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The focal mechanism of an
earthquake An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from ...
describes the
deformation Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies. * Defor ...
in the source region that generates the
seismic wave A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. S ...
s. In the case of a fault-related event it refers to the orientation of the fault plane that slipped and the slip
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
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 Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
waveforms In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronics ...
. The focal mechanism can be derived from observing the pattern of "first motions", that is, 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.


Moment tensor solutions

The moment tensor solution is typically 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 In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
(similar to those for
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
and
strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...
) 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 A nuclear explosion is an explosion that occurs as a result of the rapid release of energy from a high-speed nuclear reaction. The driving reaction may be nuclear fission or nuclear fusion or a multi-stage cascading combination of the two, t ...
, for instance, the seismic moment tensor is
isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
and this difference allows such explosions to be easily discriminated from their seismic response. This is an important part of monitoring to discriminate between earthquakes and explosions for the
Comprehensive Test Ban Treaty The Comprehensive Nuclear-Test-Ban Treaty (CTBT) is a multilateral treaty to ban nuclear weapons test explosions and any other nuclear explosions, for both civilian and military purposes, in all environments. It was adopted by the United Nat ...
.


Graphical representation ("beachball plot")

The data for an earthquake is plotted using a lower-hemisphere
stereographic projection In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the ''pole'' or ''center of projection''), onto a plane (geometry), plane (the ''projection plane'') perpendicular to ...
. The
azimuth An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematicall ...
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 are used to plot data from stations where the P-wave first motion recorded was up (a compressive wave), hollow symbols for down (a tensional wave), with dots 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 circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geomet ...
s 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 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, the T-axis in the centre of the colour-filled segment. The fault plane responsible for the earthquake will be parallel to one of the nodal planes, the other being called the auxiliary plane. It is not possible to determine solely from a focal mechanism which of the nodal planes is in fact the fault plane. For this other geological or geophysical evidence is needed to remove the ambiguity. The slip vector, which is 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. To give an example, in the
2004 Indian Ocean earthquake An earthquake and a tsunami, known as the Boxing Day Tsunami and, by the scientific community, the Sumatra–Andaman earthquake, occurred at 07:58:53 local time (UTC+7) on 26 December 2004, with an epicentre off the west coast of northern Suma ...
, 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 Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, the ...
slab as defined by historical earthquake locations and plate tectonic models. 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 the fault trace is covered by an ocean. A most beautifully simple example of a successful test of the hypothesis of
sea floor spreading Seafloor spreading or Seafloor spread is a process that occurs at mid-ocean ridges, where new oceanic crust is formed through volcanic activity and then gradually moves away from the ridge. History of study Earlier theories by Alfred Wegener an ...
was the demonstration that the sense of motion along oceanic
transform faults A transform fault or transform boundary, is a fault along a plate boundary where the motion is predominantly horizontal. It ends abruptly where it connects to another plate boundary, either another transform, a spreading ridge, or a subductio ...
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 sea floor spreading from the ridges. Fault plane solutions also played the key role in the discovery that the deep earthquake zones in some subducting slabs are under compression, others are under tension.


Beach ball calculator

There are several programs available to prepare Focal Mechanism Solutions (FMS). BBC, a
MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
-based tool box, 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.


See also

*
Seismic moment Seismic moment is a quantity used by seismologists to measure the size of an earthquake. The scalar seismic moment M_0 is defined by the equation M_0=\mu AD, where *\mu is the shear modulus of the rocks involved in the earthquake (in pascals (Pa) ...


References


External links


Focal Mechanisms
– United States Geological Survey
A Primer on Focal Mechanism Solutions for Geologists
– Baylor University

* ttps://www.youtube.com/watch?v=MomVOkyDdLo Focal Mechanisms Explained: What are those “beach balls”?
IRIS Consortium IRIS (Incorporated Research Institutions for Seismology) is a university research consortium dedicated to exploring the Earth's interior through the collection and distribution of seismographic data. IRIS programs contribute to scholarly research, ...
{{DEFAULTSORT:Focal Mechanism Seismology Structural geology