CroninProjects.org/ FocalMechanism.html |
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This is a page stub created on April 5, 2016, that will be populated with additional information during the coming month.

A primer on focal mechanisms for structural geologists, most recent edition (.pdf file, 4.3 MB)

- (in progress)

- (in progress)

Frank Scherbaum, Nicolas Kuehn, and Björn Zimmermann have written an interactive ap to make focal mechanism diagrams and computer the other nodal plane, given the strike, dip angle, and rake (slip angle) of one nodal plane. That free ap is available via http://demonstrations.wolfram.com/EarthquakeFocalMechanism/
It runs on virtually any conventional platform, using the free Wolfram CDF player, which is available via http://demonstrations.wolfram.com/download-cdf-player.html

I am interested in identifying seismogenic faults, and have found that a rather direct way of finding faults that produce earthquakes is to start with earthquake data and work backward from there. My students and I have developed the Seismo-Lineament Analysis Method (SLAM) to use data from earthquake focal mechanism solutions to predict where the ground-surface trace of seismogenic faults can be located. More on SLAM is available via http://croninprojects.org/Vince/SLAM/index.htm.

**auxiliary plane** The N axis is along the auxillary plane, and the fault is perpendicular to the auxillary plane. The auxillary plane is orthogonal to the two force couples (*i.e.*, either perpendicular or parallel to the force couples).

**beachball diagram** Lower-hemisphere equal-area stereographic projection of a focal-mechanism solution, including the two nodal planes separating opposite quadrants that are generally filled either with black (compressional quadrants in which p-wave first motion is up) or white (dilatational quadrants in which p-wave first motion is down).

**force couple** A non-zero component of a force field containing the derivative of a Dirac delta function, which can be visualized as two parallel vectors of equal magnitude but different directions acting at a short distance from one another.

**double couple** This is the simplest force condition that explains or reproduces the observed energy radiation pattern observed in earthquakes generated by fault slip. A double couple includes two force couples at right angles (90°) to each other acting at a short distance from one another.

**hanging wall** The block that is above an inclined fault surface, as contrasted with the foot wall that exists below the fault surface. The hanging wall "rests" on the foot wall. By convention, slip vectors in focal mechanism solutions reflect the motion of the hanging wall relative to the footwall.

**epicenter** The location of the point on Earth’s surface that is directly (*i.e.*, vertically) above the focus of an earthquake.

**fault plane** Surface or zone across which there is shear displacement; in this application, the fault is an assumed-planar surface containing the earthquake focus. The fault plane is a nodal plane. The N axis is in/along the fault plane. The slip vector is in the fault plane, perpendicular to the N axis.

**focal sphere** Imaginary small projection sphere that is centered on the earthquake focus.

**focus** The best mean solution for the point of origin of an earthquake, and includes the earthquake depth and the longitude and latitude of the point vertically above the focus (*i.e.*, the location of the epicenter).

**N-axis** The so-called "null" axis, the N-axis is one of the principal axes of the moment tensor. The orientation of the N-axis coincides with the orientation of one of the eigenvectors of the moment tensor — the eigenvector with the intermediate eigenvalue between that of the P and T axes. A seismograph that lies along a ray path through the N axis will not record a discernable signal from the earthquake at the expected arrival time. The N axis is along the intersection of the two nodal planes, and is orthogonal to (*i.e.*, 90° from) both the P and T axes.

**nodal plane** Each nodal plane is parallel to one of the two force couples centered on the earthquake focus, and perpendicular to the other force couple. One of the nodal planes is coincident with the fault surface, and the other is coincident with the auxiliary plane. A seismograph that lies along a ray path along one of the nodal planes will not record a discernable signal from the earthquake at the expected arrival time.

**P-axis** The so-called "pressure" or compressional axis, the P-axis is one of the principal axes of the moment tensor. The orientation of the P-axis coincides with the orientation of one of the eigenvectors of the moment tensor — the eigenvector with the smallest eigenvalue (*i.e.*, a negative value). A P-wave traveling along a ray path through the P axis will produce the largest amplitude negative (down) first motion as recorded on a distant seismograph, normalized for travel distance. The P axis bisects the dihedral angle between the two nodal planes, and is orthogonal to (*i.e.*, 90° from) both the N and T axes.

**rake** Angle measured in the plane of the fault between the reference strike (right-hand rule) and the slip vector. Vectors with a positive rake point above the strike line; vectors with a negative rake are directed downward, below the strike line.

**reference strike** or **right-hand-rule strike** The strike of a given inclined plane is the azimuth of a horizontal line contained within that plane. But since a horizontal line may be characterized by either of two azimuths, each 180° from the other, it is necessary to differentiate between these two azimuths to define one of the two directions as the reference strike. Hence, the reference strike is identified through a 90° anti-clockwise (right-handed) rotation from the dip vector. For example, the reference strike for an east-dipping plane is toward the north; for a northwest-dipping plane, the reference strike is toward the southwest. Put another way, if the trend of the dip vector is θ°, the azimuth of the reference strike is θ°—90°.

**slip vector** By convention among those who use focal mechanism solutions, the slip vector represents the direction of motion of the hanging wall relative to the foot wall. The slip vector is always contained within the fault plane (*i.e.*, the point that represents the slip vector lies along the trace of the fault plane on a stereographic plot or beachball diagram).

**T-axis** The so-called "tension" axis, the T-axis is one of the principal axes of the moment tensor. The orientation of the T-axis coincides with the orientation of one of the eigenvectors of the moment tensor — the eigenvector with the largest eigenvalue. A P-wave traveling along a ray path through the T axis will produce the largest amplitude positive (up) first motion as recorded on a distant seismograph, normalized for travel distance. The T axis bisects the dihedral angle between the two nodal planes, and is orthogonal to (*i.e.*, 90° from) both the N and P axes.

**take-off angle** The angle, measured from a vertical line extending down from an earthquake focus, that a particular ray path takes as it leaves the focus.

Brumbaugh, D.S., 1999, Earthquakes science and society: Upper Saddle River, New Jersey, Prentice-Hall, 251 p. *A very clear elementary text whose Chapter 5 deals with FMS.*

Bullen, K.E., and Bolt, B.A., 1985, An introduction to the theory of seismology: Cambridge, Cambridge University Press, 499 p. *A standard seismology textbook whose Chapter 16 provides a technical description of matters related to modeling the earthquake source.*

Cronin, V.S., and Sverdrup, K.A., 2003a, Multiple-event relocation of historic earthquakes along Blanco Transform Fault Zone, NE Pacific, Geophysical Research Letters, v. 30(19), 2001, doi:10.1029/2003GL018086. *Example of use of relocated earthquake data and FMSs to address a problem in structure/tectonics.*

Cronin, V.S., and Sverdrup, K.A., 2003b, Defining static correction for jointly relocated earthquakes along the Blanco Transform Fault Zone based on SOSUS hydrophone data: Oceans 2003 MTS/IEEE Conference Proceedings (ISBN 0-933957-30-9), p. P2721-2726. *Example of use of relocated earthquake data and FMSs to address a problem in structure/tectonics.*

Cronin, V.S., and Sverdrup, K.A., 1998, Preliminary assessment of the seismicity of the Malibu Coast Fault Zone, southern California, and related issues of philosophy and practice, *in* Welby, C.W., and Gowan, M.E. [editors], A Paradox of Power--Voices of Warning and Reason in the Geosciences: Geological Society of America, Reviews in Engineering Geology, p. 123-155. *Contains an earthquake dataset for most of the Malibu area that includes 638 events, with 107 FMSs. FMS data reported as fault dip azimuth, fault dip angle, and azimuth of inferred slip vector. The FMS data indicate that the average hanging-wall slip vector for Malibu earthquakes is nearly perpendicular to the San Andreas fault through the Transverse Ranges.*

Cronin, V.S., Millard, M.A., Seidman, L.E., and Bayliss, B.G., 2008, The Seismo-Lineament Analysis Method [SLAM] -- A reconnaissance tool to help find seismogenic faults: Environmental and Engineering Geoscience, v. 14, no. 3, p. 199-219. *Describes how the nodal planes from a focal mechanism solution can be projected to the ground surface, as represented by a hillshade map created using a digital elevation model, so that the resulting seismo-lineaments can be compared with the ground-surface trace of faults.*

Dziewonski, A.M., and Woodhouse, J.H., 1983, An experiment in the systematic study of global seismicity — centroid-moment tensor solutions for 201 moderate and large earthquakes of 1981: Journal of Geophysical Research, v. 88, p. 3247-3271. *Provides a technical explanation of CMT solutions with examples.*

Dziewonski, A.M., and Woodhouse, J.H., 1983, Studies of the seismic source using normal-mode theory, *in* Kanamori, H., and Boschi, E., eds., Earthquakes — observation, theory, and interpretation — notes from the international school of physics "Enrico Fermi" (Varenna, Italy, 1982): Amsterdam, North-Holland Publishing Company, p. 45-137. *Provides the most complete technical explanation of CMT solutions with examples.*

Dziewonski, A.M., Chou, T.-A., and Woodhouse, J.H., 1981, Determination of earthquake source parameters from waveform data for studies of global and regional seismicity: Journal of Geophysical Research, v. 86, p. 2825-2852. *Provides a technical explanation of CMT solutions with examples.*

Ekström, G., 1994, Rapid earthquake analysis utilizes the internet: Computers in Physics, v. 8, p. 632-638.

Friedman, M., 1964, Petrofabric techniques for the determination of principal stress directions in rocks, *in* Judd, W.R., ed., State of stress in the Earth’s crust: New York, American Elsevier Publishing Company, p. 451-552. *This is Mel Friedman’s classic description of basic petrofabric techniques, including the use of lower-hemisphere stereographic projections. This was the authority cited in Lynn Sykes’ paper on transform fault seismicity (Sykes, 1967).*

Gubbins, D., 1990, Seismology and plate tectonics: Cambridge, Cambridge University Press, 339 p.

Hardebeck, J. L., and Shearer, P.M., 2002, A new method for determining first-motion focal mechanisms: Bulletin of the Seismological Society of America, v. 92, p. 2264-2276. *The title says it all. This is a description of the HASH methodology.*

Hauksson, E., 1990, Earthquakes, faulting, and stress in the Los Angeles Basin: Journal of Geophysical Research, v. 95, no. B10, p. 15,365-15,394. *This is an excellent paper that sought to associate the regional seismicity of southern California with active fault trends. A significant number of FMSs are utilized with first-motion data represented on beach-ball diagrams. FMSs are tabulated using the dip azimuth and dip angle of the inferred fault plane and the rake of the hanging-wall slip vector.*

Hodgson, J.H., and Allen, J.F.J., 1954, Tables of extended distances for PKP and PcP: Pub. Dominion Obs. Ottawa, v. 16, p. 329-348.

Hodgson, J.H., and Storey, R.S., 1953, Tables extending Byerly’s fault-plane technique to earthquakes of any focal depth: Bulletin of the Seismological Society of America, v. 43, p. 49-61.

Jost, M.L. and Herrmann, R.B., 1989, A student's guide to and review of moment tensors: Seismology Research Letters, v. 60, p. 37-57. *This is a tutorial concerning focal mechanism solutions for students.*

Kasahara, K., 1981, Earthquake mechanics: Cambridge, Cambridge University Press, 248 p. *A particularly good technical discussion of earthquake mechanics, apparently meant for student seismologists.*

Lay, T., and Wallace, T.C., 1995, Modern global seismology: San Diego, Academic Press, 521 p. *Chapter 8 concerns seismic sources, and contains a clear exposition of material related to focal mechanism solutions.*

Lliboutry, L, 2000, Quantitative geophysics and geology: Chichester, UK, Praxis Publishing and Springer, 480 p.

Marrett, R., and Allmendinger, R.W., 1990, Kinematic analysis of fault-slip data: Journal of Structural Geology, v. 12, no. 8, p. 973-986.

Menke, W., and Abbott, D., 1990, Geophysical theory, New York, Columbia University Press, 458 p. *A good general geophysics textbook, but the treatment of FMSs is rather short.*

Pujol, J., 2003, Elastic wave propagation and generation in seismology: Cambridge, Cambridge University Press, 444 p. *Chapter 10 of this book concerns source mechanics and presents some interesting information about radiation patterns and the instantaneous motion of particles on the focal sphere.*

Reasenberg, P.A., and Oppenheimer, D., 1985, FPFIT, FPPLOT and FPPAGE -- Fortran computer programs for calculating and displaying earthquake fault-plane solutions: U.S. Geological Survey, Open-File Report No. 85-739, 25 p.. *These software applications provide a standard way of computing fault-plane solutions using P-wave first arrivals.*

Reiter, L., 1990, Earthquake hazard analysis, issues and insights: New York, Columbia University Press, 254 p.

Shearer, P.M., 1999, Introduction to seismology: Cambridge, Cambridge University Press, 260 p. *A particularly good recent textbook on introductory seismology.*

Sipkin, S.A., 1994, Rapid determination of global moment-tensor solutions: Geophysical Research Letters, v. 21, p. 1667-1670. *This paper provides a description of the method used by the USGS to rapidly define focal mechanism solutions.*

Sipkin, S.A., 1986, Interpretation of non-double-couple earthquake mechanisms derived from moment tensor inversion: Journal of Geophysical Research, v. 91, p. 531-547. *This paper provides a description of the method used by the USGS to rapidly define focal mechanism solutions.*

Sipkin, S.A., 1982, Estimation of earthquake source parameters by the inversion of waveform data: Synthetic waveforms: Physics of Earth and Planetary Interiors, v. 30, p. 242-259. *This paper introduces and provides the basic description of an automated method for determining focal mechanism solutions using comparisons with synthetic waveforms.*

Stein, S. and Wysession, M, 2003, An introduction to seismology, earthquakes and Earth structure: Malden, Massachusetts, Blackwell Publishing, 498 p. *Chapter 4 includes a clear and rather comprehensive summary of focal mechanism solutions.*

Stüwe, K., 2002, Geodynamics of the lithosphere: Berlin, Springer, 449 p.

Sverdrup, K.A., Schurter, G.J., and Cronin, V.S., 1994, Relocation analysis of earthquakes near Nanga Parbat-Haramosh Massif, northwest Himalaya, Pakistan: Geophysical Research Letters, v. 21, p. 2331-2334.

Sykes, L., 1967, Mechanism of earthquakes and nature of faulting on the mid-ocean ridges: Journal of Geophysical Research, v. 72, p. 2131-2153. *The classic paper that demonstrated that the transform fault model proposed by Tuzo Wilson is correct. This paper also provides a good description of how focal mechanism solutions can be derived manually, with examples of beachball diagrams that include the first-motion data.*
U.S. Geological Survey, Focal mechanisms: http://quake.wr.usgs.gov/recenteqs/beachball.html *A very brief, qualitative description of FMSs for the general public.*

Woodhouse, J.H., and Dziewonski, A.M., 1984, Mapping the upper mantle — three dimensional modeling of Earth structure by inversion of seismic waveforms: Journal of Geophysical Research, v. 89, p. 5953-5986. *Provides a technical explanation of CMT solutions with examples.*

Yeats, R.S., Sieh, K., and Allen, C.R., 1997, The geology of earthquakes: New York, Oxford University Press, 568 p. *A textbook treatment offering a (generally Californian) perspective on the geology of active faulting. Their explanation of FMSs is brief (p. 65-69), qualitative and reasonably clear, with a good illustration of first-motion waveforms and a corresponding beachball diagram showing the data (Figure 4-6, after Nabelek and others, 1987).*

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