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<doi>0704-cd</doi>
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<article-title>How Earthquake Risk Depends on the Closeness to a Fault: Symmetry-Based Geometric Analysis</article-title>
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<author>Aaron Velasco<sup>1,a</sup>, Solymar Ayala Cortez<sup>1,b</sup>, Olga Kosheleva<sup>2</sup> and Vladik Kreinovich<sup>3</sup></author>

<aff><sup>1</sup>Department of Geological Sciences, University of Texas at El Paso, USA</aff>

<email><a href="mailto:aavelasco@utep.edu"><sup>a</sup>aavelasco@utep.edu</a></email>

<email><a href="mailto:sayalacortez@miners.utep.edu"><sup>b</sup>sayalacortez@miners.utep.edu</a></email>

<aff><sup>2</sup>Department of Teacher Education, University of Texas at El Paso, USA</aff>

<email><a href="mailto:olgak@utep.edu">olgak@utep.edu</a></email>

<aff><sup>3</sup>Department of Computer Science, University of Texas at El Paso, USA</aff>

<email><a href="mailto:vladik@utep.edu">vladik@utep.edu</a></email>

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<title>ABSTRACT</title>
<p>Earthquakes can lead to a huge damage &#8211; and the big problem is that they are very difficult to predict. To be more precise, it is very difficult to predict the time of a future earthquake. However, we can estimate which earthquake locations are probable. In general, earthquakes are mostly concentrated around the corresponding faults. For some faults, all the earthquakes occur in a narrow vicinity of the fault, while for other faults, areas more distant from the fault are risky as well. To properly estimate the earthquake&#39;s risk, it is important to understand when this risk is limited to a narrow vicinity of a fault and when it not thus limited.<br/>
This problem has been thoroughly studied for the most well-studied fault in the world: San Andreas fault. This fault consists of somewhat different Northern and Southern parts. The Northern part is close to a straight line, and in this part, earthquake are mostly limited to a narrow vicinity of this line. In contrast, the Southern part is different: it is curved, and earthquakes can happen much further from the main fault. In this paper, we provide a general general explanation for this phenomenon. The existence of such a general explanations makes us expect that the same phenomenon will be observed at other not-so-well-studied faults as well.</p>
<p><italic>Keywords: </italic>Earthquake risk, Geometric approach, Geometric approach.</p>
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