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zmap a tool for analyses of seismicity patterns typical applications ...

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#define VARIANCE_30 30<br />

change to:<br />

#define VARIANCE_30 90<br />

and re-compile (cc -o msiWindow_1 msiWindow_1.c)<br />

The cumulative misfit method<br />

Stress tensor inversions are time consuming, and the resulting tensor is not easily<br />

visualized. To identify crustal volumes that satisfy one homogeneous stress tensor Lu and<br />

Wyss (1995) and Wyss and Lu (1995) introduced the cumulative misfit method. The<br />

misfit, f, <strong>for</strong> each individual earthquake can be summed up in a number <strong>of</strong> different ways,<br />

<strong>for</strong> example along the strike <strong>of</strong> a fault or plate boundary. If the stress direction along<br />

strike is uni<strong>for</strong>ms within segments, but different from other segments, the cumulative<br />

misfit will show constant, but different slope <strong>for</strong> each segment (Figure 84). We can<br />

also study the cumulative misfit as a function <strong>of</strong> latitude, depth, time, or magnitude, and<br />

try to identify segments with constant but different slope.<br />

ZMAP allows taking the cumulative misfit method one step further: A grid (in map view<br />

or cross-section) is used, and the average misfit <strong>of</strong> the n closest earthquakes in<br />

an Euclidean sense is calculated. The distribution <strong>of</strong> this average misfit can be displayed<br />

using a color representation. Maps <strong>of</strong> this type, calculated <strong>for</strong> a number <strong>of</strong> different<br />

assumed homogeneous stress tensor can identify homogeneous volumes, which then can<br />

be inverted using the stress tensor inversion method described earlier.<br />

Figure 5.9. Schematic explanation <strong>of</strong> the cumulative misfit method. Changes in the slop <strong>of</strong> the cumulative<br />

misfit curve (blue) indicate a change in the stress regime. Figure courtesy <strong>of</strong> Zhong Lu<br />

49

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