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214   PASSIVE SEISMIC METHODS FOR UNCONVENTIONAL RESOURCE DEVELOPMENT

            A focal mechanism solution, or simply focal mechanism,   of a focal mechanism solution are often treated as approxima­
            is a description of the orientation (strike and dip) of the   tions of the orientations of Smax, Sint, and Smin (respectively).
            fault plane that slipped during an earthquake and the slip   If this assumption is made, then the nodal planes of the solution
            direction and slip sense of the fault and of the strain   are  the planes  of maximum shear stress.  These planes may
              produced by the earthquake. The term fault plane solution   seem to appear to be likely orientations for new faults to form.
            is  a  synonym. The  moment tensor of an earthquake   However,
            is  a  complete mathematical description of the earth­
            quake  movement. The  moment tensor is defined as “A      • The angle between the two nodal planes is 90° so that
            mathematical representation of the movement on a fault   the angle between the nodal planes and the P axis is 45°.
            during an earthquake, comprised of nine generalized cou­    • In nature the angle between conjugate fault planes in
            ples, or nine sets of two vectors. The tensor depends on the   most rock types is about 60°, so that the angle between
            source strength and fault orientation” (U.S.  Geological   the fault planes and Smax is about 30°. This occurs
            Survey;  http://earthquake.usgs.gov/learn/glossary/). The   because of internal friction in the rock.
            focal mechanism solution is a subset of the moment tensor
            if it represents only one component of the full moment   Clearly the P and T axes cannot be equivalent to Smax and
            tensor. Often, the focal mechanism solution considers   Smin for newly formed faults.
            only the simple DC shear component of the earthquake   We define the transport plane of a fault as the plane that
            source; the moment tensor includes volumetric and other   contains the following:
            components as well. The details of earthquake mechanics
            are beyond the scope of this chapter.  Thorough discus­    • The P and T axes of the earthquake produced by the slip
            sions of moment tensors are provided by Jost and         event,
            Herrmann (1989) and Stein and Wysession (2002). Full      • The slip line of the fault,
            moment tensors are not a common deliverable for           • Smax and Smin (this assumes a uniaxial stress state).
            hydraulic fracture monitoring studies, although very
            detailed studies may provide full moment tensors for   These relationships are shown in Figure 10.6. The drawings
            some MEQs.                                           show the maximum stress axis within the transport plane of
              A DC focal mechanism solution is described completely
            by either:                                           a slipping fault under uniaxial stress conditions. The angle
                                                                 between Smax and the fault plane is approximately equal to
                                                                 or sometimes less than 30° for newly formed faults. For
                 • The 3D orientation of one of the two possible fault planes   older, reactivated fractures the angle is dependent on the
                that produced the earthquake and the slip direction of the
                hangingwall of the fault. (The hangingwall is the fault
                block above the fault plane.) Only one fault plane needs
                to be described because the other plane is perpendicular   P           T
                to it and has the conjugate slip direction and slip sense.                 P               T
                 • Two of the three principal strain axes, which are                           E       C
                mutually  orthogonal.  These  are  P  (contractional),  N   F
                (neutral, also called B), and T (extensional). Generally,                            N
                the P and T axes are provided.                                                  C       E
                                                                                           T               P
            Because the seismic radiation pattern of a slip event is sym­
            metrical, a focal mechanism solution yields two possible   FIGURE 10.3  TOP—Schematic diagram showing the direction
            fault plane solutions that cannot be distinguished from each   of initial movement for particles around the focus (F) of an earth­
            other, as shown and described in Figure 10.3. Note that the   quake on an E‐W dextral wrench fault (gray), viewed from above.
            pattern of polarities of first arrivals on any plane or line, such   The particle motion is symmetrical, so based only on the particle
            as the ground surface or a wellbore, does not reveal which   motion either the blue line or the orthogonal black line could be
            nodal plane is the fault plane and which is the auxiliary plane   the fault. (Lacazette after U.S.G.S.). The P and T axes are shown.
            (Fig. 10.4). Beach‐ball diagrams of the focal mechanisms   The neutral particle motion axis is perpendicular to the P and T
            for each basic fault type are shown in Figure 10.5.  axes so it plots at the center of the diagram and is not shown. Some
                                                                 workers associate the P‐ and  T‐axes with the principal stresses
                                                                 Smax and Smin, although this a poor assumption. BOTTOM—A
            10.3.2.2  Relationship between Stress and Focal Mechanism   beach‐ball plot showing the zones of compressional (C) and exten­
            Solutions  Focal mechanisms constrain but do not uniquely   sional (E) first motion in the seismic waves radiating outwards. The
            determine the principal stress orientations. The P, N, and T axes   diagram also shows where the P, T, and N axes plot.
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