Automatic reconstruction of fault networks from seismicity catalogs including location uncertainty

We introduce the Anisotropic Clustering of Location Uncertainty Distributions (ACLUD) method to reconstruct active fault networks on the basis of both earthquake locations and their estimated individual uncertainties. After a massive search through the large solution space of possible reconstructed fault networks, we apply six different validation procedures in order to select the corresponding best fault network. Two of the validation steps (cross-validation and Bayesian Information Criterion (BIC) process the fit residuals, while the four others look for solutions that provide the best agreement with independently observed focal mechanisms. Tests on synthetic catalogs allow us to qualify the performance of the fitting method and of the various validation procedures. The ACLUD method is able to provide solutions that are close to the expected ones, especially for the BIC and focal mechanismbased techniques. The clustering method complemented by the validation step based on focal mechanisms provides good solutions even in the presence of a significant spatial background seismicity rate. Our new fault reconstruction method is then applied to the Landers area in Southern California and compared with previous clustering methods. The results stress the importance of taking into account undersampled sub-fault structures as well as of the spatially inhomogeneous location uncertainties.

[1]  Annemarie Christophersen,et al.  Building self-consistent, short-term earthquake probability (STEP) models: improved strategies and calibration procedures , 2010 .

[2]  S. Wiemer,et al.  Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty , 2005 .

[3]  S. Wiemer,et al.  Influence of pore‐pressure on the event‐size distribution of induced earthquakes , 2012 .

[4]  Friedemann Wenzel,et al.  Simulation of MW= 6.0 earthquakes in the Upper Rhinegraben using empirical Green functions , 2002 .

[5]  P. Podvin,et al.  Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools , 1991 .

[6]  Thomas H. Jordan,et al.  Distribution of seismicity across strike‐slip faults in California , 2008 .

[7]  D. Amitrano Brittle‐ductile transition and associated seismicity: Experimental and numerical studies and relationship with the b value , 2003 .

[8]  Sergei Vassilvitskii,et al.  k-means++: the advantages of careful seeding , 2007, SODA '07.

[9]  Nicholas Deichmann,et al.  Identification of faults activated during the stimulation of the Basel geothermal project from cluster analysis and focal mechanisms of the larger magnitude events , 2014 .

[10]  C. Thurber,et al.  Theory and Observations – Seismic Tomography and Inverse Methods , 2007 .

[11]  Sergei Vassilvitskii,et al.  Scalable K-Means++ , 2012, Proc. VLDB Endow..

[12]  D. Sornette,et al.  New Approach to the Characterization of Mmax and of the Tail of the Distribution of Earthquake Magnitudes , 2007, physics/0703010.

[13]  Gerassimos A. Papadopoulos,et al.  OPERATIONAL EARTHQUAKE FORECASTING. State of Knowledge and Guidelines for Utilization , 2011 .

[14]  Didier Sornette,et al.  Multifractal scaling properties of a growing fault population , 1995 .

[15]  G. Wittlinger,et al.  Earthquake location in strongly heterogeneous media , 1993 .

[16]  Peter M. Shearer,et al.  A New Method for Determining First-Motion Focal Mechanisms , 2002 .

[17]  Stefan Wiemer,et al.  The influence of tectonic regimes on the earthquake size distribution: A case study for Italy , 2010 .

[18]  J. Tchalenko Similarities between Shear Zones of Different Magnitudes , 1970 .

[19]  D. Sornette,et al.  Segmentation of fault networks determined from spatial clustering of earthquakes , 2010, 1006.0885.

[20]  R. Di Giovambattista,et al.  Local earthquake relative location by digital records , 1987 .

[21]  Keith L. McLaughlin,et al.  A New Ground Truth Data Set For Seismic Studies , 2009 .

[22]  A. Michael,et al.  Damped regional‐scale stress inversions: Methodology and examples for southern California and the Coalinga aftershock sequence , 2006 .

[23]  J. Douglas Zechar,et al.  Bayesian Forecast Evaluation and Ensemble Earthquake Forecasting , 2012 .

[24]  J. D. Zechar,et al.  Regional Earthquake Likelihood Models I: First-Order Results , 2013 .

[25]  Reynold Cheng,et al.  Uncertain Data Mining: An Example in Clustering Location Data , 2006, PAKDD.

[26]  David Carver,et al.  Nonlinear and Linear Site Response and Basin Effects in Seattle for the M 6.8 Nisqually, Washington, Earthquake , 2002 .

[27]  J. Douglas Zechar,et al.  Simple smoothed seismicity earthquake forecasts for Italy , 2010 .

[28]  Y. Kagan,et al.  Comparison of Short-Term and Time-Independent Earthquake Forecast Models for Southern California , 2006 .

[29]  P. Shearer,et al.  Computing a Large Refined Catalog of Focal Mechanisms for Southern California (1981-2010): Temporal Stability of the Style of Faulting , 2012 .

[30]  Clifford H. Thurber,et al.  Hypocenter-velocity structure coupling in local earthquake tomography , 1992 .

[31]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[32]  E. Hauksson Spatial Separation of Large Earthquakes, Aftershocks, and Background Seismicity: Analysis of Interseismic and Coseismic Seismicity Patterns in Southern California , 2010 .

[33]  R. Stein The role of stress transfer in earthquake occurrence , 1999, Nature.

[34]  Jacques R. Ernst,et al.  Earthquake focal mechanisms of the induced seismicity in 2006 and 2007 below Basel (Switzerland) , 2009 .

[35]  Gary L. Pavlis,et al.  Appraising earthquake hypocenter location errors: A complete, practical approach for single-event locations , 1986 .

[36]  Yan Y. Kagan,et al.  Double‐couple earthquake focal mechanism: random rotation and display , 2005 .

[37]  Stephen C. Myers,et al.  Epicentre accuracy based on seismic network criteria , 2004 .

[38]  Keith L. McLaughlin,et al.  Seismic Location Bias and Uncertainty in the Presence of Correlated and Non-Gaussian Travel-Time Errors , 2009 .

[39]  D. Sornette,et al.  Hierarchical geometry of faulting , 1996 .

[40]  Stefan Wiemer,et al.  Probabilistic earthquake location in complex three‐dimensional velocity models: Application to Switzerland , 2003 .

[41]  D. Sornette,et al.  Characterization of the Frequency of Extreme Earthquake Events by the Generalized Pareto Distribution , 2000, cond-mat/0011168.

[42]  Markus Häring,et al.  Characterisation of the Basel 1 enhanced geothermal system , 2008 .

[43]  F. Waldhauser,et al.  A Double-Difference Earthquake Location Algorithm: Method and Application to the Northern Hayward Fault, California , 2000 .

[44]  A. Gabrielov,et al.  Geometric incompatibility in a fault system. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[45]  P. Gaillot,et al.  Structural analysis of hypocentral distribution of an earthquake sequence using anisotropic wavelets: Method and application , 2002 .

[46]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.

[47]  Tobias Diehl,et al.  Consistent phase picking for regional tomography models: application to the greater Alpine region , 2009 .

[48]  P. Shearer,et al.  Waveform Relocated Earthquake Catalog for Southern California (1981 to June 2011) , 2012 .

[49]  Didier Sornette,et al.  Statistical physics model for the spatiotemporal evolution of faults , 1993 .

[50]  F. Waldhauser,et al.  Large-scale relocation of two decades of Northern California seismicity using cross-correlation and double-difference methods , 2008 .

[51]  Kevin Milner,et al.  Forecasting California's earthquakes: What can we expect in the next 30 years? , 2008 .

[52]  S. Wiemer,et al.  A retrospective comparative forecast test on the 1992 Landers sequence , 2011 .

[53]  Danijel Schorlemmer,et al.  Spatial correlation of aftershock locations and on‐fault main shock properties , 2006 .

[54]  D. Sornette Self-Organized Criticality in Plate Tectonics , 1991 .

[55]  Jean Virieux,et al.  Probabilistic Earthquake Location in 3D and Layered Models , 2000 .

[56]  Stephan B. Smith,et al.  Probabilistic earthquake relocation in three-dimensional velocity models for the Yellowstone National Park region, Wyoming , 2004 .

[57]  Yann Klinger,et al.  High-Resolution Satellite Imagery Mapping of the Surface Rupture and Slip Distribution of the Mw ∼7.8, 14 November 2001 Kokoxili Earthquake, Kunlun Fault, Northern Tibet, China , 2005 .

[58]  M. Wyss,et al.  Variations in earthquake-size distribution across different stress regimes , 2005, Nature.

[59]  Didier Sornette,et al.  Linking short-timescale deformation to long-timescale tectonics , 1992, Nature.

[60]  Kunihiko Shimazaki,et al.  FAULT TRACE COMPLEXITY, CUMULATIVE SLIP, AND THE SHAPE OF THE MAGNITUDE-FREQUENCY DISTRIBUTION FOR STRIKE-SLIP FAULTS : A GLOBAL SURVEY , 1996 .

[61]  D. Sornette,et al.  Organisation of joints and faults from 1-cm to 100-km scales revealed by optimized anisotropic wavelet coefficient method and multifractal analysis , 1995 .

[62]  M. Wyss,et al.  Mapping spatial variability of the frequency-magnitude distribution of earthquakes , 2002 .

[63]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[64]  Anthony Lomax,et al.  Earthquake location, direct, global-search methods , 2009 .

[65]  J. Arthur Snoke,et al.  Error Estimates in Some Commonly Used Earthquake Location Programs , 1984 .

[66]  J. Tchalenko,et al.  Structural Analysis of the Dasht-e Bayaz (Iran) Earthquake Fractures , 1970 .

[67]  Jiancang Zhuang,et al.  Space–time ETAS models and an improved extension , 2006 .

[68]  Morgan T. Page,et al.  The magnitude distribution of earthquakes near Southern California faults , 2011 .

[69]  Philippe Gaillot,et al.  The M = 5.1 1980 Arudy earthquake sequence (western Pyrenees, France): a revisited multi-scale integrated seismologic, geomorphologic and tectonic investigation , 2009 .

[70]  Christopher John Young,et al.  An Automatic, Adaptive Algorithm for Refining Phase Picks in Large Seismic Data Sets , 2002 .

[71]  Richard Arnold,et al.  A Bayesian approach to estimating tectonic stress from seismological data , 2007 .

[72]  David G. Stork,et al.  Pattern Classification , 1973 .

[73]  Andrew J. Michael,et al.  Community online resource for statistical seismicity analysis , 2011 .

[74]  Domenico Giardini,et al.  Earthquakes Induced By the Stimulation of an Enhanced Geothermal System Below Basel (Switzerland) , 2009 .

[75]  Stefan Wiemer,et al.  Bayesian Estimation of the Spatially Varying Completeness Magnitude of Earthquake Catalogs , 2010 .

[76]  M. Wyss,et al.  Earthquake statistics at Parkfield: 1. Stationarity of b values , 2004 .

[77]  Won-Young Kim,et al.  The Applicability of Modern Methods of Earthquake Location , 2006 .

[78]  Didier Sornette,et al.  Statistical physics of fault patterns self-organized by repeated earthquakes , 1994 .

[79]  A. Tarantola,et al.  Inverse problems = Quest for information , 1982 .

[80]  Peter Molnar,et al.  Microearthquake Seismicity and Fault Plane Solutions in the Hindu Kush Region and Their Tectonic Implications (Paper 9B1560) , 1980 .

[81]  Stefan Wiemer,et al.  Statistical analysis of the induced Basel 2006 earthquake sequence: introducing a probability-based monitoring approach for Enhanced Geothermal Systems , 2011 .

[82]  D. Sornette,et al.  Automatic reconstruction of fault networks from seismicity catalogs: Three-dimensional optimal anisotropic dynamic clustering , 2007, physics/0703084.

[83]  T. Moser,et al.  Hypocenter determination in strongly heterogeneous Earth models using the shortest path method , 1992 .

[84]  Jeanne L. Hardebeck,et al.  Geometry and Earthquake Potential of the Shoreline Fault, Central California , 2013 .

[85]  Edi Kissling,et al.  Geotomography with local earthquake data , 1988 .

[86]  Joan S. Gomberg,et al.  The effect of S-wave arrival times on the accuracy of hypocenter estimation , 1990, Bulletin of the Seismological Society of America.

[87]  Jerome A. Treiman,et al.  Community Fault Model (CFM) for Southern California , 2007 .

[88]  Ernst R. Flueh,et al.  Local earthquake tomography of shallow subduction in north Chile: A combined onshore and offshore study , 2000 .

[89]  David M. Perkins,et al.  Association of Earthquakes and Faults in the San Francisco Bay Area Using Bayesian Inference , 2003 .

[90]  Nicholas Deichmann,et al.  Rupture geometry from high-precision relative hypocentre locations of microearthquake clusters , 1992 .

[91]  Roberto Basili,et al.  The European Database of Seismogenic Faults (EDSF) compiled in the framework of the Project SHARE. , 2013 .

[92]  Mark D. Petersen,et al.  Time-independent and Time-dependent Seismic Hazard Assessment for the State of California: Uniform California Earthquake Rupture Forecast Model 1.0 , 2007 .

[93]  David A. Rhoades,et al.  An Earthquake Likelihood Model Based on Proximity to Mapped Faults and Cataloged Earthquakes , 2012 .

[94]  Terry E. Tullis,et al.  Preface to the Focused Issue on Earthquake Simulators , 2012 .

[95]  Katie M. Keranen,et al.  Oblique fault systems crossing the Seattle Basin: Geophysical evidence for additional shallow fault systems in the central Puget Lowland , 2012 .

[96]  James H. Dieterich,et al.  RSQSim Earthquake Simulator , 2012 .

[97]  J. Douglas Zechar,et al.  Testing alarm‐based earthquake predictions , 2008 .

[98]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[99]  Björn Lund,et al.  Calculating horizontal stress orientations with full or partial knowledge of the tectonic stress tensor , 2007 .

[100]  Domenico Giardini,et al.  Locally triggered seismicity in the central Swiss Alps following the large rainfall event of August 2005 , 2007 .

[101]  Yan Y. Kagan,et al.  A Stochastic Forecast of California Earthquakes Based on Fault Slip and Smoothed Seismicity , 2013 .

[102]  Yosihiko Ogata,et al.  Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes , 1988 .

[103]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[104]  Keith L. McLaughlin,et al.  Validation of Regional and Teleseismic Travel-Time Models by Relocating Ground-Truth Events , 2004 .

[105]  D. Sornette,et al.  Earthquake forecasting based on data assimilation: sequential Monte Carlo methods for renewal point processes , 2009, 0908.1516.

[106]  Matthew C. Gerstenberger,et al.  Real-time forecasts of tomorrow's earthquakes in California , 2005, Nature.