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Inversion of DC Resistivity Data using Physics-Informed Neural Networks 利用物理信息神经网络反演直流电阻率数据
arXiv - PHYS - Geophysics Pub Date : 2024-08-05 DOI: arxiv-2408.02420
Rohan Sharma, Divakar Vashisth, Kuldeep Sarkar, Upendra Kumar Singh
{"title":"Inversion of DC Resistivity Data using Physics-Informed Neural Networks","authors":"Rohan Sharma, Divakar Vashisth, Kuldeep Sarkar, Upendra Kumar Singh","doi":"arxiv-2408.02420","DOIUrl":"https://doi.org/arxiv-2408.02420","url":null,"abstract":"The inversion of DC resistivity data is a widely employed method for\u0000near-surface characterization. Recently, deep learning-based inversion\u0000techniques have garnered significant attention due to their capability to\u0000elucidate intricate non-linear relationships between geophysical data and model\u0000parameters. Nevertheless, these methods face challenges such as limited\u0000training data availability and the generation of geologically inconsistent\u0000solutions. These concerns can be mitigated through the integration of a\u0000physics-informed approach. Moreover, the quantification of prediction\u0000uncertainty is crucial yet often overlooked in deep learning-based inversion\u0000methodologies. In this study, we utilized Convolutional Neural Networks (CNNs)\u0000based Physics-Informed Neural Networks (PINNs) to invert both synthetic and\u0000field Schlumberger sounding data while also estimating prediction uncertainty\u0000via Monte Carlo dropout. For both synthetic and field case studies, the median\u0000profile estimated by PINNs is comparable to the results from existing\u0000literature, while also providing uncertainty estimates. Therefore, PINNs\u0000demonstrate significant potential for broader applications in near-surface\u0000characterization.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Do earthquakes "know" how big they will be? a neural-net aided study 神经网络辅助研究:地震 "知道 "会有多大吗?
arXiv - PHYS - Geophysics Pub Date : 2024-08-04 DOI: arxiv-2408.02129
Neri Berman, Oleg Zlydenko, Oren Gilon, Yossi Matias, Yohai Bar-Sinai
{"title":"Do earthquakes \"know\" how big they will be? a neural-net aided study","authors":"Neri Berman, Oleg Zlydenko, Oren Gilon, Yossi Matias, Yohai Bar-Sinai","doi":"arxiv-2408.02129","DOIUrl":"https://doi.org/arxiv-2408.02129","url":null,"abstract":"Earthquake occurrence is notoriously difficult to predict. While some aspects\u0000of their spatiotemporal statistics can be relatively well captured by\u0000point-process models, very little is known regarding the magnitude of future\u0000events, and it is deeply debated whether it is possible to predict the\u0000magnitude of an earthquake before it starts. This is due both to the lack of\u0000information about fault conditions and to the inherent complexity of rupture\u0000dynamics. Consequently, even state of the art forecasting models typically\u0000assume no knowledge about the magnitude of future events besides the\u0000time-independent Gutenberg Richter (GR) distribution, which describes the\u0000marginal distribution over large regions and long times. This approach\u0000implicitly assumes that earthquake magnitudes are independent of previous\u0000seismicity and are identically distributed. In this work we challenge this view\u0000by showing that information about the magnitude of an upcoming earthquake can\u0000be directly extracted from the seismic history. We present MAGNET - MAGnitude\u0000Neural EsTimation model, an open-source, geophysically-inspired neural-network\u0000model for probabilistic forecasting of future magnitudes from cataloged\u0000properties: hypocenter locations, occurrence times and magnitudes of past\u0000earthquakes. Our history-dependent model outperforms stationary and\u0000quasi-stationary state of the art GR-based benchmarks, in real catalogs in\u0000Southern California, Japan and New-Zealand. This demonstrates that earthquake\u0000catalogs contain information about the magnitude of future earthquakes, prior\u0000to their occurrence. We conclude by proposing methods to apply the model in\u0000characterization of the preparatory phase of earthquakes, and in operational\u0000hazard alert and earthquake forecasting systems.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PRIME-DP: Pre-trained Integrated Model for Earthquake Data Processing PRIME-DP:地震数据处理预训练综合模型
arXiv - PHYS - Geophysics Pub Date : 2024-08-04 DOI: arxiv-2408.01919
Ziye Yu, Yuqi Cai, Weitao Wang, Yanru An, Lu Li, Yueyang Xia, Yunpeng Zhang
{"title":"PRIME-DP: Pre-trained Integrated Model for Earthquake Data Processing","authors":"Ziye Yu, Yuqi Cai, Weitao Wang, Yanru An, Lu Li, Yueyang Xia, Yunpeng Zhang","doi":"arxiv-2408.01919","DOIUrl":"https://doi.org/arxiv-2408.01919","url":null,"abstract":"We introduce a new seismic wave representation model called PRIME-DP, which\u0000stands for Pre-trained Integrated Model for Earthquake Data Processing. Unlike\u0000most of the models, which are designed to specifically a singular problem,\u0000PRIME-DP is used for multi-task single station seismic waveform processing.\u0000PRIME-DP can be used to Pg/Sg/Pn/Sn phase picking, P polarization\u0000classification. And can be fine-tunned to wide range of tasks, such as event\u0000classification, without architecture modifications. PRIME-DP can achieve over\u000085% recall on Pg and Sg phases, when picking continuous waveform and achieves\u0000over 80% accuracy in P polarization classification. By fine-tunning\u0000classification decoder with NeiMeng dataset, PRIME-DP can achieve 95.1%\u0000accuracy on event.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transformer for seismic image super-resolution 地震图像超分辨率变换器
arXiv - PHYS - Geophysics Pub Date : 2024-08-03 DOI: arxiv-2408.01695
Shiqi Dong, Xintong Dong, Kaiyuan Zheng, Ming Cheng, Tie Zhong, Hongzhou Wang
{"title":"Transformer for seismic image super-resolution","authors":"Shiqi Dong, Xintong Dong, Kaiyuan Zheng, Ming Cheng, Tie Zhong, Hongzhou Wang","doi":"arxiv-2408.01695","DOIUrl":"https://doi.org/arxiv-2408.01695","url":null,"abstract":"Seismic images obtained by stacking or migration are usually characterized as\u0000low signal-to-noise ratio (SNR), low dominant frequency and sparse sampling\u0000both in depth (or time) and offset dimensions. For improving the resolution of\u0000seismic images, we proposed a deep learning-based method to achieve\u0000super-resolution (SR) in only one step, which means performing the denoising,\u0000interpolation and frequency extrapolation at the same time. We design a seismic\u0000image super-resolution Transformer (SIST) to extract and fuse local and global\u0000features, which focuses more on the energy and extension shapes of effective\u0000events (horizons, folds and faults, etc.) from noisy seismic images. We extract\u0000the edge images of input images by Canny algorithm as masks to generate the\u0000input data with double channels, which improves the amplitude preservation and\u0000reduces the interference of noises. The residual groups containing\u0000Swin-Transformer blocks and residual connections consist of the backbone of\u0000SIST, which extract the global features in a window with preset size and\u0000decrease computational cost meanwhile. The pixel shuffle layers are used to\u0000up-sample the output feature maps from the backbone to improve the edges,\u0000meanwhile up-sampling the input data through a skip connection to enhance the\u0000amplitude preservation of the final images especially for clarifying weak\u0000events. 3-dimensional synthetic seismic volumes with complex geological\u0000structures are created, and the amplitudes of half of the volumes are mixtures\u0000of strong and weak, then select 2-dimensional slices randomly to generate\u0000training datasets which fits field data well to perform supervised learning.\u0000Both numerical tests on synthetic and field data in different exploration\u0000regions demonstrate the feasibility of our method.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Deep CNN Model for Ringing Effect Attenuation of Vibroseis Data 用于减弱震荡数据振铃效应的深度 CNN 模型
arXiv - PHYS - Geophysics Pub Date : 2024-08-03 DOI: arxiv-2408.01831
Zhuang Jia, Wenkai Lu
{"title":"A Deep CNN Model for Ringing Effect Attenuation of Vibroseis Data","authors":"Zhuang Jia, Wenkai Lu","doi":"arxiv-2408.01831","DOIUrl":"https://doi.org/arxiv-2408.01831","url":null,"abstract":"In the field of exploration geophysics, seismic vibrator is one of the widely\u0000used seismic sources to acquire seismic data, which is usually named vibroseis.\u0000\"Ringing effect\" is a common problem in vibroseis data processing due to the\u0000limited frequency bandwidth of the vibrator, which degrades the performance of\u0000first-break picking. In this paper, we proposed a novel deringing model for\u0000vibroseis data using deep convolutional neural network (CNN). In this model we\u0000use end-to-end training strategy to obtain the deringed data directly, and skip\u0000connections to improve model training process and preserve the details of\u0000vibroseis data. For real vibroseis deringing task we synthesize training data\u0000and corresponding labels from real vibroseis data and utilize them to train the\u0000deep CNN model. Experiments are conducted both on synthetic data and real\u0000vibroseis data. The experiment results show that deep CNN model can attenuate\u0000the ringing effect effectively and expand the bandwidth of vibroseis data. The\u0000STA/LTA ratio method for first-break picking also shows improvement on deringed\u0000vibroseis data using deep CNN model.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"186 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inner core heterogeneity induced by a large variation in lower mantle heat flux 下地幔热通量大幅变化诱发的内核异质性
arXiv - PHYS - Geophysics Pub Date : 2024-08-03 DOI: arxiv-2408.03158
Aditya Varma, Binod Sreenivasan
{"title":"Inner core heterogeneity induced by a large variation in lower mantle heat flux","authors":"Aditya Varma, Binod Sreenivasan","doi":"arxiv-2408.03158","DOIUrl":"https://doi.org/arxiv-2408.03158","url":null,"abstract":"Seismic mapping of the top of the inner core indicates two distinct areas of\u0000high P-wave velocity, the stronger one located beneath Asia, and the other\u0000located beneath the Atlantic. This two-fold pattern supports the idea that a\u0000lower-mantle heterogeneity can be transmitted to the inner core through outer\u0000core convection. In this study, a two-component convective dynamo model, where\u0000thermal convection is near critical and compositional convection is strongly\u0000supercritical, produces a substantial inner core heterogeneity in the rapidly\u0000rotating strongly driven regime of Earth's core. While the temperature profile\u0000that models secular cooling ensures that the mantle heterogeneity propagates as\u0000far as the inner core boundary (ICB), the distribution of heat flux at the ICB\u0000is determined by the strength of compositional buoyancy. A large heat flux\u0000variation $q^*$ of $O(10)$ at the core-mantle boundary (CMB), where $q^*$ is\u0000the ratio of the maximum heat flux difference to the mean heat flux at the CMB,\u0000produces a core flow regime of long-lived convection in the east and\u0000time-varying convection in the west. Here, the P-wave velocity estimated from\u0000the ICB heat flux in the dynamo is higher in the east than in the west, with\u0000the hemispherical difference of the same order as the observed lower bound,\u00000.5%. Additional observational constraints are satisfied in this regime -- the\u0000variability of high-latitude magnetic flux in the east is lower than that in\u0000the west; and the stratified F-layer at the base of the outer core, which is\u0000fed by the mass flux from regional melting of the inner core and magnetically\u0000damped, attains a steady-state height of $sim$ 200 km.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modelling the three-dimensional, diagnostic anisotropy field of an ice rise 冰隆的三维诊断性各向异性场建模
arXiv - PHYS - Geophysics Pub Date : 2024-08-02 DOI: arxiv-2408.01069
A. Clara J. Henry, Carlos Martín, Reinhard Drews
{"title":"Modelling the three-dimensional, diagnostic anisotropy field of an ice rise","authors":"A. Clara J. Henry, Carlos Martín, Reinhard Drews","doi":"arxiv-2408.01069","DOIUrl":"https://doi.org/arxiv-2408.01069","url":null,"abstract":"Polar ice develops anisotropic crystal orientation fabrics under deformation,\u0000yet ice is most often modelled as an isotropic fluid. We present\u0000three-dimensional simulations of the crystal orientation fabric of Derwael Ice\u0000Rise including the surrounding ice shelf using a crystal orientation tensor\u0000evolution equation corresponding to a fixed velocity field. We use a\u0000semi-Lagrangian numerical method that constrains the degree of crystal\u0000orientation evolution to solve the equations in complex flow areas. We perform\u0000four simulations based on previous studies, altering the rate of evolution of\u0000the crystal anisotropy and its dependence on a combination of the strain rate\u0000and deviatoric stress tensors. We provide a framework for comparison with radar\u0000observations of the anisotropy field, outlining areas where the assumption of\u0000one vertical eigenvector may not hold and provide resulting errors in measured\u0000eigenvalues. We recognise the areas of high horizontal divergence at the ends\u0000of the flow divide as important areas to make comparisons with observations.\u0000Here, poorly constrained model parameters result in the largest difference in\u0000fabric type. These results are important in the planning of future campaigns\u0000for gathering data to constrain model parameters and as a link between\u0000observations and computationally-efficient, simplified models of anisotropy.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Calibration of the strain amplitude recorded with DAS using a strainmeter array 使用应变计阵列校准 DAS 记录的应变振幅
arXiv - PHYS - Geophysics Pub Date : 2024-08-02 DOI: arxiv-2408.01151
Thomas ForbrigerKarlsruhe Institute of Technology, Nasim KaramzadehKarlsruhe Institute of Technologynow at University of Münster Institut für Geophysik, Münster, Germany, Jérôme AzzolaKarlsruhe Institute of Technology, Emmanuel GaucherKarlsruhe Institute of Technology, Rudolf Widmer-SchnidrigInstitute of Geodesy, University of Stuttgart, Stuttgart, Germany, Andreas RietbrockKarlsruhe Institute of Technology
{"title":"Calibration of the strain amplitude recorded with DAS using a strainmeter array","authors":"Thomas ForbrigerKarlsruhe Institute of Technology, Nasim KaramzadehKarlsruhe Institute of Technologynow at University of Münster Institut für Geophysik, Münster, Germany, Jérôme AzzolaKarlsruhe Institute of Technology, Emmanuel GaucherKarlsruhe Institute of Technology, Rudolf Widmer-SchnidrigInstitute of Geodesy, University of Stuttgart, Stuttgart, Germany, Andreas RietbrockKarlsruhe Institute of Technology","doi":"arxiv-2408.01151","DOIUrl":"https://doi.org/arxiv-2408.01151","url":null,"abstract":"The power of distributed acoustic sensing (DAS) lies in its ability to sample\u0000deformation signals along an optical fiber at hundreds of locations with only\u0000one interrogation unit (IU). While the IU is calibrated to record 'fiber\u0000strain', the properties of the cable and its coupling to the rock control the\u0000'strain transfer rate' and hence how much of 'rock strain' is represented in\u0000the recorded signal. We use DAS recordings in an underground installation\u0000colocated with an array of strainmeters in order to calibrate the 'strain\u0000transfer rate' in situ, using earthquake signals between 0.05 Hz and 0.1 Hz. A\u0000tight-buffered cable and a standard loose-tube telecommunication cable (running\u0000in parallel) are used, where a section of both cables loaded down by loose sand\u0000and sand bags is compared to a section, where cables are just unreeled on the\u0000floor. The 'strain transfer rate' varies between 0.13 and 0.53 depending on\u0000cable and installation type. The sandbags show no obvious effect and the\u0000tight-buffered cable generally provides a larger 'strain transfer rate'.\u0000Calibration of the 'strain transfer rate' with respect to the strainmeter does\u0000not depend on wave propagation parameters. Hence it is applicable to the large\u0000amplitude surface wave signal in a strain component almost perpendicular to the\u0000great-circle direction for which a waveform comparison with seismometer data\u0000does not work. The noise background for 'rock strain' in the investigated band\u0000is found at about an rms-amplitude of 0.1 nstrain in 1/6 decade for the\u0000tight-buffered cable. This allows a detection of marine microseisms at times of\u0000high microseism amplitude.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Evaluation of Performance Measures for Qualifying Flood Models with Satellite Observations 评估利用卫星观测鉴定洪水模型的性能指标
arXiv - PHYS - Geophysics Pub Date : 2024-08-01 DOI: arxiv-2408.00571
Jean-Paul Travert, Sébastien Boyaval, Cédric Goeury, Vito Bacchi, Fabrice Zaoui
{"title":"Evaluation of Performance Measures for Qualifying Flood Models with Satellite Observations","authors":"Jean-Paul Travert, Sébastien Boyaval, Cédric Goeury, Vito Bacchi, Fabrice Zaoui","doi":"arxiv-2408.00571","DOIUrl":"https://doi.org/arxiv-2408.00571","url":null,"abstract":"This work discusses how to choose performance measures to compare numerical\u0000simulations of a flood event with one satellite image, e.g., in a model\u0000calibration or validation procedure. A series of criterion are proposed to\u0000evaluate the sensitivity of performance measures with respect to the flood\u0000extent, satellite characteristics (position, orientation), and\u0000measurements/processing errors (satellite raw values or extraction of the flood\u0000maps). Their relevance is discussed numerically in the case of one flooding\u0000event (on the Garonne River in France in February 2021), using a distribution\u0000of water depths simulated from a shallow-water model parameterized by an\u0000uncertain friction field. After identifying the performance measures respecting\u0000the most criteria, a correlation analysis is carried out to identify how\u0000various performance measures are similar. Then, a methodology is proposed to\u0000rank performance measures and select the most robust to observation errors. The\u0000methodology is shown useful at identifying four performance measures out of 28\u0000in the study case. Note that the various top-ranked performance measures do not\u0000lead to the same calibration result as regards the friction field of the\u0000shallow-water model. The methodology can be applied to the comparison of any\u0000flood model with any flood event.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An axiomatic method for studying the truth or falsity of the Hirano-Utsu law describing aftershocks 研究描述余震的平野宇津定律真假的公理方法
arXiv - PHYS - Geophysics Pub Date : 2024-07-31 DOI: arxiv-2407.21446
A. V. Guglielmi
{"title":"An axiomatic method for studying the truth or falsity of the Hirano-Utsu law describing aftershocks","authors":"A. V. Guglielmi","doi":"arxiv-2407.21446","DOIUrl":"https://doi.org/arxiv-2407.21446","url":null,"abstract":"The power law of aftershock evolution was proposed by Hirano in 1924 and\u0000introduced by Utsu into seismology in the second half of the last century. The\u0000Hirano-Utsu law is widely used in studying the relaxation of earthquake source\u0000after the main shock of an earthquake. The prevailing view in the literature is\u0000that the Hirano-Utsu law is an improved version of Omori's hyperbolic law,\u0000formulated in 1894. The author disagrees with this notion. The paper proposes\u0000an axiomatic approach to the study of aftershocks. A phenomenological parameter\u0000of the source, called the deactivation coefficient, was introduced. The theory\u0000is based on axioms that do not contain any a priori statements regarding the\u0000form of the law of aftershock evolution. Formulas for the deactivation\u0000coefficient are derived from the axioms, allowing one to experimentally\u0000establish the truth or falsity of the Hirano-Utsu and Omori laws. A two-stage\u0000mode of source relaxation was discovered. In the first stage, called the Omori\u0000epoch, the Omori law is strictly followed. The Omori epoch ends with a\u0000bifurcation, after which aftershock activity becomes unpredictable. Omori's law\u0000is not fulfilled at the second stage of evolution. The Hirano-Utsu law is not\u0000fulfilled either at the first or second stage. Keywords: earthquake source,\u0000main shock, relaxation, deactivation coefficient, evolution equation, inverse\u0000problem, Omori epoch, bifurcation, two-stage relaxation mode.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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