0 0.2 0.4
0 0.2 0.4 0.6 0.8 1
(sn - Pp)/Sv t/Sv
N a .
b .
m = 0 . 6 m = 1 . 0
Figure 5.10. (a) Stereographic representation of fault data detected through wellbore image analysis in highly fractured granitic rock encountered in the Cajon Pass research well from 1750 to 3500 m depth (after Barton and Zoback1992). (b) Representation of the same data utilizing a three-dimensional Mohr diagram normalized by the vertical stress. While many fractures appear to be critically stressed, most are not and thus reflect the rock’s geologic history (after Barton, Zoback et al.1995).
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 per- pendicular 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 earth- quake 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 is a cross-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. In this 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).
View from Side View from Above
“Beach Ball”
Depth
E A RT H ’ S S U R FA C E FA U LT
P L A N E
Fault-plane pro
jecti F O C A L S P H E R E on Auxiliary
plane
F a u l t p l a n e A u x i l i a r y
p l a n e c .
Double-Couple Model
a .
b .
F a u l t p l a n e
A u x i l i a r y p l a n e
P T
Figure 5.11. (a) Schematic illustration of the radiation pattern and force-couple associated with earthquakes as the basis earthquake focal plane mechanisms. An east–west striking, vertical right-lateral strike slip fault intersecting a half space is shown. The polarity of the P-waves defines the compressional and dilatational quadrants. (b) Cross-sectional view of the nodal planes, radiation pattern and P- and T-axes associated with an east-dipping normal fault. The radiation pattern does not uniquely distinguish the fault plane from the auxiliary plane. (c) Lower hemisphere stereonet representation of the normal faulting focal mechanism.
Earthquake focal mechanisms associated with normal, strike slip and reverse faults are illustrated in Figure 5.1. Note that while the conjugate shear faults are at angles
±30◦on either side of the maximum principal stress, the focal mechanism illustrates orthogonal nodal planes, one of which is the fault. As a point of historical interest, focal plane mechanisms were instrumental in establishing the theory of plate tectonics as they
illustrated that extensional normal faulting was occurring along mid-ocean spreading centers and the appropriate sense of lateral slip occurred on transform faults (see the review by Stein and Klosko 2002).
With respect to the orientation of in situ stress, the advantages of utilizing well- constrained earthquake focal plane mechanisms to map the stress field are fairly obvious: earthquakes record stress-induced deformation at mid-crustal depths, they sample relatively large volumes of rock and, due to the continued improvement of regional and global networks, more well-constrained focal mechanisms for mapping the stress field are available now than ever before. However, it is important to keep in mind that focal plane mechanisms record deformation and not stress. The P- and T-axes shown in Figure 5.11 are, by definition, the bisectors of the dilatational and compressional quadrants of the focal mechanism. Thus, they are not the maxi- mum and minimum principal stress directions (as is sometimes assumed) but are the compressional and extensional strain directions for slip on either of the two possible faults. As most crustal earthquakes appear to occur on pre-existing faults (rather than resulting from new fault breaks), the slip vector is a function both of the orientation of the fault and the orientation and relative magnitude of the principal stresses, and the P- and T-axes of the focal plane mechanism do not correlate directly with principal stress directions. In an attempt to rectify this problem, Raleigh, Healy et al. (1972) showed that if the nodal plane of the focal mechanism corresponding to the fault is known, it is preferable not to use the P-axes of the focal-plane mechanism but instead to assume an angle between the maximum horizontal stress and the fault plane defined by the coefficient of friction of the rock. Because the coefficient of friction of many rocks is often about 0.6, Raleigh, Healy et al. (1972) suggested that the expected angle between the fault plane and the direction of maximum principal stress would be expected to be about 30◦. Unfortunately, for intraplate earthquakes (those of most interest here), we usually do not know which focal plane corresponds to the fault plane. Nevertheless, in most intraplate areas, P-axes from well-constrained focal plane mechanisms do seem to represent a reasonable approximation of the maximum horizontal stress direction, apparently because intraplate earthquakes do not seem to occur on faults with extremely low friction (Zoback and Zoback 1980, 1989; Zoback, Zoback et al. 1989) and give an indication of relative stress magnitude (normal, strike-slip or reverse faulting). This will be discussed in more detail in Chapter 9.
As mentioned in Chapter 1, if the coefficient of friction of the fault is quite low, the direction of maximum compression can be anywhere in the dilatational quadrant and the P-axis can differ from the true maximum stress direction by as much as 45◦ (MacKenzie 1969). In fact, studies such as Zoback, Zoback et al. (1987) excluded as tectonic stress indicators right-lateral strike-slip focal plane mechanisms right on the San Andreas fault as did subsequent stress compilations at global scale as discussed in Chapter 9. In the case of the San Andreas, appreciable heat flow data collected in the vicinity of the San Andreas show no evidence of frictionally generated heat
A
D
C B
5 0 k m
A r e a o f F i g u r e 5 - 8
Figure 5.12. Stress map (direction of SHmax) of western California in the Point Arguello area (after Finkbeiner, Barton et al.1997). Earthquake focal mechanisms within the rectangle were inverted using the technique of Gephart (1990) to obtain a direction of SHmaxshown by the heavy arrow. The SHmaxdirection from wellbore breakouts studied with wellbore image data is shown for wells A–D discussed in the text. The P-axes of reverse faulting focal mechanisms are shown by the lines with a dot in the center. AAPGC 1997 reprinted by permission of the AAPG whose permission is required for futher use.
(Lachenbruch and Sass 1992) and appears to limit average shear stresses acting on the fault to depths of∼15 km to about 20 MPa, approximately a factor of 5 below the stress levels predicted by the Coulomb criterion assuming that hydrostatic pore pressure at depth and the applicability of laboratory-derived friction coefficients of∼0.6. Stress orientation data near the San Andreas fault also imply low resolved shear stresses on the fault at depth (Mount and Suppe 1987; Zoback, Zoback et al. 1987; Hickman 1991;
Lachenbruch and Sass 1992; Townend and Zoback 2001; Hickman and Zoback 2004;
Boness and Zoback 2006).
To optimize the use of focal plane mechanism data for determining stress orientations it is necessary to consider multiple events in a given region and use either the average P-axis direction as the maximum horizontal stress direction or, preferably, to formally invert a group of focal-plane mechanisms to determine the orientation and relative
magnitude of the principal stress tensor (see Angelier 1979; Angelier 1984; Gephart and Forsyth 1984; Gephart 1990; Michael 1987).
Figure 5.12 is a map showing SHmax directions in the area shown in Figure 5.8.
The lines with inward pointed arrows are derived from wellbore breakouts (Chapters 6 and 9) and those with a circle in the middle show the P-axis of reverse-faulting focal plane mechanisms. For slip on pure reverse faults, the horizontal projection of the P- axis is quite similar to the SHmaxdirection because the projection of the P-axis onto a horizontal plane will be the same as the SHmaxdirection regardless of either the choice of nodal plane or the coefficient of friction of the fault. The SHmaxdirection shown by the heavy arrows was obtained from inversion of earthquake focal plane mechanisms in the area enclosed by the rectangle (Finkbeiner 1998). Note that this direction compares quite well with the stress orientations obtained from wells A–D, wellbore breakouts in other wells and individual earthquake focal plane mechanisms. Because the majority of earthquakes in this region are reverse faulting events, the direction of SHmaxis not greatly affected by uncertainties in knowing either the coefficient of friction of the fault or which nodal plane in the focal mechanism is the fault and which is the auxiliary plane.