the number of nearby events. Results show that seven sequences with numerous events recorded leading up to the main earthquake exhibited accelerating moment release. Two occurred near in time and space to other earthquakes preceded by AMR. The remaining three sequences had very few events in the catalog so the lack of AMR detected in the analysis may be related to catalog incompleteness. Spatio-temporal scanning of AMR parameters shows that 80% of the areas in which AMR occurred experienced large events. In areas of similar background seismicity with no large events, 10 out of 12 cases exhibit no AMR, and two others are false alarms where AMR was observed but no large event followed. The relationship between AMR and Load-Unload Response Ratio (LURR) was studied. Both methods predict similar critical region sizes, however, the critical point time using AMR is slightly earlier than the time of the critical point LURR anomaly.

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/(kT) 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, AT/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.

Load-Unload Response Ratio and Accelerating Moment/Energy Release Critical Region Scaling and Earthquake Prediction

— The main idea of the Load-Unload Response Ratio (LURR) is that when a system is stable, its response to loading corresponds to its response to unloading, whereas when the system is approaching an unstable state, the response to loading and unloading becomes quite different. High LURR values and observations of Accelerating Moment/Energy Release (AMR/AER) prior to large earthquakes have led different research groups to suggest intermediate-term earthquake prediction is possible and imply that the LURR and AMR/AER observations may have a similar physical origin. To study this possibility, we conducted a retrospective examination of several Australian and Chinese earthquakes with magnitudes ranging from 5.0 to 7.9, including Australia's deadly Newcastle earthquake and the devastating Tangshan earthquake. Both LURR values and best-fit power-law time-to-failure functions were computed using data within a range of distances from the epicenter. Like the best-fit power-law fits in AMR/AER, the LURR value was optimal using data within a certain epicentral distance implying a critical region for LURR. Furthermore, LURR critical region size scales with mainshock magnitude and is similar to the AMR/AER critical region size. These results suggest a common physical origin for both the AMR/AER and LURR observations. Further research may provide clues that yield an understanding of this mechanism and help lead to a solid foundation for intermediate-term earthquake prediction.

Simulation of the Load-Unload Response Ratio and Critical Sensitivity in the Lattice Solid Model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.