reservoir geomecanics

159 Faults and fractures at depth
For simplicity, let us consider right-lateral slip on a vertical, east–west trending strike
slip fault at the surface of a half-space (Figure 5.11a). When the fault slips, P-waves
radiate outward with both positive and negative polarities that map onto symmetric
compressional and dilatational quadrants. The four lobes shown in the figure illustrate
the variation of wave amplitude with the direction of wave propagation relative to the
fault plane. Note that the P-wave amplitude is zero in the direction parallel and perpendicular
to the fault plane, such that these planes are referred to as nodal planes. If
there were seismometers distributed over the surface of this half space, the orientation
of the two nodal planes and the sense of motion on the planes could be determined
by mapping the polarity of the first arriving waves from the earthquake. Thus, in the
idealized case shown, data from a number of seismometers distributed on the surface
of the half space could be used to determine both the orientation of the fault plane and
the fact that right-lateral slip occurred on this plane. There is, however, a 90 ◦ ambiguity
in the orientation of the fault plane as left-lateral slip on a north–south trending fault
plane would produce exactly the same pattern of seismic radiation as right lateral slip on
an east–west striking plane. Thus, an earthquake focal plane mechanism contains two
orthogonal nodal planes, one of which is the fault plane and the other is referred to as
the auxiliary plane. In the absence of additional data (such as coincidence of the earthquake
hypocenter with the location of a mapped fault or the alignment of aftershocks
along the fault surface), it cannot be determined which of the two planes is the actual
fault.
Actual earthquakes are more complicated in several regards. First, they usually occur
at depth such that seismic radiation propagates outward in all directions; it also quite
common for faults to be dipping and, of course, strike-slip, reverse or normal fault slip
(or a combination of strike-slip with normal or strike-slip with reverse) could occur.
Figure 5.11b isacross-section illustrating the radiation pattern for a dipping normal
fault. By constructing an imaginary sphere around the hypocenter, we can portray
the radiation pattern on a lower-hemisphere stereographic projection (Figure 5.11c),
producing figures that look like beach balls where the compressional quadrants are
shaded dark and the dilatational quadrants are shown in white. Thus, for the case
illustrated in Figure 5.11c, we know from the dilatational arrivals in the center of the
figure that it was a normal faulting event. By definition, the P-axis bisects the dilatational
quadrant, the T-axis bisects the compressional quadrant and B-axis is orthogonal to
P and T. Inthis simple case, the orientation of the two nodal planes trend north–
south but knowing that the east dipping plane is the fault plane requires additional
information, as noted above. Of course, if the seismic waves are recorded on relatively
few seismographs, the planes of the focal mechanism will be poorly constrained, as will
the P- and T-axes. Nonetheless, as discussed in more detail in Chapter 9 (and illustrated
in the stress maps presented in Chapter 1), earthquake focal plane mechanisms prove
useful for determining both the style of faulting and approximate directions of the
principal stresses (see below).