The inverse problem in Seismology is tackled in this paper under three particular circumstances. First, the inverse problem is defined as the determination of the seismic-moment tensor from the far-field seismic waves (P and S waves). We use the analytical expression of the seismic waves in a homogeneous isotropic body with a seismic-moment source of tensorial forces, the source being localized both in space and time. The far-field waves provide three equations for the sixth unknown parameters of the general tensor of the seismic moment. Second, the Kostrov vectorial (dyadic) representation of the seismic moment is used. Third, the fourth missing equation is derived from the energy conservation and the covariance condition. The four equations derived here are solved, and the seismic moment is determined, thus solving the inverse problem in the conditions described above. It is shown that a useful picture of the seismic moment is the conic represented by the associated quadratic form, which is a hyperbola (seismic hyperbola). Also, it is shown that the far-field seismic waves allow an estimation of the volume of the focal region, focal strain, duration of the earthquake and earthquake energy; the later quantity is a direct measure of the magnitude of the seismic moment. The special case of an isotropic seismic moment is presented.
Earthquake monitoring across the globe is currently achieved with networks of seismic stations. The data from these networks have been instrumental in advancing our understanding of the Earth's interior structure and dynamic behaviour. However, almost all seismic stations are located on land and earthquakes of magnitude smaller than 4 at the bottom of the oceans remain largely undetected. Here we show that ordinary telecommunication optical fibre links can detect seismic events when combined with state-of-the-art frequency metrology techniques. We have detected earthquakes over terrestrial and…
The Earth's electric field, recorded by two different and distant monitoring sites located in Greece, is analyzed in terms of monochromatic signals (T=24h). The analysis is based on the mapping procedures borrowed from the study of non-linear dynamic systems and chaos. The specific analysis applied on the electric field recorded for some weeks before the occurrence of 3 large EQs which occurred in Greece shows some very interesting results. Long before the EQ occurrence the phase map generated by the uncorrelated each other signals recorded by a pair of distant monitoring sites is characterize…
Earthquakes are complex physical processes driven by the stick-slip motion of a sliding fault. After the main quake, a series of aftershocks typically follows. These are loosely defined as events that follow a given event and occur within prescribed space-time windows. In seismology, it is however impossible to establish a causal relation and the popular Nearest-Neighbor metric is commonly used to distinguish aftershocks from independent events. Here we employ a model for earthquake dynamics, previously shown to be able to correctly reproduce the phenomenology of earthquakes, and a technique t…
Recent advances in large ring laser gyroscopes (RLG) technologies opened the possibility to observe rotations of the ground with sensitivities up to $10^{-11}$ $\frac{rad}{s}$ over the frequency band of seismological interest (0.01-1Hz), thus opening the way to a new geophysical discipline, i.e. rotational seismology. A measure of rotations in seismology is of fundamental interest for (a) the determination of all the six degrees of freedom that characterize a rigid body motion, and (b) the quantitative estimate of the rotational motions contaminating ground translation measurements obtained fr…
TRACE: A Multi-Agent System for Autonomous Physical Reasoning for Seismology
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电子信息与电气工程学院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；School of Earth and Space Sciences, University of Science and Technology of China（中国科学技术大学地球和空间科学学院）；Department of Earth and Planetary Sciences, Harvard University（哈佛大学地球与行星科学系）；Institute of Earthquake Forecasting, China Earthquake Administration（中国地震局地震预报研究所）
Fundamentally related to the UV divergence problem in Physics, conventional wisdom in seismology is that the smallest earthquakes, which are numerous and often go undetected, dominate the triggering of major earthquakes, making the prediction of the latter difficult if not inherently impossible. By developing a rigorous validation procedure, we show that, in fact, large earthquakes (above magnitude 6.3 in California) are preferentially triggered by large events. Because of the magnitude correlations intrinsic in the validated model, we further rationalize the existence of earthquake doublets. …
Swiss Federal Institute of Technology（瑞士联邦理工学院）；Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology（南方科技大学高等跨学科研究学院）；Swiss Seismological Service（瑞士地震服务中心）；Institute of Geophysics（地球物理研究所）；Institute of Risk Analysis, Prediction and Management（风险分析、预测与管理研究所）；Institute of Structural Engineering（结构工程学院）
In the last few years, deep learning has solved seemingly intractable problems, boosting the hope to find approximate solutions to problems that now are considered unsolvable. Earthquake prediction, the Grail of Seismology, is, in this context of continuous exciting discoveries, an obvious choice for deep learning exploration. We review the entire literature of artificial neural network (ANN) applications for earthquake prediction (77 articles, 1994-2019 period) and find two emerging trends: an increasing interest in this domain, and a complexification of ANN models over time, towards deep lea…
The hypocentral depth is a key requirement in seismology and earthquake engineering, but it is very difficult to be determined. The current accepted improvement is taking advantage of the depth phases, such as the pP, to constrain this parameter. However, it is not easy to pick such a phase in a seismogram from the other phases and the backgound noises. Here we propose the use of the minimum entropy deconvolution (MED) to detect it. Synthetic tests show that impulse(s) hidden in the seimic noises, eg. discrete unit impulses or the Gaussian mono impulses, can be detected completely. Further, we…
Based on the geodynamics, an earthquake does not take place until the momentum-energy excess a faulting threshold value of rock due to the movement of the fluid layer under the rock layer and the transport and accumulation of the momentum. From the nonlinear equations of fluid mechanics, a simplified nonlinear solution of momentum corresponding the accumulation of the energy could be derived. Otherwise, a chaos equation could be obtained, in which chaos corresponds to the earthquake, which shows complexity on seismology, and impossibility of exact prediction of earthquakes. But, combining the …
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total number of events of all magnitudes, approximates to a Poisson distribution for a sufficiently small probability associated with that range. In this paper, we examine four earthquake catalogues: New Zealand (…
We report an empirical determination of the probability density functions $P_{\text{data}}(r)$ of the number $r$ of earthquakes in finite space-time windows for the California catalog. We find a stable power law tail $P_{\text{data}}(r) \sim 1/r^{1+μ}$ with exponent $μ\approx 1.6$ for all space ($5 \times 5$ to $20 \times 20$ km$^2$) and time intervals (0.1 to 1000 days). These observations, as well as the non-universal dependence on space-time windows for all different space-time windows simultaneously, are explained by solving one of the most used reference model in seismology (ETAS), which …
Indian Institute of Science Education and Research Pune（印度科学教育研究所浦那分校）；Observatoire de la Côte d’Azur, Université Côte d’Azur（蔚蓝海岸天文台，蔚蓝海岸大学）；CNRS, IRD, Géoazur（法国国家科学研究中心、海外发展研究院、Géoazur）；University of California, Riverside（加州大学河滨分校）
Learning Physics for Unveiling Hidden Earthquake Ground Motions via Conditional Generative Modeling
Lawrence Berkeley National Lab（劳伦斯伯克利国家实验室）；Earthquake Research Institute, University of Tokyo（东京大学地震研究所）；University of California, Berkeley（加州大学伯克利分校）；Ben Gurion University of the Negev（本-古里安大学内盖夫分校）；MIT（麻省理工学院）；International Computer Science Institute（国际计算机科学研究所）
Seismic measurements are an important tool for exploration of planetary interiors, but may not be included in missions due to perceived complexity in placement of sensitive instruments on the surface. To help address this concern, we assess the fidelity of recordings of ground motion by an instrument placed on the deck of the engineering model of the Mars Science Laboratory compared with an identical instrument placed on the ground directly beneath. Comparison of the recordings reveals clear recordings of teleseismic earthquakes on both instruments. The transfer function between the instrument…
A web application prototype is described, aimed at the generation of synthetic seismograms for user-defined earthquake models. The web application graphical user interface hides the complexity of the underlying computational engine, which is the outcome of the continuous evolution of sophisticated computer codes, some of which saw the light back in the middle '80s. With the web application, even the non-experts can produce ground shaking scenarios at the local or regional scale in very short times, depending on the complexity of the adopted source and medium models, without the need of a deep …
Earthquake Aftershock Forecasting using Conditional Generative Models
Department of Earth and Planetary Science, University of California, Berkeley（加州大学伯克利分校地球与行星科学系）；Berkeley Seismological Laboratory, University of California, Berkeley（加州大学伯克利分校伯克利地震实验室）
GreenPhase: A Green Learning Approach for Earthquake Phase Picking
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（美国南加州大学明希斯电气与计算机工程系）；Center for Earth and Environmental Studies, National Central University（中华大学地球与环境研究所）；Department of Computer Science & Information Engineering, National Central University（中华大学计算机科学与信息工程系）
Integrating Artificial Intelligence and Geophysical Insights for Earthquake Forecasting: A Cross-Disciplinary Review
University of Science and Technology Beijing（北京科技大学）；Beijing Engineering Research Center of Industrial Spectrum Imaging（北京市工业光谱成像工程研究中心）；New York University Abu Dhabi（纽约大学阿布扎比分校）；Southern University of Science and Technology（南方科技大学）；China University of Geosciences (Beijing)（中国地质大学（北京））
Detecting Spatiotemporal b-Value Anomalies with a Progressive Deep Learning Architecture
Frankfurt Institute of Advanced Studies（法兰克福高等研究院）；Institute of Geosciences, Goethe-University Frankfurt（法兰克福歌德大学地球科学研究所）；Institute for Theoretical Physics, Goethe Universität（法兰克福歌德大学理论物理研究所）
Seismology is the main tool for inferring the deep interior structures of Earth and potentially also of other planetary bodies in the solar system. Terrestrial seismology is influenced by the presence of the ocean-generated microseismic signal, which sets a lower limit on the earthquake detection capabilities but also provides a strong energy source to infer the interior structure on scales from local to continental. Titan is the only other place in the solar system with permanent surface liquids and future lander missions there might carry a seismic package. Therefore, the presence of microse…
Seismic-phase detection using multiple deep learning models for global and local representations of waveforms
Earthquake Research Institute, The University of Tokyo（东京大学地震研究所）；Graduate School of Information Science and Technology, The University of Tokyo（东京大学信息科学与技术研究生院）
Learning Earthquake Wave Arrival Time Picking from Labels with Inaccuracies
Department of Earth and Planetary Sciences, Harvard University（哈佛大学地球与行星科学系）；School of Computer Science and Technology, China University of Mining and Technology（中国矿业大学（北京）计算机科学与技术学院）；School of Mines, China University of Mining and Technology（中国矿业大学（北京）矿院）；State Key Laboratory of Coal Exploration and Intelligent Mining, China University of Mining and Technology（中国矿业大学（北京）煤炭勘探与智能开采国家重点实验室）
High-Rate Phase Association with Travel Time Neural Fields
University of Basel（巴塞尔大学）；La Sapienza Università di Roma（罗马大学（萨皮恩扎））；Pennsylvania State University（宾夕法尼亚州立大学）；Rice University（莱斯大学）；University of Illinois at Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）
Seismic phase association is a fundamental task in seismology that pertains to linking together phase detections on different sensors that originate from a common earthquake. It is widely employed to detect earthquakes on permanent and temporary seismic networks, and underlies most seismicity catalogs produced around the world. This task can be challenging because the number of sources is unknown, events frequently overlap in time, or can occur simultaneously in different parts of a network. We present PhaseLink, a framework based on recent advances in deep learning for grid-free earthquake ph…
