<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:creator>A. Frankel</dc:creator>
  <dc:date>1991</dc:date>
  <dc:description>&lt;div class=""&gt;&lt;div class="article-section__content en main"&gt;&lt;p&gt;The high-frequency falloff ω&lt;sup&gt;−γ&lt;/sup&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;of earthquake displacement spectra and the&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;b&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;value of aftershock sequences are attributed to the character of spatially varying strength along fault zones. I assume that the high frequency energy of a main shock is produced by a self-similar distribution of subevents, where the number of subevents with radii greater than&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;R&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;is proportional to&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;R&lt;sup&gt;−D&lt;/sup&gt;&lt;/i&gt;,&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;D&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;being the fractal dimension. In this model, an earthquake is composed of a hierarchical set of smaller earthquakes. The static stress drop is parameterized to be proportional to&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;R&lt;/i&gt;&lt;sup&gt;η&lt;/sup&gt;, and strength is assumed to be proportional to static stress drop. I find that a distribution of subevents with&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;D&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;= 2 and stress drop independent of seismic moment (η = 0) produces a main shock with an ω&lt;sup&gt;−2&lt;/sup&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;falloff, if the subevent areas fill the rupture area of the main shock. By equating subevents to “islands” of high stress of a random, self-similar stress field on a fault, I relate&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;D&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;to the scaling of strength on a fault, such that&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;D&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;= 2 − η. Thus&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;D&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;= 2 corresponds to constant stress drop scaling (η = 0) and scale-invariant fault strength. A self-similar model of aftershock rupture zones on a fault is used to determine the relationship between the&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;b&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;value, the size distribution of aftershock rupture zones, and the scaling of strength on a fault. The&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;b&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;value for aftershock sequences on a fault is found to equal (3 − 1.5η)/(3 + η). Therefore this model indicates that the typically observed spectral falloffs of ω&lt;sup&gt;−2&lt;/sup&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;and&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;b&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;values of 1 can be entirely caused by scale-invariant strength (η = 0) along fault zones.&lt;/p&gt;&lt;/div&gt;&lt;/div&gt;</dc:description>
  <dc:format>application/pdf</dc:format>
  <dc:identifier>10.1029/91JB00237</dc:identifier>
  <dc:language>en</dc:language>
  <dc:publisher>American Geophysical Union</dc:publisher>
  <dc:title>High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults</dc:title>
  <dc:type>article</dc:type>
</oai_dc:dc>