Earthquake parameters and seismicity

An entire book, let alone a chapter, could be dedicated to the issue of seismicity models. Herein, however, a very brief overview, with key references, is presented, ith the ai of introducing definitions for the key parameters and the main concepts behind seismicity models.

With the exception of some classes of volcanic seismicity and very deep events, earthquakes are generally produced by sudden rupture of geological faults, releasing elastic strain energy stored in the surrounding crust, which then radiates from the fault rupture in the form of seismic waves.

he location of the earthquake is specified by the location of the focus or hypocentre, hich is the point on the fault here the rupture initiates and from where the first seismic waves are generated. This point is specified by the geographical coordinates of the epicentre, which is the projection of the hypocentre on the Earth's surface, and the focal depth, which is the distance of the hypocentre below the Earth's surface, measured in kilometres. Although for the purposes of observatory seismology, using recordings obtained on sensitive instruments at distances of hundreds or thousands of kilometres from the earthquake, the source can be approximated as a point, it is important to emphasise that in reality the earthquake source can be very large. The source is ultimately the part of the crust that experiences relaxation as a result of the fault slip; the dimensions of the earthquake source are controlled by the length of the fault rupture and, to a lesser extent, the amount of slip on the fault during the earthquake. The rupture and slip lengths both gro exponentially ith the agnitude of the earthquake, as shown in Figure 2.2. Two good texts on the geological origin of earthquakes and the nature of faulting are Yeats et al. (1997) and Scholz (2002).

The magnitude of an earthquake is in effect a measure of the total amount of energy released in the form of seismic waves. There are several different magnitude scales, each of which is measured from the amplitude of different waves at different periods. The first magnitude scale proposed was the Richter scale, generally denoted by ML, where the subscript stands for local. Global earthquake catalogues generally report event size in terms of body-wave magnitude, mb, or surface-wave magnitude, Ms, which will often give

Figure 2.2 Median predicted values of rupture length and slip from the empirical equations of Wells and Coppersmith (1994)

different values for the same earthquake. All of the scales mentioned so far share a common deficiency in that they saturate at a certain size and are therefore unable to distinguish the sizes of the very largest earthquakes. This shortcoming does not apply to moment magnitude, designated as M or M, which is determined from the very long-period part of the seismic radiation. This scale is based on the parameter seismic moment, which is the product of the area of the fault rupture, the average slip on the fault plane and the rigidity of the crust.

A seismicity model needs to specify the expected location and frequency of future earthquakes of different agnitudes. ide range of data can be used to build up seismicity models, generally starting with regional earthquake catalogues. Instrumental recordings of earthquakes are only available since the end of the nineteenth century and even then the sparse nature of early networks and low sensitivity of the instruments means that catalogues are generally incomplete for smaller magnitudes prior to the 1960s. The catalogue for a region can be extended through the study of historical accounts of earthquakes and the inference, through empirical relationships derived from ttventieth-century earthquakes, of magnitudes. For some parts of the world, historical seismicity can extend the catalogue fro 100 years to several centuries. he record can be extended even further through paleoseismological studies (McCalpin, 1996), which essentially means the field study of geological faults to assess the date and amplitude of previous co-seismic ruptures. Additional constraint on the seismicity model can be obtained from the tectonic framework and more specifically from the field study of potentially active structures and their signature on the landscape. Measurements of current crustal deformation, using traditional geodesy or satellite-based techniques, also provide useful input to estimating the total seismic moment budget (e.g. Jackson, 2001).

The seismicity model needs to first specify the spatial distribution of future earthquake events, which is achieved by the definition of seismic sources. here active geological faults are identified and their degree of activity can be characterised, the seismic sources will be lines or planes that reflect the location of these structures. Since in any cases active faults ill not have been identified and also because it is generally not possible to unambiguously assign all events in a catalogue to known faults, source zones will often be defined. These are general areas in which it is assumed that seismicity is uniform in terms of mechanism and type of earthquake, and that events are equally likely to occur at any location ithin the source. ven here fault sources are specified, these ill generally lie ithin areal sources that capture the seismicity that is not associated with the fault.

Once the boundaries of the source zones are defined, which fixes the spatial distribution of the seismicity model, the next step is to produce a model for the temporal distribution of seismicity. These models are generally referred to as recurrence odels as they define the average rates of occurrence of earthquakes of agnitude greater than or equal to a particular value. The most widely used model is that known as the Gutenberg-Richter (G-R) relationship, which defines a simple power law relationship bettveen the number of earthquakes per unit time and magnitude. The relationship is defined by two parameters, the activity (i.e. the annual rate of occurrence of earthquakes of magnitude greater than or equal to zero or some other threshold level) and the b-value, hich is the slope of the recurrence relation and defines the relative proportions of small and large earthquakes; ¿-values for large areas in much of the world are very often close to unity. The relationship must be truncated at an upper limit, M , which is the largest earthquake that the seismic source zone is considered capable of producing; this may be inferred from the dimensions of capable geological structures and empirical relations such as that shown in Figure 2.2 or simply by adding a small increment to the largest historical event in the earthquake catalogue. The typical form of the G-R relationship is illustrated in Figure 2.3.

For major faults, it is believed that the G—R recurrence relationship may not hold and that large agnitude earthquakes occur quasi-periodically ith relatively little activity at oderate agnitudes. his leads to alternative models, also illustrated in Figure 2.3: if only large earthquakes occur, then the maximum magnitude model is adopted, whereas if there is also some activity in the smaller magnitude ranges then a model is adopted which combines a G—R relationship for lower magnitudes with the occurrence of larger characteristic earthquakes at higher rates than ould be predicted by the extrapolation of the G—R relationship. The recurrence rate of characteristic events will generally be inferred from paleoseismological studies rather than fro the earthquake catalogue, since such earthquakes are generally too infrequent to have multiple occurrences in catalogues. Highly recommended references on recurrence relationships include Reiter (1990), Utsu (1999) and McGuire (2004).

Figure 2.3 Typical forms of earthquake recurrence relationships, shown in non-cumulative (upper row) and cumulative (lower row) forms. From left to right: Gutenberg-Richter model, maximum magnitude model, and characteristic earthquake odel

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