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.

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 RiboA: a web application to identify ribosome A-site locations in ribosome profiling data

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Danying Shao ◽  
Nabeel Ahmed ◽  
Nishant Soni ◽  
Edward P. O’Brien
Keyword(s):  
Integer Programming ◽  
Web Application ◽  
Stop Codon ◽  
Ribosome Profiling ◽  
Programming Method ◽  
Analysis Tool ◽  
Site Location ◽  
Link Type ◽  
Wide Range ◽  
A Site

Abstract Background Translation is a fundamental process in gene expression. Ribosome profiling is a method that enables the study of transcriptome-wide translation. A fundamental, technical challenge in analyzing Ribo-Seq data is identifying the A-site location on ribosome-protected mRNA fragments. Identification of the A-site is essential as it is at this location on the ribosome where a codon is translated into an amino acid. Incorrect assignment of a read to the A-site can lead to lower signal-to-noise ratio and loss of correlations necessary to understand the molecular factors influencing translation. Therefore, an easy-to-use and accurate analysis tool is needed to accurately identify the A-site locations. Results We present RiboA, a web application that identifies the most accurate A-site location on a ribosome-protected mRNA fragment and generates the A-site read density profiles. It uses an Integer Programming method that reflects the biological fact that the A-site of actively translating ribosomes is generally located between the second codon and stop codon of a transcript, and utilizes a wide range of mRNA fragment sizes in and around the coding sequence (CDS). The web application is containerized with Docker, and it can be easily ported across platforms. Conclusions The Integer Programming method that RiboA utilizes is the most accurate in identifying the A-site on Ribo-Seq mRNA fragments compared to other methods. RiboA makes it easier for the community to use this method via a user-friendly and portable web application. In addition, RiboA supports reproducible analyses by tracking all the input datasets and parameters, and it provides enhanced visualization to facilitate scientific exploration. RiboA is available as a web service at https://a-site.vmhost.psu.edu/. The code is publicly available at https://github.com/obrien-lab/aip_web_docker under the MIT license.

scholarly journals Development of an inversion method to extract information on fault geometry from teleseismic data

2019 ◽  
Vol 220 (2) ◽  
pp. 1055-1065 ◽  
Author(s):  
Kousuke Shimizu ◽  
Yuji Yagi ◽  
Ryo Okuwaki ◽  
Yukitoshi Fukahata
Keyword(s):  
Fault Plane ◽  
Slip Rate ◽  
Rate Function ◽  
Fault Slip ◽  
Body Waves ◽  
Fault System ◽  
Inversion Method ◽  
Fault Geometry ◽  
Finite Fault ◽  
Extract Information

SUMMARY Teleseismic waveforms contain information on fault slip evolution during an earthquake, as well as on the fault geometry. A linear finite-fault inversion method is a tool for solving the slip-rate function distribution under an assumption of fault geometry as a single or multiple-fault-plane model. An inappropriate assumption of fault geometry would tend to distort the solution due to Green’s function modelling errors. We developed a new inversion method to extract information on fault geometry along with the slip-rate function from observed teleseismic waveforms. In this method, as in most previous studies, we assumed a flat fault plane, but we allowed arbitrary directions of slip not necessarily parallel to the assumed fault plane. More precisely, the method represents fault slip on the assumed fault by the superposition of five basis components of potency-density tensor, which can express arbitrary fault slip that occurs underground. We tested the developed method by applying it to real teleseismic P waveforms of the MW 7.7 2013 Balochistan, Pakistan, earthquake, which is thought to have occurred along a curved fault system. The obtained spatiotemporal distribution of potency-density tensors showed that the focal mechanism at each source knot was dominated by a strike-slip component with successive strike angle rotation from 205° to 240° as the rupture propagated unilaterally towards the south-west from the epicentre. This result is consistent with Earth’s surface deformation observed in optical satellite images. The success of the developed method is attributable to the fact that teleseismic body waves are not very sensitive to the spatial location of fault slip, whereas they are very sensitive to the direction of fault slip. The method may be a powerful tool to extract information on fault geometry along with the slip-rate function without requiring detailed assumptions about fault geometry.

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