FaulTED: a new user-friendly MATLAB-based code to assess probabilistic fault displacement hazard

In tectonically active regions, surface faulting and offset of the ground surface caused by capable faults pose significant hazard to urban settlements and critical infrastructures. Given the challenges in fully parametrizing the geometry, kinematics, and activity of a capable fault, Probabilistic Fault Displacement Hazard Analysis (PFDHA) is widely employed. PFDHA is a relatively recent methodology that estimates the probability and magnitude of expected surface displacement at a given site during an earthquake.Current methods for Fault Displacement Hazard Analysis (FDHA) are commonly tailored to specific kinematic scenarios and often rely on scaling laws that are based on the characteristic earthquake magnitude. These approaches typically distinguish between displacements occurring along the primary fault (PF) and those occurring at distributed off-fault ruptures (DR). However, only a limited number of these methods are associated with computational tools, and their accessibility to users varies widely.This study introduces a new Matlab-based tool that integrates published scaling laws, surface rupture models, and fault displacement models into a PFDHA framework. The tool supports hazard assessment for both PF and DR displacements and incorporates the concept of floating rupture along faults, a common practice in probabilistic seismic hazard assessment.The modular design of the code provides users flexibility in generating hazard curves and maps by allowing them to select a variety of kinematic-specific components within the PFDHA. Furthermore, it allows the hazard assessment that considers distinct frequency-magnitude distributions.Moreover, a novel approach to address co-seismic ruptures that may be shorter than the total length of the main fault is proposed. It involves translating fault segments along the fault trace, with the co-seismic rupture length evaluated over a range of Mw values, such as those derived from a truncated Gutenberg-Richter distribution. The conditional probability of exceedance is then determined by recalculating the x/L points corresponding to the site location (x) in each rupture length (L) translating along the total length of the fault. Contributions from all scenarios are aggregated to produce the total hazard for distributed ruptures.This new tool aims to advance the current state of PFDHA by addressing variability among current models, facilitating direct comparisons between published methodologies for both PF and DR.

This study is part of the Probabilistic Fault Displacement Hazard Analysis (PFDHA) framework, which assesses the hazard posed by coseismic surface faulting to infrastructure systems (e.g., lifelines, nuclear power plants, and dams) located on or near an earthquake fault trace. The primary objective of this study is to estimate the probability of surface rupture on the principal fault—the main fault responsible for seismic moment release—based on faulting style, seismogenic thickness, fault geometry, and rupture size (i.e., earthquake magnitude). Current methods for estimating the probability of surface rupture on the principal fault are primarily based on empirical models. These models rely on observations of surface rupture occurrences versus non-occurrences, analyzed through logistic regressions using global or regional datasets of historical crustal earthquakes. However, empirical models have several limitations, including potential biases, catalog incompleteness (i.e., missing surface rupture data), and inconsistencies in fault geometry information and seismotectonic settings (e.g., seismogenic thickness). To overcome these limitations, we propose a numerical approach to compute the Conditional Probability of Surface Rupture (CPSR). This approach incorporates faulting style (normal, reverse, strike-slip), seismogenic thickness, fault dip, magnitude-dependent scaling relations for rupture shape and size, nucleation position within the rupture, and the statistical distribution of hypocenters within the seismogenic crust. These parameters are derived from statistical analyses of global fault rupture databases and earthquake distributions in various non-subduction seismotectonic settings. Our results indicate that CPSR probabilities are strongly influenced by seismogenic thickness and fault dip angle. Moreover, comparison between numerical results and empirical models suggests that CPSR depends on the specific characteristics of the study area. This model can be integrated into PFDHA as an epistemic alternative to purely empirical approaches. Additionally, the numerical code for CPSR computation has been developed and is openly available on GitHub.

For structures that cross active faults, the seismic loading includes both the vibratory ground motion and the fault displacement. Design ground-motion values are commonly based on probabilistic seismic hazard analysis (PSHA), whereas design fault displacement values have often been estimated using deterministic seismic hazard analysis. To treat ground motion and fault displacement consistently, there has been a growing demand for probabilistic fault-displacement hazard analysis (PFDHA) for selecting design fault displacements; however, choosing the fault displacement from a PFDHA based on the same return period as used for the ground motion may not lead to consistent levels of risk for moderate-activity faults (slip rate between 0.2 and 2 mm/yr) if the hazard curve has a flat slope at the selected return period. In this case, the epistemic uncertainty in the slip rate on the fault will lead to a very large range for the fault displacement at the selected return period. For moderate activity rates, alternative approaches for selecting a design fault displacement are described: risk-targeted displacement approach, high-fractile hazard approach, and median displacement given surface rupture at the site approach. If it is not practical to design for the fault displacement, an alternative approach is described in which an emergency action plan is developed to respond to the expected damage from fault displacement rather than design the structure to withstand the fault displacement.

<p>Probabilistic fault displacement hazard analysis (PFDHA) estimates the probability of occurrence and the expected exceedance of on-fault (principal fault rupturing; PF) and off-fault (dist ributed rupturing; DR) surface displacement during an earthquake. Here we concent rate on off-fault rupturing on dip-slip earthquakes, and present an original probability model for the occurrence of DR and for the expected exceedance of displacement dist ribution based on an approach named “slicing” (an alternative to the “gridding” approach commonly used). The method is developed based on the compilation and reappraisal of surface ruptures from 32 historical crustal dip-slip earthquakes, with magnitudes ranging from M<sub>w</sub> 4.9 to 7.9. A ranking scheme is applied to distinguish PF (rank 1) from simple DR (rank 2) and t riggered faulting (rank 3). Thus modellers can use prediction equations based on or excluding ruptures st rongly related to local st ructural setting depending on the site of concern. In the case of a st ructural setting at a site where large-scale bending (rank 21, 22) and pre-existing faults (rank 1.5, 3) is considered irrelevant, modelling can be performed considering only the unpredictable DR (rank 2). To minimize bias due to the incomplete nature of the database, we int roduce the “slicing” approach, which considers that the probability of having a surface rupture within slices parallel to the PF is homogeneous along the st rike of each slice. “Slicing” probabilities, computed as a function of magnitude of the earthquake and distance from the PF, are then combined with Monte Carlo simulations that model the dependence of the probability of occurrence of rupture and exceedance of displacement with the dimensions and position of the site of interest with respect to the PF. Finally, both probabilities are combined with existing predictive equations of exceedance of displacement on the PF to calculate fault-displacement hazard curves for sites of interest.</p>

We present a methodology for conducting a site-specific probabilistic analysis of fault displacement hazard. Two approaches are outlined. The first relates the occurrence of fault displacement at or near the ground surface to the occurrence of earthquakes in the same manner as is done in a standard probabilistic seismic hazard analysis (PSHA) for ground shaking. The methodology for this approach is taken directly from PSHA methodology with the ground-motion attenuation function replaced by a fault displacement attenuation function. In the second approach, the rate of displacement events and the distribution for fault displacement are derived directly from the characteristics of the faults or geologic features at the site of interest. The methodology for probabilistic fault displacement hazard analysis (PFDHA) was developed for a normal faulting environment and the probability distributions we present may have general application in similar tectonic regions. In addition, the general methodology is applicable to any region and we indicate the type of data needed to apply the methodology elsewhere.

Fault displacement is a localized source of hazard for infrastructure located near active and capable faults, such as critical buildings and distributed facilities. This issue can be overcome through zoning and avoidance strategies, but facilities may sometimes not benefit from this option. In the last 20 years, several authors have developed a probabilistic approach to analyse this hazard, known as probabilistic fault displacement hazard analysis (PFDHA), for both principal fault and distributed rupturing. In this work, we apply the approach proposed by YOUNGS et alii (2003) to the Anghiari-Città di Castello fault, a NE-dipping normal fault located in the northern Apennines of Italy, which shows evidence of Quaternary activity. We explore two different rupturing scenarios to obtain displacement hazard curves and maps for different probabilities of exceedance in 200 years at different distances along and from the principal fault trace for both the principal and distributed rupturing. The expected displacement values for the principal fault rupturing are up to 130 cm for a return period of 10,000 years (2% in 200 years), and the distributed rupturing hazard is 3–4% of the principal fault rupturing hazard. It is null in the footwall of the fault and slightly variable in its hanging wall as a function of distance from the fault trace and fault tip. The variability of the distributed rupturing hazard within the first hundreds of metres from the principal fault can assist to define mitigation strategies for existing facilities located in proximity of the fault.

The southwestern continuation of the East Anatolian Fault Zone (EAFZ), specifically its relationship with Iskenderun Basin, the Dead Sea Fault Zone (DSFZ) and Cyprus Slap is still enigmatic. In 2023, nearby splays of EAFZ in the southwest are ruptured by two large earthquakes that are nine hours apart. At first, Pazarcık earthquake (M7.8) initiated at a secondary fault, later jump to the main strand of EAFZ and propagated bilaterally producing a surface rupture exceeding 315 km in length. The Ekinözü earthquake (M7.7) triggered nine hours later also displayed bilateral rupture propagation and produced a 140 km long surface rupture. Surface deformations associated to both events that ruptured multiple fault segments with left-lateral strike-slip mechanism, are mapped in detail using satellite images and field observations. Surface offsets of both events are highly variable, reaches up to 8 m, and controlled mainly by subsurface slip. The accuracy of mapped active faults prior to the doublet, reduce significantly along plains where distributed deformations are common and occasionally surface rupture follows mapped inactive faults suggesting reactivation of old faults or unrecognized active faulting in the area.Large 19th century earthquakes previously associated to the faults ruptured during this doublet, are likely mislocated and these segments were accumulating stress at least for 500 years. Earthquake mechanisms recorded before and after the doublet revealed strike-slip regime corresponding well with EAFZ but towards south, extensional events become abundant. Based on the computed stress field, east-west striking Çardak fault ruptured during the second event, is not optimally oriented for left-lateral failure but suffered from noticeable static stress increase and rate-and-state friction based simulations including both static and dynamic effects suggested that it was at the end of its seismic cycle. Static stress changes resulted from the doublet also indicate pronounced increases, especially along Malatya, Savrun, Türkoğlu and Antakya fault segments which are remained as seismic gaps.GPS based slip models along multiple profiles constrained left-lateral slip rates of ruptured faults and suggested an increase in slip rate from south to north across EAFZ. During Pazarcık earthquake, rupture made a sharp bend towards south rather than following parallel fault segments towards Adana which are previously proposed as the western continuation of EAFZ. Our field observations indicated a fault traversing the Amanos mountains parallel to EAFZ along which fault kinematics and compiled GPS data together suggest left-lateral motions. Based on these findings, alternative regional kinematic models assuming Iskenderun and Maras blocks as independent or intact are established and later utilized for probabilistic seismic hazard analysis throughout the Adana basin by considering variable site conditions and basin effect in long spectral periods.

On 22 January 2024, a moment magnitude (Mw) 7.0 earthquake occurred in the southern Tian Shan region of western China, followed by an Mw 5.7 aftershock on 29 January. The Mw 7.0 mainshock occurred on a northwest-dipping fault plane, at a hypocentral depth of 13 km. Both Interferometric Synthetic Aperture Radar (InSAR) and optical satellite imagery observations indicate a lack of surface rupture for the Mw 7.0 earthquake. However, mapping and subpixel correlation of high-resolution optical satellite imagery and InSAR observations spanning the 29 January Mw 5.7 thrust-faulting aftershock support the interpretation of fault surface rupture. We observed ∼4.8 km of discontinuous surface rupture associated with the Mw 5.7 aftershock. The surface rupture trace trends subparallel to the northeast–southwest bedding orientation within the limb of a syncline. Subpixel image correlation and digital elevation model (DEM) differencing indicate mean on-fault offsets of 1 m, with a peak of ∼1.4 m, along the fault. Given these observations, we interpret the Mw 5.7 aftershock produced surface rupture on an unmapped flexural-slip fault within a syncline in the hanging wall of the Maidan fault or on a back thrust associated with the Maidan fault. Pre-existing fault features along the surface rupture trace in the landscape from pre-earthquake DEMs indicate that the fault that ruptured in the Mw 5.7 aftershock may have ruptured in the past. Surface rupture only from an aftershock in a seismic sequence is a critical observation that highlights the need to understand secondary or distributed faulting in larger earthquakes for seismic and fault displacement hazard analysis.

Earthquake ground surface ruptures provide insights into faulting mechanics and inform seismic hazard analyses. We analyze surface ruptures for 11 historical (1968–2018) moment magnitude (Mw) 4.7–6.6 reverse earthquakes in Australia using statistical techniques and compare their characteristics with magnetic, gravity, and stress trajectory data sets. Of the total combined (summative) length of all surface ruptures (∼148 km), 133 km (90%) to 145 km (98%) align with the geophysical structure in the host basement rocks. Surface rupture length (SRL), maximum displacement (MD), and probability of surface rupture at a specified Mw are high compared with equivalent Mw earthquakes globally. This is attributed to (1) a steep cratonic crustal strength gradient at shallow depths, promoting shallow hypocenters (∼1–6 km) and limiting downdip rupture widths (∼1–8.5 km), and (2) favorably aligned crustal anisotropies (e.g., bedrock foliations, faults, fault intersections) that enhanced lateral rupture propagation and/or surface displacements. Combined (modeled and observed) MDs are in the middle third of the SRL with 68% probability and either the ≤33rd or ≥66th percentiles of SRL with 16% probability. MD occurs proximate to or directly within zones of enhanced fault geometric complexity (as evidenced from surface ruptures) in 8 of 11 earthquakes (73%). MD is approximated by 3.3 ± 1.6 (1σ) × AD (average displacement). S-transform analyses indicates that high-frequency slip maxima also coincide with fault geometric complexities, consistent with stress amplifications and enhanced slip variability due to geometric and kinematic interactions with neighboring faults. Rupture slip taper angles exhibit large variations (−90% to +380% with respect to the mean value) toward rupture termini and are steepest where ruptures terminate at obliquely oriented magnetic lineaments and/or lithology changes. Incremental slip approximates AD between the 10th and 90th percentiles of the SRL. The average static stress drop of the studied earthquakes is 4.8 ± 2.8 MPa. A surface rupture classification scheme for cratonic stable regions is presented to describe the prevailing characteristics of intraplate earthquakes across diverse crustal structural-geophysical settings. New scaling relationships and suggestions for logic tree weights are provided to enhance probabilistic fault displacement hazard analyses for bedrock-dominated intraplate continental regions.

Research Article| December 17, 2013 Inferring a Thrust‐Related Earthquake History from Secondary Faulting: A Long Rupture Record of La Laja Fault, San Juan, Argentina Thomas K. Rockwell; Thomas K. Rockwell aDepartment of Geological Sciences, San Diego State University, 5500 Campanile Drive, San Diego, California 92182‐102 Search for other works by this author on: GSW Google Scholar Daniel E. Ragona; Daniel E. Ragona bBP p.l.c., 1 St James's Square, London, SW1Y 4PD, United Kingdom Search for other works by this author on: GSW Google Scholar Andrew J. Meigs; Andrew J. Meigs cCollege of Earth, Ocean, and Atmospheric Sciences, 104 CEOAS Administration Hall, Oregon State University, Corvallis, Oregon 97331‐5506 Search for other works by this author on: GSW Google Scholar Lewis A. Owen; Lewis A. Owen dDepartment of Geology, University of Cincinnati, Cincinnati, Ohio 45221 Search for other works by this author on: GSW Google Scholar Carlos H. Costa; Carlos H. Costa eDepartamento de Geología, Universidad Nacional de San Luis, 5700 San Luis, Argentina Search for other works by this author on: GSW Google Scholar Emilio A. Ahumada Emilio A. Ahumada eDepartamento de Geología, Universidad Nacional de San Luis, 5700 San Luis, Argentina Search for other works by this author on: GSW Google Scholar Author and Article Information Thomas K. Rockwell aDepartment of Geological Sciences, San Diego State University, 5500 Campanile Drive, San Diego, California 92182‐102 Daniel E. Ragona bBP p.l.c., 1 St James's Square, London, SW1Y 4PD, United Kingdom Andrew J. Meigs cCollege of Earth, Ocean, and Atmospheric Sciences, 104 CEOAS Administration Hall, Oregon State University, Corvallis, Oregon 97331‐5506 Lewis A. Owen dDepartment of Geology, University of Cincinnati, Cincinnati, Ohio 45221 Carlos H. Costa eDepartamento de Geología, Universidad Nacional de San Luis, 5700 San Luis, Argentina Emilio A. Ahumada eDepartamento de Geología, Universidad Nacional de San Luis, 5700 San Luis, Argentina Publisher: Seismological Society of America First Online: 14 Jul 2017 Online ISSN: 1943-3573 Print ISSN: 0037-1106 Bulletin of the Seismological Society of America (2014) 104 (1): 269–284. https://doi.org/10.1785/0120110080 Article history First Online: 14 Jul 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Thomas K. Rockwell, Daniel E. Ragona, Andrew J. Meigs, Lewis A. Owen, Carlos H. Costa, Emilio A. Ahumada; Inferring a Thrust‐Related Earthquake History from Secondary Faulting: A Long Rupture Record of La Laja Fault, San Juan, Argentina. Bulletin of the Seismological Society of America 2013;; 104 (1): 269–284. doi: https://doi.org/10.1785/0120110080 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyBulletin of the Seismological Society of America Search Advanced Search Abstract Trenches excavated across the surface rupture of the 15 January 1944 Mw 7 San Juan, Argentina, earthquake show evidence for repeated rupture of La Laja fault in the late Pleistocene and Holocene. The 1944 rupture extended for about 7 km striking ∼N35°E, and dipping 42° E parallel to Neogene bedding, with a maximum east‐side‐up vertical displacement of 30 cm. We interpret nine discrete colluvial wedges, each capped by a soil, as evidence for nine surface ruptures in the past ∼32–35 ka. Our topographic profile of the T3 terrace surface projected across the fault suggests these nine events collectively produced ∼10.3 m of dip displacement. We used radiocarbon and optically stimulated luminescence dating to define the timing of past events, yielding an average recurrence interval of 3.9±0.3 ka. The average estimate for displacement per event is about 1.1 m, compared with the 0.5 m of dip slip that occurred in 1944. Using a fault‐related fold model that infers ∼28 m of shortening based on the axial surface migration for the T3 terrace, along with the ∼35 ka age of the terrace, yields a shortening rate of ∼0.8 mm/yr by the 1944 source thrust fault, which is about 20% of the Global Positioning System—constrained total shortening rate across the Precordillera. Using this shortening rate and an assumed fault dip of 30° implies a fault slip rate of about 1.1 mm/yr, which combined with the average recurrence interval, implies ∼4 m of average slip per event on the causative fault at depth.Online Material: Unit descriptions from the trenches, stepwise reconstruction from trench 1, and annotated photographs of the La Laja region. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Probabilistic Seismic Hazard Analysis (PSHA) is the evaluation of annual frequencies of exceedance of ground motion levels. Probabilistic seismic hazard for the site specific Punasa dam has been estimated. Punasa dam is located in the Khandwa district on the life line river Narmada of Madhya Pradesh state of India. The PSHA of the Punasa dam site has been estimated considering the seismically active faults out of the total faults available in the area. Effects of all the faults, which can produce earthquake equal to or more than 3.5 magnitudes has been considered. The fault considered in the present work consists of 35 active faults out of total 126 faults, for which a minimum amount of information was available (i.e. length, maximum magnitude, etc.). For this purpose, an area of radius 500–550 km is selected. There are 154 earthquakes (moment magnitude 3.5–6.6) occurred in this region during last 210 years from 1808 to 2017. Completeness of this data is checked by Stepp’s method. For this data Gutenberg-Richter (G-R) parameters (a and b values) are estimated by regression analysis. Results are presented in a form of Peak Ground Acceleration (PGA) and seismic hazard curves.

Quantifying slip deficit rates on active faults in Tibet is essential for understanding fault kinematics and assessing seismic hazards, but has not been fully characterized, particularly on secondary faults. In this study, we integrate an updated interseismic Global Navigation Satellite Systems velocity field from 4,458 stations across continental China and its surroundings to calculate surface strain rates in Tibet, which we then use to invert for slip deficit rates on 263 crustal faults (383 segments). Our results reveal that ∼73% of strain rates are due to elastic strain accumulation on fault planes, and only a portion of the remaining strain rates may originate from unmodeled fault deformation. Quantitative calculations of seismic moment budgets on these fault segments indicate that they can produce earthquakes ranging from Mw 5.8 to 8.6, with 43 segments capable of generating earthquakes of Mw ≥ 7.5. Our findings provide a foundation for probabilistic seismic hazard analysis in Tibet.

Probabilistic seismic hazard analysis (PSHA) has become a fundamental tool in assessing seismic hazards and for estimating seismic design and seismic safety evaluation of ground motions. This report describes a study to test and verify the numerical approaches and software used in PSHA on Semnan, one of the important cities of Iran country. The geological and seismological data are integrated into a probabilistic seismic hazard model for the region. Historical and instrumental earthquake data, geology, tectonics, fault activity, and seismic source models associated with seismic events are taken into account. A probabilistic approach within a logic-tree framework is used to calculate seismic hazard for Semnan. The results were also displayed in terms of uniform hazard spectra for rock sites for return periods of 100, 475 and 2475 years, which is deemed appropriate for structural design standards in the Iran building code. As the results of this study have been displayed on the map for different return periods and different natural periods, it can provide the basis for the preparation of new seismic risk maps.

To provide a detailed record of a relatively rare thrust surface rupture and examine its active tectonic implications, we have conducted field mapping of the surface rupture associated with the 2005 M w 7.6 Kashmir earthquake. Despite the difficulty arising from massive earthquake-induced landslides along the surface rupture, we found that typical pressure ridges and warps extend northwestward for a distance of ∼70 km, with a northeast-side-up vertical separation of up to ∼7 m. Neither the main frontal thrust nor the main boundary thrust is responsible for the earthquake, but three active faults or fault segments within the Sub-Himalaya, collectively called the Balakot–Bagh fault, compose the causative fault. Although the fault exhibits substantial geomorphic expression of repeated similar surface ruptures, only a part of it had been mapped as active before the earthquake. The location of the hypocenter suggests that the rupture was initiated at a deep portion of the northern–central segment boundary and propagated bilaterally to eventually break all three segments. Our obtained surface rupture traces and the along-strike-slip distribution are both in good agreement with results of prompt analyses of satellite images, indicating that space geodesy can greatly aid in time-consuming field mapping of surface ruptures. Assuming that the extensive fill terrace in the meizoseismal area was abandoned during 10–30 ka, we tentatively estimate the earthquake recurrence interval and shortening rate on the Balakot–Bagh fault to be 1000–3300 yr and 1.4–4.1 mm/yr, respectively. These estimates indicate that the Balakot–Bagh fault is not a main player of Himalayan contraction accommodation. ![Graphic][1] Selected field photographs and ArcGIS files of the mapped surface rupture traces and measured vertical separations are available in the electronic supplement to this article. [1]: /embed/inline-graphic-1.gif

Holocene displacement along branch and secondary faults in the San Andreas fault zone, southern California