EARTHQUAKE FOCAL MECHANISMS (FAULT PLANE SOLUTIONS)

EARTHQUAKE FOCAL MECHANISMS (FAULT PLANE SOLUTIONS)

  • Focal mechanisms: body wave radiation pattern

  • Focal mechanisms: stereographic fault plane representations

  • Fault plane solution

  • Use of polarities

  • Use of polarities and amplitude ratios

  • Regional moment tensor inversion using waveforms

  • Practical demonstration

Elastic rebound model

The elastic rebound model of earthquakes assumes that between earthquakes, material on the two sides of a fault undergoes relative motion. Because the fault is locked, features across it that were linear at the time (a), such as a fence, are slowly deformed with time (b). Finally, the strain becomes so great that the fault breaks in a earthquake, offsetting the features (time c).

A minority of faults break the surface; how is the orientation of the fault plane and the direction of slip determined if the fault does not break to the surface?

Focal mechanism parameters

  1. Strike: Direction of the fault

  2. Dip: inclination of the fualt

  3. Rake/slip: direction of motion

These parameters can be determined from earthquake data

Sandres Fault

The elastic rebound model of earthquakes assumes that between earthquakes, material on the two sides of a fault undergoes relative motion. Because the fault is locked, features across it that were linear at time (a), such as a fence, are slowly deformed with time (b). Finally the strain becomes so great that the fault breaks in an earthquake, offsetting the features (time c). (Courtesy of S. Wesnousky.)

Elastic rebound theory

Focal mechanisms

Fault geometry

To describe the geometry of a fault, we assume that the fault is a planar surface across which relative motion occurred during an earthquake.

Fault geometry used in earthquake studies. The fault plane, with normal vector 4, separates the lower, or foot wall, block from the upper hanging wall block (not shown). The slip vector, 2, describes the motion of the hanging wall block with respect to the foot wall block. The coordinate axes are chosen with x3 vertical and x1 oriented along the fault in the plane of the earth's surface, such that the fault dip angle, δ, measured from the −x2 axis, is less than 90°. The slip angle λ is easured between the x1 axis and 2 in the fault plane. φf is the strike of the fault measured clockwise from north. (After Kanamori and Cipar, 1974. Phys. Earth Planet. Inter., 9, 128–36, with permission from Elsevier Science.)

Basic types of faulting. Strike-slip motion can be either right- or left-lateral. Dip-slip faulting can occur as either reverse (thrust) or normal faulting. (Eakins, 1987.)

First motions of P waves observed at seismometers located in various directions about the earthquake provide information about the fault orientation. The two nodal planes separate regions of compressional and dilatational first arrivals. One nodal plane is the fault plane, and the other is the auxiliary plane, but these data cannot distinguish which is the actual fault plane.

The body wave radiation pattern for a double couple source has symmetry in the spherical coordinate system shown, corresponding to the axes in Fig. 4.2-5. θ is measured from the x3 axis, the normal to the fault (x1 −x2 ) plane, and φ is measured in the fault plane. The P-wave radiation pattern has four lobes that go to zero at the nodal planes, which are the fault and auxiliary (x2 −x3 ) planes. The S-wave radiation pattern describes a vector displacement that does not have nodal planes but is perpendicular to the P-wave nodal planes. S-wave motion converges toward the T axis, diverges from the P axis, and is zero on the null axis. (After Pearce, 1977, 1980.)

Radiation amplitude patterns of P and S waves in the x1 −x3 plane. a: Fault geometry, showing the symmetry of the double couple about the x2 axis. b: Radiation pattern for P waves, showing the amplitude (left) and direction (right). c: Same as (b), but for S waves.

The angle of incidence at the earthquake source is the angle from the vertical at which the ray leaves the source, and thus the angle at which the ray intersects the lower focal hemisphere.