During earthquakes the release of crustal stresses is believed generally to involve the fracturing of the rock along a plane which passes through the point of origin (the hypocentre or focus) of the event (Figure 4.25). Sometimes, especially in larger shallower earthquakes, this rupture plane, called a fault, breaks through to the ground surface, where it is known as a fault trace (Figure 4.41).
The cause and nature of earthquakes is the subject of study of the science of seismology, and further background may be obtained from the books by Richter (1958), Bolt (2003) and Lay and Wallace (1995).
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Unfortunately, for non-seismologists at least, understanding the general literature related to earthquakes is impeded by the difficulty of finding precise definitions of fundamental seismological terms. For assistance in the use of this book, definitions of some basic terms are set out below. Further definitions may be found elsewhere in this book or in the references given above.
The strength of an earthquake is not an official technical term, but is used in the normal language sense of ‘How strong was that earthquake?’ Earthquake strength is defined in two ways: first the strength of shaking at any given place (called the intensity) and second, the total strength (or size) of the event itself (called magnitude, seismic moment, or moment magnitude). These entities are described below.
Intensity is a qualitative or quantitative measure of the severity of seismic ground motion at a specific site. Over the years, various subjective scales of what is often called felt intensity have been devised, notably the European Macroseismic and the Mercalli scale, which are very similar. The most widely used in the English speaking world is the Modified Mercalli scale (commonly denoted MM), which has 12 grades denoted by Roman numerals I-XII. A detailed description of this intensity scale is given in Appendix A, taken from Dowrick et al. (2008).
Quantitative instrumental measures of intensity include engineering parameters such as peak ground acceleration, peak ground velocity, the Housner spectral intensity, and response spectra in general. Because of the high variability of both subjective and instrumental scales, the correlation between these two approaches to describing intensity is inherently weak (Figure 4.23).
Magnitude is a quantitative measure of the size of an earthquake, related indirectly to the energy released, which is independent of the place of observation. It is calculated from amplitude measurements on seismograms, and is on a logarithmic scale expressed in ordinary numbers and decimals. Unfortunately several magnitude scales exist, of which the four most common ones are described here (ML, MS, mb and MW).
The most commonly used magnitude scale is that devised by and named after Richter, and is denoted M or ML. It is defined as
where A is the maximum recorded trace amplitude for a given earthquake at a given distance as written by a Wood-Anderson instrument, and A0 is that for a particular earthquake selected as standard.
The Wood-Anderson seismograph ceases to be useful for shocks at distances beyond about 1000 km, and hence Richter magnitude is now more precisely called local magnitude (Ml) to distinguish it from magnitude measured in the same way but from recordings on long-period instruments, which are suitable for more distant events. When these latter magnitudes are measured from surface wave impulses they are denoted by MS. Gutenburg proposed what he called ‘unified magnitude’, denoted m or mb, which is dependent on body waves, and is now generally named body wave magnitude (mb). This magnitude scale is particularly appropriate for events with a focal depth greater than c. 45 km. All three scales ML, mb and MS suffer from saturation at higher values.
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The most reliable and generally preferred magnitude scale is moment magnitude, MW. This is derived from seismic moment, M0, which measures the size of an earthquake directly from the energy released (Wyss and Brune, 1968), through the expression
where i is the shear modulus of the medium (and is usually taken as 3 x 1010 Nm), A is the area of the dislocation or fault surface, and D is the average displacement or slip on that surface. Seismic moment is a modern alternative to magnitude, which avoids the shortcomings of the latter but is not so readily determined. Up to 1985, seismic moment had generally only been used by seismologists.
Moment magnitude is a relatively recent magnitude scale from Kanamori (1977) and Hanks and Kanamori (1979), which overcomes the above-mentioned saturation problem of other magnitude scales by incorporating seismic moment into its definition, such that moment magnitude is given by
Mw = – log M0 – 6.03 (M0 in Nm). (2.3)
Local magnitude ML is inherently a poor magnitude scale, as shown by the plot in Figure 2.6 of New Zealand data from Dowrick and Rhoades (1998), who found that the best fit relationship for estimating MW from ML and depth, hc, was
Mw = 0.96[±0.49] + 0.84[±0.08]Ml – 0.0055[±0.0015](hc – 25). (2.4)
The regression explains only 59% of the variance and has a residual standard error of 0.31. The Ml scale as estimated in other parts of the world, as well as New Zealand, is similarly unreliable.
The relation between moment magnitude MW, surface-wave magnitude MS and centroid depth hc, using data restricted to modern MW determinations (i.e. from March 8, 1964 onwards), is shown in Figure 2.7. For earthquakes of hc < 30 km, MS and MW are close to being equal above magnitude 6.5. At lower magnitudes MS is consistently smaller than MW, and is as much as a quarter-unit smaller between magnitude 5.0 and 5.5. Depth also influences the discrepancy between MS and MW; for deep New Zealand earthquakes (hc > 50 km) MS is about a half-unit smaller than MW between magnitude 5.0 and 5.5. This results from the tendency for MS to decrease with depth for earthquakes of a given seismic moment. Karnik (1969) first dealt with this effect by proposing a focal depth correction term for MS in relation to mb for various parts of Europe, while Ambraseys and Free (1997) more recently estimated a focal depth correction term in relation to log M0 for European earthquakes. Considering the New Zealand data (Figure 2.7), Dowrick and Rhoades (1998) found the best fit for finding MW in terms of MS and hc was the quadratic expression
Mw = 1.27[±0.16] + 0.80[±0.03]Ms + 0.087[±0.031](Ms – 6)2 + 0.0031
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Figure 2.6 Scatter plot of local magnitude ML against moment magnitude MW for New Zealand earthquakes distinguishing events in different classes of centroid depth hC. Also shown are the linear and quadratic regression fits for ML evaluated at hC = 25 km and a local regression trend curve of ML on MS for events with hC < 50 km (from Dowrick and Rhoades, 1998)
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Figure 2.6 Scatter plot of local magnitude ML against moment magnitude MW for New Zealand earthquakes distinguishing events in different classes of centroid depth hC. Also shown are the linear and quadratic regression fits for ML evaluated at hC = 25 km and a local regression trend curve of ML on MS for events with hC < 50 km (from Dowrick and Rhoades, 1998)
The above expression explains 93% of the variance. In equation (2.5) it can be seen that the quadratic term contributes significantly to the regression because the coefficient of this term is more than twice its standard error. It is of interest to note that, although their expression is different from ours, Ambraseys and Free obtained a coefficient for their depth term of 0.0036, which is very similar to the coefficient of 0.003 in equation (2.5).
Also shown in Figure 2.7 is the relation of Ekstrom and Dziewonski (1988), derived from global data, between log MO and MS for events with h < 50 km. In terms of MW, this relation is
9.40 – V41.09-5.07Ms, 5.3 < Ms < 6.8,
As seen in Figure 2.7, there is no great difference between this relation and the linear and quadratic fits for shallow New Zealand events over the magnitude range of the data, but the latter also describe the effect of depth.
Figure 2.7 Scatter plot of moment magnitude MW against surface wave magnitude MS for earthquakes distinguishing events in different classes of centroid depth hC. Also shown are the linear and quadratic (equation (2.5)) regression fits for MW evaluated at hC = 25 km and a local regression trend curve of MW on MS for events with hC < 50 km, and the relation of Ekstrom and Dziewonski (equation (2.4)) (from Dowrick and Rhoades, 1998)
Figure 2.7 Scatter plot of moment magnitude MW against surface wave magnitude MS for earthquakes distinguishing events in different classes of centroid depth hC. Also shown are the linear and quadratic (equation (2.5)) regression fits for MW evaluated at hC = 25 km and a local regression trend curve of MW on MS for events with hC < 50 km, and the relation of Ekstrom and Dziewonski (equation (2.4)) (from Dowrick and Rhoades, 1998)
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