Combinatorial Framework for Obtaining the Optimal Spatial Distribution of Earthquakes on Complex Fault Systems

2021 ◽  
Author(s):  
Eric Geist ◽  
Tom Parsons
Keyword(s):  
Spatial Distribution ◽  
Combinatorial Optimization ◽  
Objective Function ◽  
Slip Rate ◽  
Optimization Methods ◽  
Fault System ◽  
Sequential Algorithm ◽  
Power Law Distribution ◽  
Frequency Distributions ◽  
Complex Fault

<p>A critical component of seismic hazard analysis is understanding the frequency and spatial distribution of earthquakes with different magnitudes on nearby faults.  A framework for determining the optimal spatial distribution of earthquakes on a complex fault system is developed using combinatorial optimization methods. Input to the framework is a millennia-scale sample of earthquakes taken from a regional Gutenberg-Richter (G-R) relation.  We then determine the optimal spatial arrangement of each earthquake in the fault system according to an objective function and constraints.  Our previously published results focus on minimizing the total misfit in slip rates as the objective function; constraints were maximum and minimum slip rate values that incorporate uncertainty in slip-rate values for each fault.  Both global and local combinatorial optimization methods have been developed to solve these problems: integer programming and the greedy sequential algorithm, respectively. Resulting on-fault magnitude distributions cannot be simply classified as being either purely characteristic or G-R. For example, faults may exhibit multiple “characteristic” magnitudes or a power-law distribution of magnitudes over a restricted range. Current research involves adapting the general combinatorial framework to include other and multiple objective functions, including minimizing the variation in accumulated stress over millennia.  The framework can also accommodate branching and step-over connections for the slip-rate objective, while current research is underway to include interaction stress loading among the different faults in the fault system for stress-based objectives.  Results from these methods are valuable for verifying the assumed magnitude-frequency distributions for faults in probabilistic seismic and tsunami hazard analyses.</p>

scholarly journals A combinatorial approach to determine earthquake magnitude distributions on a variable slip-rate fault

2019 ◽  
Vol 219 (2) ◽  
pp. 734-752 ◽  
Author(s):  
Eric L Geist ◽  
Tom Parsons
Keyword(s):  
Spatial Distribution ◽  
Integer Programming ◽  
Slip Rate ◽  
Rate Function ◽  
Programming Method ◽  
Sequential Algorithm ◽  
Rate Variation ◽  
Finite Sample ◽  
Decision Vector ◽  
Lower Magnitude

SUMMARY Combinatorial methods are used to determine the spatial distribution of earthquake magnitudes on a fault whose slip rate varies along strike. Input to the problem is a finite sample of earthquake magnitudes that span 5 kyr drawn from a truncated Pareto distribution. The primary constraints to the problem are maximum and minimum values around the target slip-rate function indicating where feasible solutions can occur. Two methods are used to determine the spatial distribution of earthquakes: integer programming and the greedy-sequential algorithm. For the integer-programming method, the binary decision vector includes all possible locations along the fault where each earthquake can occur. Once a set of solutions that satisfy the constraints is found, the cumulative slip misfit on the fault is globally minimized relative to the target slip-rate function. The greedy algorithm sequentially places earthquakes to locally optimize slip accumulation. As a case study, we calculate how earthquakes are distributed along the megathrust of the Nankai subduction zone, in which the slip rate varies significantly along strike. For both methods, the spatial distribution of magnitudes depends on slip rate, except for the largest magnitude earthquakes that span multiple sections of the fault. The greedy-sequential algorithm, previously applied to this fault (Parsons et al., 2012), tends to produce smoother spatial distributions and fewer lower magnitude earthquakes in the low slip-rate section of the fault compared to the integer-programming method. Differences in results from the two methods relate to how much emphasis is placed on minimizing the misfit to the target slip rate (integer programming) compared to finding a solution within the slip-rate constraints (greedy sequential). Specifics of the spatial distribution of magnitudes also depend on the shape of the target slip-rate function: that is, stepped at the section boundaries versus a smooth function. This study isolates the effects of slip-rate variation along a single fault in determining the spatial distribution of earthquake magnitudes, helping to better interpret results from more complex, interconnected fault systems.

scholarly journals Evidence for quaternary seismic activity of the La Alberca-Teremendo fault, Morelia region, Trans-Mexican Volcanic Belt

2019 ◽  
Vol 36 (2) ◽  
pp. 242-258
Author(s):  
Diana Cinthia Soria-Caballero ◽  
Victor Hugo Garduño-Monroy ◽  
María Alcalá ◽  
María Magdalena Velázquez-Bucio ◽  
Laura Grassi
Keyword(s):  
Slip Rate ◽  
Volcanic Belt ◽  
Vertical Displacement ◽  
Fault System ◽  
Morphological Evidence ◽  
Rupture Length ◽  
Mexican Volcanic Belt ◽  
Complex Fault ◽  
Tectonic Earthquakes ◽  
A Minor

The La Alberca-Teremendo fault is a 26 km-long, complex fault composed of an en échelon array of short crustal fault segments, belonging to the Morelia-Acambay fault system. This fault system shows parallel scarps with morphological evidence of recent activity such as drainage alteration, maximum throws of 50 m and minimum throws of 1.4 m that displace the recent soils. The fault acted as a conduit for the formation of the La Alberca de Guadalupe maar (23000 to 21000 years ago) and displaced afterwards its phreatomagmatic sequences. The paleoseismic analysis indicates that the La Alberca-Teremendo fault moved three times in the past 23000 years (age of the maar); this activity caused an average vertical displacement of 87 cm, and might have generated earthquakes with magnitudes Mw between 6.6 and 7, as well as volcano-tectonic earthquakes with magnitudes Mw between 4 and 5.5. The displacements were identified on the fault through the superposition of soils differentiated by a disconformity and an anomalous increase in the percentage of clay and organic matter. The La Alberca-Teremendo fault has dominant dip slip with a minor left-lateral component, a slip rate of 0.114 mm/year, and an average recurrence interval of 7726 ± 68 years. According to scaling relations that use the surface rupture length, if we assume that the La Alberca-Teremendo fault moves tectonically, it could generate earthquakes with maximum magnitudes of Mw between 6.7 and 7.3, however because of the active volcanic processes in the area, we could expect moderate volcano-tectonic earthquakes (Mw 4–5.5) rather than catastrophic ones.

Aftershock Sequence and Statistics of the 2017 Mw 5.5 Pohang, South Korea, Earthquake: Implications of Fault Heterogeneity and Postseismic Relaxation

2020 ◽  
Vol 110 (5) ◽  
pp. 2031-2046
Author(s):  
Jeong-Ung Woo ◽  
Minook Kim ◽  
Junkee Rhie ◽  
Tae-Seob Kang
Keyword(s):  
Spatial Distribution ◽  
Stress Field ◽  
South Korea ◽  
Aftershock Sequence ◽  
Fault System ◽  
Postseismic Deformation ◽  
Earthquake Catalog ◽  
B Values ◽  
Complex Fault ◽  
Anisotropic Expansion

ABSTRACT The sequence of foreshocks, mainshock, and aftershocks associated with a fault rupture is the result of interactions of complex fault systems, the tectonic stress field, and fluid movement. Analysis of shock sequences can aid our understanding of the spatial distribution and magnitude of these factors, as well as provide seismic hazard assessment. The 2017 Mw 5.5 Pohang earthquake sequence occurred following fluid-induced seismic activity at a nearby enhanced geothermal system site and is an example of reactivation of a critically stressed fault system in the Pohang basin, South Korea. We created an earthquake catalog based on unsupervised data mining and measuring the energy ratio between short- and long-window seismograms recorded by a temporary seismic network. The spatial distribution of approximately 4000 relocated aftershocks revealed four fault segments striking southwestward. We also determined that the three largest earthquakes (ML>4) were located at the boundary of two fault segments. We infer that locally concentrated stress at the junctions of the faults caused such large earthquakes and that their ruptures on multiple segments can explain the high proportion of non-double-couple components. The area affected by aftershocks continues to expand to the southwest and northeast by 0.5 and 1  km decade−1, respectively, which may result from postseismic deformation or sequentially transferred static coulomb stress. The b-values of the Gutenberg–Richter relationship temporarily increased for the first three days of the aftershock sequence, suggesting that the stress field was perturbed. The b-values were generally low (<1) and locally variable throughout the aftershock area, which may be due to the complex fault structures and material properties. Furthermore, the mapped p-values of the Omori law vary along strike, which may indicate anisotropic expansion speeds in the aftershock region.

scholarly journals Late Pleistocene‐Holocene Slip Rate Along the Hasi Shan Restraining Bend of the Haiyuan Fault: Implication for Faulting Dynamics of a Complex Fault System

Tectonics ◽  
2019 ◽  
Vol 38 (12) ◽  
pp. 4127-4154
Author(s):  
R. Matrau ◽  
Y. Klinger ◽  
J. Van der Woerd ◽  
J. Liu‐Zeng ◽  
Z. Li ◽  
...  
Keyword(s):  
Late Pleistocene ◽  
Slip Rate ◽  
Fault System ◽  
Complex Fault ◽  
Restraining Bend ◽  
Complex Fault System

A More Effective Formulation of the Path Generation Mechanism Synthesis Problem

1994 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Error Function ◽  
Mathematical Optimization ◽  
Optimization Methods ◽  
Complex Nature ◽  
Mechanism Synthesis ◽  
Structural Error ◽  
Crank Angle ◽  
The Common ◽  
Selection Of

Abstract Use of mathematical optimization methods for synthesis of path-generating mechanisms has had only limited success due to the very complex nature of the commonly used Structural Error objective function. The complexity arises, in part, because the objective function represents not only the error in the shape of the coupler curve, but also the error in location, orientation and size of the curve. Furthermore, the common introduction of timing (or crank angle), done generally to facilitate selection of corresponding points on the curve for calculating structural error, has little practical value and unnecessarily limits possible solutions. This paper proposes a new objective function, based on Fourier Descriptors, which allows search for coupler curve of the desired shape without reference to location, orientation, or size. The proposed objective function compares overall shape properties of curves rather than making point-by-point comparison and therefore does not requires prescription of timing. Experimental evidence is provided to show that it is much easier to search the space of the proposed objective function compared to the structural error function.

scholarly journals Multi-View Laser Point Cloud Global Registration for a Single Object

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3729 ◽  
Author(s):  
Shuai Wang ◽  
Hua-Yan Sun ◽  
Hui-Chao Guo ◽  
Lin Du ◽  
Tian-Jian Liu
Keyword(s):  
Spatial Distribution ◽  
Objective Function ◽  
Point Cloud ◽  
Point Clouds ◽  
Low Rank ◽  
Single Object ◽  
Loop Closure Detection ◽  
Global Registration ◽  
Distribution Features ◽  
Better Than

Global registration is an important step in the three-dimensional reconstruction of multi-view laser point clouds for moving objects, but the severe noise, density variation, and overlap ratio between multi-view laser point clouds present significant challenges to global registration. In this paper, a multi-view laser point cloud global registration method based on low-rank sparse decomposition is proposed. Firstly, the spatial distribution features of point clouds were extracted by spatial rasterization to realize loop-closure detection, and the corresponding weight matrix was established according to the similarities of spatial distribution features. The accuracy of adjacent registration transformation was evaluated, and the robustness of low-rank sparse matrix decomposition was enhanced. Then, the objective function that satisfies the global optimization condition was constructed, which prevented the solution space compression generated by the column-orthogonal hypothesis of the matrix. The objective function was solved by the Augmented Lagrange method, and the iterative termination condition was designed according to the prior conditions of single-object global registration. The simulation analysis shows that the proposed method was robust with a wide range of parameters, and the accuracy of loop-closure detection was over 90%. When the pairwise registration error was below 0.1 rad, the proposed method performed better than the three compared methods, and the global registration accuracy was better than 0.05 rad. Finally, the global registration results of real point cloud experiments further proved the validity and stability of the proposed method.

scholarly journals Assembly of a large earthquake from a complex fault system: Surface rupture kinematics of the 4 April 2010 El Mayor–Cucapah (Mexico) Mw 7.2 earthquake

Geosphere ◽  
2014 ◽  
Vol 10 (4) ◽  
pp. 797-827 ◽  
Author(s):  
John M. Fletcher ◽  
Orlando J. Teran ◽  
Thomas K. Rockwell ◽  
Michael E. Oskin ◽  
Kenneth W. Hudnut ◽  
...  
Keyword(s):  
Large Earthquake ◽  
Fault System ◽  
Surface Rupture ◽  
Complex Fault ◽  
Rupture Kinematics ◽  
Complex Fault System

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

scholarly journals Optimizing community detection in social networks using antlion and K-median

2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Amany A. Naem ◽  
Neveen I. Ghali
Keyword(s):  
Social Networks ◽  
Objective Function ◽  
Community Detection ◽  
Optimization Problem ◽  
Real Life ◽  
Optimization Methods ◽  
Population Based ◽  
Detection Problem ◽  
Network Communities ◽  
Antlion Optimization

Antlion Optimization (ALO) is one of the latest population based optimization methods that proved its good performance in a variety of applications. The ALO algorithm copies the hunting mechanism of antlions to ants in nature. Community detection in social networks is conclusive to understanding the concepts of the networks. Identifying network communities can be viewed as a problem of clustering a set of nodes into communities. k-median clustering is one of the popular techniques that has been applied in clustering. The problem of clustering network can be formalized as an optimization problem where a qualitatively objective function that captures the intuition of a cluster as a set of nodes with better in ternal connectivity than external connectivity is selected to be optimized. In this paper, a mixture antlion optimization and k-median for solving the community detection problem is proposed and named as K-median Modularity ALO. Experimental results which are applied on real life networks show the ability of the mixture antlion optimization and k-median to detect successfully an optimized community structure based on putting the modularity as an objective function.

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