Ambiguity in focal mechanism solutions

It is apparent from Fig. 2.7 that the same distribution of compressional and dilational quadrants would be obtained if either nodal plane represented the actual fault plane. Thus, the same pattern of first motions would be obtained for sinistral motion along a north-south plane as for dextral motion along an east-west plane.

Earthquake Focal Mechanics Solution

Figure 2.8 Ambiguity in the focal mechanism solution of a thrust fault. Shaded areas represent regions of compressional first motions (C), unshaded areas represent regions of dilational first motions (D), f refers to a fault plane, ap to an auxiliary plane. Changing the nature of the nodal planes as in (a) and (c) does not alter the pattern of first motions shown in (b), the projection of the lower hemisphere of the focal sphere.

Figure 2.8 Ambiguity in the focal mechanism solution of a thrust fault. Shaded areas represent regions of compressional first motions (C), unshaded areas represent regions of dilational first motions (D), f refers to a fault plane, ap to an auxiliary plane. Changing the nature of the nodal planes as in (a) and (c) does not alter the pattern of first motions shown in (b), the projection of the lower hemisphere of the focal sphere.

In Fig. 2.8a an earthquake has occurred as a result of faulting along a westerly dipping thrust plane fj. fj and its associated auxiliary plane apj divide the region around the focus into quadrants which experience either compression or dilation as a result of the fault movement. The directions in which compressional first motions Cj and C2 and dilational first motions Dj and D2 leave the focus are shown., and C2 and D2 are plotted on the projection of the focal sphere in Fig. 2.8b, on which the two nodal planes are also shown. Because Fig. 2.8a is a vertical section, the first motions indicated plot along an east-west azimuth. Arrivals at stations at other azimuths would occupy other locations within the projection space. Consider now Fig. 2.8c, in which plane apj becomes the fault plane f2 and fj the auxiliary plane ap2. By considering the movement along the thrust plane it is obvious that the same regions around the fault are compressed or dilated, so that an identical

Focal Mechanism

focal sphere projection is obtained. Similar results are obtained when the faulting is normal (Fig. 2.9). In theory the fault plane can be distinguished by making use of Anderson's simple theory of faulting (Section 2.10.2) which predicts that normal faults have dips of more than 45° and thrusts less than 45°. Thus, f1 is the fault plane in Fig. 2.8 and f2 the fault plane in Fig. 2.9.

It is apparent that the different types of faulting can be identified in a focal mechanism solution by the distinctive pattern of compressional and dilational regions on the resulting focal sphere. Indeed, it is also possible to differentiate earthquakes that have originated by a combination of fault types, such as dip-slip accompanied by some strike-slip movement. The precision with which the directions of the nodal planes can be determined is

Earthquake Source Mechanism
Figure 2.10 (a) P wave radiation pattern for a type I and type II earthquake source mechanism; (b) S wave radiation pattern from a type I source (single couple); (c) S wave radiation pattern from a type II source (double couple).

dependent upon the number and distribution of stations recording arrivals from the event. It is not possible, however, to distinguish the fault and auxiliary planes.

At one time it was believed that distinction between the nodal planes could be made on the basis of the pattern of S wave arrivals. P waves radiate into all four quadrants of the source region as shown in Fig. 2.10a. However, for this simple model, which is known as a type I, or single-couple source, S waves, whose corresponding ground motion is shearing, should be restricted to the region of the auxiliary plane (Fig. 2.10b). Recording of the S wave radiation pattern should then make it possible to determine the actual fault plane. It was found, however, that instead of this simple pattern, most earthquakes produce S wave radiation along the direction of both nodal planes (Fig. 2.10c). This observation initially cast into doubt the validity of the elastic rebound theory. It is now realized, however, that faulting occurs at an angle, typically rather less than 45% to the maximum compressive stress, G1, and the bisectors of the dilational and compressional quadrants, termed P and T, respectively, approximate to the directions of maximum and minimum principal compressive stress, thus giving an indication of the stress field giving rise to the earthquake (Fig. 2.10c) (Section 2.10.2).

This type II, or double-couple source mechanism gives rise to a four-lobed S wave radiation pattern (Fig. 2.10c) which cannot be used to resolve the ambiguity of a focal mechanism solution. Generally, the only constraint on the identity of the fault plane comes from a consideration of the local geology in the region of the earthquake.

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Responses

  • selassie
    How can you identity fault plane?
    2 years ago

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