The focal mechanism of an earthquake describes the deformation in the source region that generates the seismic waves. In the case of a fault-related event, it refers to the orientation of the fault plane that slipped, and the slip vector and is also known as a fault-plane solution. Focal mechanisms are derived from a solution of the moment tensor for the earthquake, which itself is estimated by an analysis of observed seismicwaveforms. The focal mechanism can be derived from observing the pattern of "first motions", whether the first arriving P waves break up or down. This method was used before waveforms were recorded and analysed digitally, and this method is still used for earthquakes too small for easy moment tensor solution. Focal mechanisms are now mainly derived using semi-automatic analysis of the recorded waveforms.[1]
The moment tensor solution is displayed graphically using a so-called beachball diagram. The pattern of energy radiated during an earthquake with a single direction of motion on a single fault plane may be modelled as a double couple, which is described mathematically as a special case of a second order tensor (similar to those for stress and strain) known as the moment tensor.
Earthquakes not caused by fault movement have quite different patterns of energy radiation. In the case of an underground nuclear explosion, for instance, the seismic moment tensor is isotropic, and this difference allows such explosions to be easily discriminated from their seismic response. This is an essential part of monitoring to distinguish between earthquakes and explosions for the Comprehensive Test Ban Treaty.
Fault types with corresponding beach ball plots[2]
Left-lateral
strike slip
Right-lateral
strike slip
Normal
dip-slip
Thrust/reverse
dip-slip
Graphical representation ("beachball plot")edit
The data for an earthquake is plotted using a lower-hemisphere stereographic projection. The azimuth and take-off angle are used to plot the position of an individual seismic record. The take-off angle is the angle from the vertical of a seismic ray as it emerges from the earthquake focus. These angles are calculated from a standard set of tables that describe the relationship between the take-off angle and the distance between the focus and the observing station. By convention, filled symbols plot data from stations where the P-wave first motion recorded was up (a compressive wave), hollow symbols for down (a tensional wave), and crosses for stations with arrivals too weak to get a sense of motion. If there are sufficient observations, one may draw two well-constrained orthogonal great circles that divide the compressive from the tensional observations, and these are the nodal planes. Observations from stations with no clear first motion normally lie close to these planes. By convention, the compressional quadrants are colour-filled, and the tensional left is white. The two nodal planes intersect at the N (neutral)-axis. The P and T axes are also often plotted; with the N axis, these three directions respectively match the directions of the maximum, minimum, and intermediate principal compressive stresses associated with the earthquake. The P-axis is plotted in the centre of the white segment, and the T-axis in the centre of the colour-filled segment.
USGS focal mechanism for the 2004 Indian Ocean earthquake
The fault plane responsible for the earthquake will parallel one of the nodal planes; the other is called the auxiliary plane. It is impossible to determine solely from a focal mechanism which of the nodal planes is the fault plane. Other geological or geophysical evidence is needed to remove the ambiguity. The slip vector, the direction of motion of one side of the fault relative to the other, lies within the fault plane, 90 degrees from the N-axis.
For example, in the 2004 Indian Ocean earthquake, the moment tensor solution gives two nodal planes, one dipping northeast at 6 degrees and one dipping southwest at 84 degrees. In this case, the earthquake can be confidently associated with the plane dipping shallowly to the northeast, as this is the orientation of the subducting slab as defined by historical earthquake locations and plate tectonic models.[3]
Fault plane solutions are useful for defining the style of faulting in seismogenic volumes at depth for which no surface expression of the fault plane exists or where an ocean covers the fault trace. A simple example of a successful test of the hypothesis of sea floor spreading was the demonstration that the sense of motion along oceanic transform faults[4] is opposite to what would be expected in classical geologic interpretation of the offset oceanic ridges. This was done by constructing fault plane solutions of earthquakes in oceanic faults, which showed beach ball plots of strike-slip nature (see figures), with one nodal plane parallel to the fault and the slip in the direction required by the idea of seafloor spreading from the ridges.[5]
Fault plane solutions also played a crucial role in discovering that the deep earthquake zones in some subducting slabs are under compression while others are under tension.[6][7]
Beach ball calculatoredit
There are several programs available to prepare Focal Mechanism Solutions (FMS). BBC, a MATLAB-based toolbox, is available to prepare the beach ball diagrams. This software plots the first motion polarity data as it arrives at different stations. The compression and dilation are separated using mouse help. A final diagram is prepared automatically.[8]
^Sipkin, Stuart A. (1994). "Rapid determination of global moment-tensor solutions". Geophysical Research Letters. 21 (16): 1667–1670. Bibcode:1994GeoRL..21.1667S. doi:10.1029/94GL01429.
^Yongliang Wang, Yang Ju, Yongming Yang (2018), "Adaptive Finite Element-Discrete Element Analysis for Microseismic Modelling of Hydraulic Fracture Propagation of Perforation in Horizontal Well considering Pre-Existing Fractures", Shock and Vibration, vol. 2018, pp. 1–14, doi:10.1155/2018/2748408, ISSN 1070-9622{{citation}}: CS1 maint: multiple names: authors list (link)
^Sibuet, Jean-Claude; Rangin, Claude; Lepichon, Xavier Le; Singh, Satish; Cattaneo, Antonio; Graindorge, David; Klingelhoefer, Frauke; Lin, Jing-Yi; Malod, Jacques; Maury, Tanguy; Schneider, Jean-Luc; Sultan, Nabil; Umber, Marie; Yamaguchi, Haruka; "Sumatra Aftershocks" team (2007). "26th December 2004 great Sumatra–Andaman earthquake: Co-seismic and post-seismic motions in northern Sumatra" (PDF). Earth and Planetary Science Letters. 263 (1–2): 88–103. Bibcode:2007E&PSL.263...88S. doi:10.1016/j.epsl.2007.09.005.
^Wilson, J. Tuzo (1965). "A new class of faults and their bearing on continental drift". Nature. 207 (4995): 343–347. Bibcode:1965Natur.207..343W. doi:10.1038/207343a0. S2CID 4294401.
^Sykes, Lynn R. (1967). "Mechanism of earthquakes and nature of faulting on the mid-oceanic ridges". Journal of Geophysical Research. 72 (8): 2131–2153. Bibcode:1967JGR....72.2131S. doi:10.1029/JZ072i008p02131.
^Isacks, Bryan; Molnar, Peter (1971). "Distribution of stresses in the descending lithosphere from a global survey of focal-mechanism solutions of mantle earthquakes". Reviews of Geophysics and Space Physics. 9 (1): 103–174. Bibcode:1971RvGSP...9..103I. doi:10.1029/RG009i001p00103.
^Vassiliou, Marius S. (1984). "The state of stress in subducting slabs as revealed by earthquakes analysed by moment tensor inversion". Earth and Planetary Science Letters. 69 (1): 195–202. Bibcode:1984E&PSL..69..195V. doi:10.1016/0012-821X(84)90083-9.
^Shahzad, Faisal (2006). Software development for fault plane solution and isoseismal map (MSc). Islamabad: Quaid-i-Azam University.
External linksedit
– United States Geological Survey
A Primer on Focal Mechanism Solutions for Geologists – Baylor University
Focal Mechanisms – enter fault parameters and a 'beachball' diagram is created
Focal Mechanisms Explained: What are those "beach balls"? – IRIS Consortium
February 16, 2024
focal, mechanism, focal, mechanism, earthquake, describes, deformation, source, region, that, generates, seismic, waves, case, fault, related, event, refers, orientation, fault, plane, that, slipped, slip, vector, also, known, fault, plane, solution, derived, . The focal mechanism of an earthquake describes the deformation in the source region that generates the seismic waves In the case of a fault related event it refers to the orientation of the fault plane that slipped and the slip vector and is also known as a fault plane solution Focal mechanisms are derived from a solution of the moment tensor for the earthquake which itself is estimated by an analysis of observed seismic waveforms The focal mechanism can be derived from observing the pattern of first motions whether the first arriving P waves break up or down This method was used before waveforms were recorded and analysed digitally and this method is still used for earthquakes too small for easy moment tensor solution Focal mechanisms are now mainly derived using semi automatic analysis of the recorded waveforms 1 Contents 1 Moment tensor solutions 1 1 Graphical representation beachball plot 1 2 Beach ball calculator 2 See also 3 References 4 External linksMoment tensor solutions edit nbsp The moment tensor solution is displayed graphically using a so called beachball diagram The pattern of energy radiated during an earthquake with a single direction of motion on a single fault plane may be modelled as a double couple which is described mathematically as a special case of a second order tensor similar to those for stress and strain known as the moment tensor Earthquakes not caused by fault movement have quite different patterns of energy radiation In the case of an underground nuclear explosion for instance the seismic moment tensor is isotropic and this difference allows such explosions to be easily discriminated from their seismic response This is an essential part of monitoring to distinguish between earthquakes and explosions for the Comprehensive Test Ban Treaty Fault types with corresponding beach ball plots 2 Left lateral strike slip Right lateral strike slip Normal dip slip Thrust reverse dip slip nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Graphical representation beachball plot edit nbsp The data for an earthquake is plotted using a lower hemisphere stereographic projection The azimuth and take off angle are used to plot the position of an individual seismic record The take off angle is the angle from the vertical of a seismic ray as it emerges from the earthquake focus These angles are calculated from a standard set of tables that describe the relationship between the take off angle and the distance between the focus and the observing station By convention filled symbols plot data from stations where the P wave first motion recorded was up a compressive wave hollow symbols for down a tensional wave and crosses for stations with arrivals too weak to get a sense of motion If there are sufficient observations one may draw two well constrained orthogonal great circles that divide the compressive from the tensional observations and these are the nodal planes Observations from stations with no clear first motion normally lie close to these planes By convention the compressional quadrants are colour filled and the tensional left is white The two nodal planes intersect at the N neutral axis The P and T axes are also often plotted with the N axis these three directions respectively match the directions of the maximum minimum and intermediate principal compressive stresses associated with the earthquake The P axis is plotted in the centre of the white segment and the T axis in the centre of the colour filled segment nbsp USGS focal mechanism for the 2004 Indian Ocean earthquakeThe fault plane responsible for the earthquake will parallel one of the nodal planes the other is called the auxiliary plane It is impossible to determine solely from a focal mechanism which of the nodal planes is the fault plane Other geological or geophysical evidence is needed to remove the ambiguity The slip vector the direction of motion of one side of the fault relative to the other lies within the fault plane 90 degrees from the N axis For example in the 2004 Indian Ocean earthquake the moment tensor solution gives two nodal planes one dipping northeast at 6 degrees and one dipping southwest at 84 degrees In this case the earthquake can be confidently associated with the plane dipping shallowly to the northeast as this is the orientation of the subducting slab as defined by historical earthquake locations and plate tectonic models 3 Fault plane solutions are useful for defining the style of faulting in seismogenic volumes at depth for which no surface expression of the fault plane exists or where an ocean covers the fault trace A simple example of a successful test of the hypothesis of sea floor spreading was the demonstration that the sense of motion along oceanic transform faults 4 is opposite to what would be expected in classical geologic interpretation of the offset oceanic ridges This was done by constructing fault plane solutions of earthquakes in oceanic faults which showed beach ball plots of strike slip nature see figures with one nodal plane parallel to the fault and the slip in the direction required by the idea of seafloor spreading from the ridges 5 Fault plane solutions also played a crucial role in discovering that the deep earthquake zones in some subducting slabs are under compression while others are under tension 6 7 Beach ball calculator edit There are several programs available to prepare Focal Mechanism Solutions FMS BBC a MATLAB based toolbox is available to prepare the beach ball diagrams This software plots the first motion polarity data as it arrives at different stations The compression and dilation are separated using mouse help A final diagram is prepared automatically 8 See also editSeismic momentReferences edit Sipkin Stuart A 1994 Rapid determination of global moment tensor solutions Geophysical Research Letters 21 16 1667 1670 Bibcode 1994GeoRL 21 1667S doi 10 1029 94GL01429 Yongliang Wang Yang Ju Yongming Yang 2018 Adaptive Finite Element Discrete Element Analysis for Microseismic Modelling of Hydraulic Fracture Propagation of Perforation in Horizontal Well considering Pre Existing Fractures Shock and Vibration vol 2018 pp 1 14 doi 10 1155 2018 2748408 ISSN 1070 9622 a href Template Citation html title Template Citation citation a CS1 maint multiple names authors list link Sibuet Jean Claude Rangin Claude Lepichon Xavier Le Singh Satish Cattaneo Antonio Graindorge David Klingelhoefer Frauke Lin Jing Yi Malod Jacques Maury Tanguy Schneider Jean Luc Sultan Nabil Umber Marie Yamaguchi Haruka Sumatra Aftershocks team 2007 26th December 2004 great Sumatra Andaman earthquake Co seismic and post seismic motions in northern Sumatra PDF Earth and Planetary Science Letters 263 1 2 88 103 Bibcode 2007E amp PSL 263 88S doi 10 1016 j epsl 2007 09 005 Wilson J Tuzo 1965 A new class of faults and their bearing on continental drift Nature 207 4995 343 347 Bibcode 1965Natur 207 343W doi 10 1038 207343a0 S2CID 4294401 Sykes Lynn R 1967 Mechanism of earthquakes and nature of faulting on the mid oceanic ridges Journal of Geophysical Research 72 8 2131 2153 Bibcode 1967JGR 72 2131S doi 10 1029 JZ072i008p02131 Isacks Bryan Molnar Peter 1971 Distribution of stresses in the descending lithosphere from a global survey of focal mechanism solutions of mantle earthquakes Reviews of Geophysics and Space Physics 9 1 103 174 Bibcode 1971RvGSP 9 103I doi 10 1029 RG009i001p00103 Vassiliou Marius S 1984 The state of stress in subducting slabs as revealed by earthquakes analysed by moment tensor inversion Earth and Planetary Science Letters 69 1 195 202 Bibcode 1984E amp PSL 69 195V doi 10 1016 0012 821X 84 90083 9 Shahzad Faisal 2006 Software development for fault plane solution and isoseismal map MSc Islamabad Quaid i Azam University External links editFocal Mechanisms United States Geological Survey A Primer on Focal Mechanism Solutions for Geologists Baylor University Focal Mechanisms enter fault parameters and a beachball diagram is created Focal Mechanisms Explained What are those beach balls IRIS Consortium Retrieved from https en wikipedia org w index php title Focal mechanism amp oldid 1179864365, wikipedia, wiki, book, books, library,
