2.3 Methods of Rating Individual Earthquakes
2.4.8 Local Magnitude Scale (M L )
In 1930, Charles Richter introduced what is now called the local magnitude, ML. This was determined by measuring the largest amplitude, A, recorded on a standard instrument, the Wood-Anderson seismograph. He noticed that plots of LogA versus range for different earthquakes generally exhibited a similar decay rate. This suggested that a range-independent
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measure of earthquake size could be provided by the offset in LogA from a reference event at the same range.
ML = Log10A(Δ) – Log10A0(Δ) 2.38 Where
A0 is the amplitude of the reference event, Δ is the epicentral distance.
(Shearer,1999)
A relationship between intensity and magnitude was developed by Gutenberg and Richter,(1956) and is given as :
ML =(2/3)I0 + 1 2.39 Where I0 is the highest intensity of the earthquake.
However, a relationship was established by Ambraseys and Boomer(1990) as :
Ms = 1.33ML – 1.73 2.40 Where Ms is the surface wave magnitude.
2.5 Global Seismicity
The earth‘s major earthquakes occur mainly in belts coinciding with the margins of tectonic plates (fig 2.1). This have long been apparent from early catalogs of felt earthquakes and is even more readily discernable in mordern seismicity maps, which show instrumentally determined epicenters.
The most important earthquake belt is the circum-Pacific belt, which affects many populated castal regions around the Pacific ocean – as for example, those of New zealand, New Guinea, Japan, the Aleutian Islands, Alaska, and the western coasts of North and south America.
It is estimated that 80 percent of the energy presently released in earthquakes comes from those whose epicenters are in this belt. The seismic activity is by no means uniform throughout the belt, and there are a number of branches at various points. Because at many places the circum-Pacific belt is associated with volcanic activity it has been popularly dubbed the ―Pacific Ring of Fire‖.
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A second belt, known as the Alpine belt, passes through the Mediterranean region eastward through Asia and joins the cicum-Pacific belt in the East Indies. The energy released in earthquakes from this belt is about 15 percent of the world‘s total. There are also striking connected belts of seismic activity, mainly along oceanic ridges – including those in the Arctic Ocean and along the rift valleys of East Africa.
This global seismicity distribution is best understood in terms of its plate tectonic setting. An earthquake occurs when there is a sudden release of energy within a confined region of the earth. This may be due to elastic strain energy, kinetic energy, gravitational potential energy or chemical energy.
Earthquakes resulting from the release of elastic energy are known as tectonic earthquakes. They constitute about 90% of the global events while those resulting from volcanic activities are known as volcanic earthquake. These are relatively small both in size and in number.
Earthquakes are also classified based on their focal depths. Earthquakes with focal depths less than 70km are called shallow earthquakes (fig 2.2a). They occur in all the seismically active zones and constitute 70% of global events. Shallow earthquakes occur only in the oceanic ridges.
Intermediate earthquake have focal depth of 70-300km (fig 2.2b) and account for 12% of the global events and deep earthquakes have focal depth (fig 2.2c) greater than 300km (Lowrie, 1997). Both intermediate and deep earthquakes occur in the circum-pacific and Mediterranean-Transasiatic/Alphine zones and follow the process of plate subduction (fig 2.2d). Though there is a debate on the physical mechanism of deep earthquakes, H. Turner located some earthquakes at a significant depth. But his analyses were not accepted since he also located some events in the air above the surface. According to Shearer (1999), deep earthquakes are observed along dipping planes of seismicity called the Wadati-Benioff zones that extend to almost 700km depth.
A recent explanation of the strong patterns of seismically active belts surrounding largely aseismic areas is the plate tectonic theory. The theory describes the lithosphere of the earth as consisting of about seven large, and several smaller stable plates. The relative motions between adjacent plates give rise to earthquakes, mountain building, volcanism and other phenomena along the plate boundaries.
26 Fig. 2.1: Global Earthquake Epicentres ( USGS, 2000).
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Figure 2.2a Global Shallow Earthquakes with Magnitude 5 and above (USGS, 2000).
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Figure 2.2b Global Intermediate Earthquakes with Magnitude 5 and above (USGS, 2000).
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Figure 2.2c Global Deep Earthquakes with Magnitude 5 and above (USGS 2000).
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Figure 2.2d Global Earthquakes of Magnitude 5 and above (USGS 2000).
31 2.6 The Gutenberg – Richter Relation
Ishimoto and Iida first discovered the size distribution of earthquakes in a seismogenic volume in Japan in 1939 using the maximum trace amplitude of an earthquake. Later in 1944 Gutenberg and Richter established the magnitude frequency relationship. Their aim was to improve the estimation of the frequency of destructive earthquakes in California by mans of statistical method rather than rely on historical records alone. Their original formula Log N = a +b (8 –M) relates the frequency of earthquakes to the magnitude using the local magnitude M1 as a magnitude scale. The more general non-cumulative form of the Gutenberg-Richter‘s relationship, that was employed this study is given by
Log N (M) = a- bM 2.41
Where N=number of earthquakes of magnitude > M that occurred in the region over a period of time.
a and b are regression constants a is a constant representing the total number of earthquakes with magnitude > 0 and is dependent on the location and time of the sample used. It also describes the level of seismicity in a given region b is the proportion of earthquakes of small and large magnitudes. The slope of the graph determines b. A steep slope corresponds to a high b-value, when the slope flattens;
the b- value is getting lower.
Utsu (1965) proposed that b is given by:
min min
4343 .
0 log
M M
M M
b e
2.42
Which Aki (1965) identified as equivalent to the maximum likelihood estimate for b.
From Equation 2.41 it is observed that the number of earthquakes decreases logarithmically with the increase in the magnitude.
The nature of the earthquake frequency – magnitude distribution is of fundamental importance in probabilistic seismic hazard calculation and accordingly has attracted a great deal of concern. However, there are some arguments in favour of the quadratic form of Gutenberg-Richter‘s relationship because it is the most common. The log-linear relationship works well in the certain magnitude range and fails at the smallest magnitudes because the recording instruments under record small magnitudes. The relationship also fails at high magnitudes because maximum magnitude is achievable. Maximum magnitude arises because all traditional magnitude scales saturate i.e. they do not go beyond a certain value of magnitude. Secondly, a given fault or tectonic region has physical constraints on the maximum size of the event it can generate (Dowrick, 1977).
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From the seminar on b-value by Kulhanek (2005), the G-R relation (Equation. 2.41), applies to cummulative number N as well as to incremental numbers,n. In other words, N is the cummulative number of earthquakes with magnitudes larger than M, while n is the number of events with magnitudes in the range M ± ΔM (increamental or interval distribution). A choice of proper ΔM is a crucial task in any incremental b evaluation. However, cummulative distribution provides a better fit since numbers are larger and less degreded by statistics of small numbers. It also avoid the problem of designing a proper ΔM. Once a and b are determined, for a given region and time window, then one already has the information necessary to access parameters of seismic hazard. It should however be noted that the relation should not be expected to extrapolate without limits, the frequency of the smaller events to determine the threat of the rare large earthquakes.
2.7 Explanations of b-Value
Spatial and temporal variations of the b-value have earlier been employed in numerous seismicity studies. After pioneering works of Mogi (1962), Scholz (1968) and Wyss (1973), they have been extensively used (with varying degree of success) by other scientists e.g. to identify volumes of active magma bodies (Wiemer and Benoit, 1996; Wiemer et al., 1998), roots of regional volcanism (Monterroso and Kulhanek, 2003) and to forecast major tectonic earthquakes (Monterroso, 2003;
Nuanin et al., 2005).
According to Kulhanek (2005), the linear relation holds only for magnitudes in the certain range M1 ≤ M ≤ M2 . For small and large magnitudes, the frequency decreases more rapidly than linearly and consequently a non-linear fit may in some cases be a better approximation of observed data. He stated two explanations for the deviations from linearity as :
(i) At small magnitudes, there is incompleteness of data owing to under-recording of small events.
Recent studies suggest that the decrease of b is just an artifact of catalog incompleteness but that small earthquakes are really not as numerous as a constant b-value extrapolated from larger events would predict. And so the decline in frequency may to a certain extent be real.
(ii) The saturation of magnitude scales at large magnitudes. Another is the length of available catalogs. To address this problem, the seismic moment, M0, or the moment magnitude, Mw is used.
A significant increase in b is observed around M = 7.3 or around M0 = 1020 Nm (Pacheo et al., 1992) is interpreted as expressing the simultaneous saturation of fault dimension, W, and the slip, D, on the fault. But if the rate at which earthquakes occur is compared with predicted rates by plate rates, it will be too small.
Kulhanek (2005) concluded that plate motion does not take place on the earthquake faults.
From some works e.g. Kagan (1999), it is advocated that b is essentially constant, but others e.g.
Kulhanek, (1997); Wiemer et al., (1998); Gerstenbergeret et al., (2001), argue that spatial and temporal variations in b exist. Some of the observed scatter are :
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1.0 ≤ b ≤ 1.6 Mogi, global seismicity, b~1.0 for lat. ≥ 400, whereas b~1.6 for lat. ≤ 400 0.3 ≤ b ≤ 1.8 Hurtig and Stiller (1984), global seimicity
0.6 ≤ b ≤ 1.5 Udias and Mezcua (1997), global siesmicity 0.8 ≤ b ≤ 1.2 McGarr (1989), global seismicity
0.5 ≤ b ≤ 1.5 McGarr (1984), mining tremors (South Africa) and tectonic earthquakes 0.6 ≤ b ≤ 1.6 Monterroso and Kulhanek (2003), central America seismicity
0.6 ≤ b ≤ 2.6 Nuannin et al., (2002), mining tremors, Zinkgruvan, Sweden
2.7.1 Applications of b-Value
High and low stresses : According to the works of Scholz, (1968) and Wyss, (1973), high and low stresses cause earthquakes series with low and high b-values respectively. This is employed in the works of Wiemer and Benoit, (1996); Wiemer et al., (1998), to predict earthquakes and identify volumes of magma bodies.
Material heterogeniety : It is shown from the work of Mogi, (1962), that large heterogeneities in sub-surface materials correspond to higher b-values.
Thermal gradient : The work of Warren and Latham, (1970), showed that an increase of thermal gradient caused an increase of b-values from 1.2 to 2.7.
Aftershocks and foreshocks : From the works of Suyehiro et al.,(1964), it is found that aftershocks have large b-value while foreshocks have low b-value.
Swarms : Large departures from b~1 is shown in swarms sometimes as large as b =2.5.
Swarms, by definition, lack a clear main shock and result from processes such as migration of magmatic fluids or caldera development.
Variation with depth : It has been observed that b varies laterally and with depth, low b implies shorter recurrence time. Patches with low b may be interpreted as possible stress concentrations reflecting variations in frictional properties along the fault, which may control the reccurence of the next large event.
Paleoseismic studies : There is a usual deviation of paleoseismic studies from the seismologically determined G-R relation. But the opposite is also observed, i.e. instrumental data show that large earthquakes (M≥ 7.2) are less frequent than expected from smaller events.
Small time-sampling : The b-value is reasonably well estimated from smaller earthquakes than for large ones.
Focal mechanism : Current research reveals that thrust fault events are associated with lower b-values compared with normal-fault events.
In the experiments of Mogi (1962), the effect of heterogeneity on b-value is demonstrated.
The b-value and the fractal dimension, D, can be determined, following experiments involving acoustic emission by Main et al.,(1990). Temporal variations in D can be explained by fracture mechanics criteria for failure. The spatial variations of the b-values can be interpreted from both
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experiments and field observations of seismicity. It was shown that D=1 (b = 0.5) reflects critical stress concentration; with the probability of repeated fracture at a particular site at a maximum.
With D = 2 (b = 1), the probability is independent of previous events, corresponding to random process equivalent to background seismicity.
With D < 2 (b < 1), there is stress concentration leading to localisation of deformation with positive feed-back at low stress intensities such as dilatency, leading to highly diffuse fracture system.
In conclusion, fractal dimensions of flaws increases as stress intensities decrease because lenght distribution of cracks become more heterogeneous. However, conditions in the laboratory and in the field are obviously different in that the schizosphere is more heterogeneous than intact rock samples in the laboratory and b =1, D = 2 in the field, because the schizospere already contains major faults and stresses.
The effect of stress is demonstrated by experiments of Wiemer and Wyss (1997) where b-values decreased when ambient stress is increased in the laboratory. b is proportional to pore pressure in cases of fluid-induced seismicity; b decreases during mine burst; b is lower in compressive than in extensional tectonic regimes; and b increases with depth along strike-slip faults in California.
The effects of temperature shown by experiments of Wiemer and McNutt, 1998; Wyss et al., 1973, showed that there is an increase in b-value from regional values of b = 0.7 to values of b > 1.3 or even b = 1.5 in volcanic regions as we approach active magma chambers. This change in b-values can be explained if fractal dimension, D, is twice the b-value.
Conclusions obtained by Steacy et al., (1996), from a two-dimensional cellular automation with strength heterogeneity, but homogeneous tectonic loading was that the b-value increases with increasing range of fractal dimension of strength or roughness of the active fault zone.
The spatial mapping of b-value at Galeras volcano, Colombia, using earthquake data recorded from 1995 to 2002, a work carried out by Acevedo et al., (2005), involved the analysis of the catalog of volcano – tectonic earthquakes at Galeras volcano, Colombia, to determine the magnitude of completeness of seismograph network and also to explore the subsurface structure by mapping the b-value of the frequency-magnitude distribution. From observation of the two and three-dimensional mapping of b-value, a vertically elongated structure beneath the active active crater of Galeras down to a depth of 6km was illuminated. It could be associated with a conduit, or magma storage. This is the first discovery of its kind in previous studies of b-value on volcanoes around the world.
In the on-going b-value mapping of the Yellowstone volcanic and hydrothermal system by Farell et al. (2007), variations in b-values were observed and are been compared with existing crustal tomography results, to distinguish between causes which could be material heterogeneity, the applied shear stress, the effective stress and/or the thermal gradient of the area.
In the mapping of the b-value anomalies in Colfiorito tectonic zone (central Italy) and beneath Mt.
Etna volcano (Sicily, Italy), a work by Murru et al. (2008), it was shown that spatial variations in
b-35
value observed was correlated to a process of lateral magma uprising, ending with a high velocity vertical dike emplacement which heralded to the 2001 lateral eruption.
In the work of Papazachos, (1999), Greece and the surrounding area was organised into a grid, the a and b values are simultaneously determined for the whole grid by solving an appropriate linear system. The results obtained were in good agreement with previous studies and further enhanced the knowledge of the study area.
Drakopoulous (1968) divided the region of Greece into many parts and obtained b for each case. His results showed that for almost all parts, values of b range between 0.4 and 1.7. One can therefore infer from this that b varies much more vertically than horizontally.
In addition, some authors have speculated that b-values may be influenced by thermal gradient causing the b-value to increase from 1.2 to 2.7 (Warren and Latham, 1970).
Minakami (1974) reported that A-type earthquakes (i.e. seismic events with clear P-waves and S-waves occurring beneath volcanoes) have b value of about 1.5 and for B-type earthquakes (i.e.
seismic events occurring under volcanoes with emergent onset of P-waves, no distinct S-waves) b-values are higher than 2.0.
Some researchers are of the view that b-value varies from 0.5 to 1.0 for tectonic earthquakes and for volcanic events b-values are higher (Gresta and Patane, 1983).
Studies by Hurtig and Stiller (1984), Udias and Mezcua (1997) on global seismicity revealed that b-values range from 0.3 to 1.8, 0.8 to 1.2 and 0.6 to 1.5. McGarr (1984) on mining tremors (South Africa) and tectonic earthquakes revealed that b varies from 0.5 to 1.5 Agrawal (1991) confirmed this fact that tectonic earthquakes are characterized by the b-values from 0.5 to 1.5 and are more frequently at 1.0.
However, many researchers have investigated temporal changes of b. Most of these studies addressed bulk changes rather than temporal changes in sub volumes (Wiemer and Wyss, 2002).
Some studies have investigated both spatial and temporal variability of b simultaneously (Ogata, 1991).
The rock burst in a mine and its related micro-seismicity (-2>M>0.5) before and after the mainshock was used by Urbancic et al. (1992) to investigate temporal and spatial changes in the b-value. They found that decreasing b-values correlate with increasing stress release estimates and that larger events tend to occur where the value has its steepest gradient. They further concluded that b-values ―provide the best estimates for stress conditions within the seismogenic volume as they include information from both spectral – (seismic moment) and time domains ‗(peak amplitudes)‘.
Holub (1996) investigated space-time variations of the frequency-energy relation for mining-induced seismicity in the4 Ostrava-Karvina mine district Czech Republic. He stated that lower b-values correspond to a higher level of induced seismic activity while high b-b-values correspond to a low and moderate seismic activity.
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Systematic studies have been carried out by some researchers to examine the potential of temporal changes in b-value as a short-term, medium-term and long-term earthquake precursor.
Results showed that large earthquakes are often preceded by a medium-term increase in b, followed by a decrease in the weeks-months before the earthquake (Sammonds et al., 1999). Molchan and Dmitrieve (1990) have studied temporal b-value variations for foreshocks during hours, days before the main shock. Molchan et al. (1999) found, from both regional and global earthquake catalogues, that the b-value of foreshocks drops by about 50%. From earthquake data for Central America from preliminary determination of epicenters (PDE) and E-catalogs Monterroso (2003) found evidence that supports the hypothesis that b-value decreases significantly prior to the occurrence of large earthquakes.
Wiemer and Wyss (1997) noted that the b-value in the Park field and Morgan Hill regions of California systematically decreases from high b>1.1 in the top 5km to b<0.8 below 6km depth.
Mori and Abercrombie (1997) confirmed this decrease with depth for several other regions in California and proposed that the lower b at depth corresponds to a higher probability of larger earthquakes to nucleate at depth. Though a decrease of b with depth has been firmly established for California, but the physical cause of this decrease is not yet established with certainty. Wiemer and Wyss (2002) have speculated that the change in ambient stress plays an important role.
Monterroso and Kulhanek (2003) investigated b-value variations with depth in the subduction zone of Central America. They observed high b-values in the upper part of the slab at depths around 80-110km beneath the volcanic chain in Guatemala-El Salvador. Nakaya (2004) analyzed seismicity data from the subducting slab along Kurile Trench. Results revealed a zone of anomalously low b-values near the hypocenter of the 26 September 2003, Tokachi-oki earthquake (M=8).
Though more facts have been established on spatial variation of b on a local region scale, arguments still exists about regional to global scale. Studies by Frohlich and Davies (1993) and Kagan (1999) reported that there is little variation of b between different tectonic regions and that the observed differences are at least partially as a result of artifacts rather than natural.
Moreover, the variation of b in subducting slabs has been studied. Wiemer and Benoit (1996) mapped well-defined anomalies similar to those found in the crust at a few kilometers beneath volcanoes at about 100km depths in the subduction zones of Alaska and New Zealand. They interpreted these anomalies as due to dehydration of the descending oceanic crust at top of the slab and proposed that their locations mark the origin of magma, feeding subduction zone volcanism.
Wiemer and Wyss (2002) reported that earthquake-size distribution in many tectonic regions on a local to regional scale reveal statistically significant variations in the range of at least 0.4 to 2.0 for the b-values in the frequency-magnitude distribution.
Also that explosion especially quarry blasts frequently contaminate seismicity data and this will cause bias in the b-estimates locally toward large values because on average, explosions are smaller than earthquakes.
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They corroborated the fact that b-value underneath volcanoes is not, as initially thought to be, generally higher but that the pockets of anomalously high b-values are embedded in average crust. By comparing the anomalies of high values with other geophysical and geodetic data regarding the location and extend of magma chambers, they concluded that in the seismogenic surrounding of magma chambers high b-values are present and especially at shallow depths. The factors causing these high values were attributed to the presence of hot fluids in geothermal systems, or external cracking which a volume may have acquired during past eruptions. Hence high b-values give rise to high heterogeneity, high pore pressure and high thermal gradient. With regards to changes in b with time, they speculated that the fact that spatial variations of b on large scales have not been established could be as a result of lack of high quality earthquake catalogues with low magnitude of completeness on this scale; lack of rigorous studies or because heterogeneity in the earth exists mainly on smaller scales.
Enescu and Ito (2002) showed that b-values vary from 0.8 to 1.4. They discovered that areas that experienced larger slip during the main shock and during previous seismic activity have low stress because of more fracture and hence favour high b-values for the aftershocks. A large value of b in a give region or area shows a relative abundance in small earthquakes. Areas with low b-values on the other hand are probably under higher applied stress after the main shock. They also suggested that the rupture process in an earthquake and previous earthquake activity are the major factors controlling the spatial distribution of b-value.
Results on the investigation of the brittle ductile transition in rocks and associated seismicity (Amitrano, 2003) suggested that the b-value might be controlled by variation of the internal friction angle induced through changes in confining pressure/
Schorlemmer et al. (2004) have shown that b-value systematically varies from different styles of faulting. Normal faulting is associated with the higher b-values (about 1.1); strike-slip events show intermediate values (about 0.95) and thrust events the lowest values (about 0.75). It is possible b is related to focal mechanism (Kulhanek, 2005).
The findings of studies by Rao and Lakshmi (2005) on analysis of b- value of acoustic emissions accompanying rock fracture have revealed that while testing the material undergoing brittle failure b-value was found to range from 1.5 to 2.5 in the early stages. It later decreased with an increase in stress to attain values approximately 1.0 and less indicating temporal fluctuations as the impending failure approaches in the material. A high b-value was attributed to a large number of small acoustic events showing new crack growth. Whereas low b-values showed faster or unstable cracks growth accompanied by relatively high amplitude emission in large numbers.
Recent studies by Kullhanek (2005) has revealed that changes in b towards higher magnitudes may be due to the inability of the fault dimensions, especially width to keep growing indefinitely with the increasing earthquake size. He also suggested that the decrease of b-value (below threshold magnitude) is not just an artifact of catalogue incompleteness but that small earthquakes are not really