Variable | Input | Units | Notes |
---|---|---|---|
Magnitude | |||
km. | Distance to earthquake producing fault | ||
Variable | Output - Hough and Avni (2009) | Units | Notes |
unitless | Local Intensity - Inputs are M (unspecified) and R_{epi} | ||
m/s^{2} | Conversion from Intensity to PGA using Wald et al (1999) |
Al-Qaryouti, M. (2008). "Attenuation relations of peak ground acceleration and velocity in the Southern Dead Sea Transform
region." Arabian Journal of Geosciences - ARAB J GEOSCI 1: 111-117.
Ben-Menahem, A., Vered, M., and Brooke, D. (1982). "Earthquake Risk In The Holy Land." Bollettino di Geofisica Teorica e Applicata XXIV(95).
Darvasi, Y. and A. Agnon (2019). "Calibrating a new attenuation curve for the Dead Sea region using
surface wave dispersion surveys in sites damaged by the 1927 Jericho earthquake." Solid Earth 10(2): 379-390.
Hough, S. E., and R. Avni (2009). "The 1170 and 1202 Dead Sea Rift earthquakes and
long-term magnitude distribution on the Dead Sea fault zone." Isr. J. Earth Sci. 58(3-4): 295-308.
Husein Malkawi, A. I. and K. J. Fahmi (1996). "Locally derived earthquake ground motion attenuation
relations for Jordan and conterminous areas." Quarterly Journal of Engineering Geology and Hydrogeology 29(4): 309-319.
Lu, Y., et al. (2020). "A 220,000-year-long continuous large earthquake record on a slow-slipping plate boundary." Science Advances 6: 1-10.
Wald, D. J., et al. (1999). "Relationships between Peak Ground Acceleration, Peak
Ground Velocity, and Modified Mercalli Intensity in California." Earthquake Spectra 15(3): 557-564.
Wells and Coppersmith (1994) examined a global dataset of earthquakes and developed a series of empirically based equations to estimate moment magnitude of an earthquake from local observations of displacement or fault rupture length and the type of fault (e.g., strike-slip, normal, reverse). Such equations are known as scaling relationships. Other researchers have also developed scaling relationships. It is anticipated that future updates to this Encyclopedia will include a multiplicity of scaling relations along with suggested criteria to help decide which equation is most appropriate for a given situation.
For Surface Magnitude (M_{S}) and Moment Magnitude (M_{W}) estimates based on Rupture Length (L) in km.,
Ambraseys and Jackson (1998) presented the following equations:
M_{S} = 5.13 + 1.14 log(L) (2)
M_{S} = 5.27 + 1.04 log(L) (3)
M_{W} = 4.9 + 1.33 log(L) (11)^{note}
while noting that Equation (3) is almost identical to that derived by Wells and Coppersmith (1994).
Ambraseys and Jackson (1998:397) noted the following
it is important, particularly for palaeoseismological investigations, to have some indication of whether the rupture length and offset estimated from historical sources are likely to be seriously under- or overestimated, given the magnitude of the event. This is a principal use of magnitude—length relationships. For an assessment of individual events or particular regions, it may be more informative to make such estimates from a combination of first principles and more closely constrained empirical relationships, along the following lines:The advantage of this approach over some global empirical relationship is that it is more explicit where the assumptions are: A is known to vary regionally (Ekstrom & Dziewonski 1988) and so is d. Moreover, for earthquakes in which the fault length is small compared with the seismogenic thickness, the relationships between moment and magnitude and between moment and fault length are both known to be different from those given above, such that B≈1.0 (Ekstrom and Dziewonski 1988) and M_{o} is proportional to L^{3}. Thus a single relationship over the whole magnitude range of Fig. 3 (and over the magnitude ranges discussed by Wells & Coppersmith 1994) is not likely to be valid anyway. The explicit approach illustrated here is therefore more likely to be useful for detailed palaeoseismological investigation of specific events.
- for earthquakes that rupture the entire thickness (d) of the seismogenic upper crust, the downdip width of the fault is d/sinϴ, where ϴ is the fault dip, and the moment is then
M_{o} = (μcd/sin ϴ)L^{2} (8)
where
- µ is the rigidity modulus
- c is the ratio of average displacement (u) to fault length (L), which is observed to be close to 5 x 10^{-5} for intracontinental earthquakes (Scholz 1982; Scholz et al. 1986)
- both observationally and theoretically it is known that for such earthquakes the relationship between moment and magnitude (M, whether M_{S} or M_{W} ) is of the form
log(M_{o})= A + BM (9)
where A and B are constants, with B ≈ 1.5 (e.g. Kanamori and Anderson 1975; Ekstrom and Dziewonski 1988))
- combining these expressions gives a relationship between moment and fault length of the form
M = (1/B) log(µcd/sin ϴ) — (A/B) + (2/B) (log L) (10)
For illustration, if we take
- µ=3 x 10^{10} N m^{-2}
- c = 5 x 10^{-5}
- A = 9.0 (for M_{o} in units of N m, see Ekstrom and Dziewonski 1988)
- B=1.5
then for a seismogenic layer of thickness d=15 km and a vertical strike-slip fault (ϴ = 90°), the relationship is
M_{W} = 4.9+1.33L (11)
with L in kilometres, which is similar to the empirical relationships given above and in Wells & Coppersmith (1994) and is a reasonable fit to the earthquakes of M ≥ 6.0 in Fig. 3
Ambraseys and Jackson (1998) produced an equation to estimate
Surface Magnitude (M_{S}) from the average radii of isoseismals (r_{i}) at a specific value of Intensity (I_{i}).
M_{S} = −1.54+0.65(I_{i})+0.0029(R_{i})+2.14 log(R_{i})+0.32p (1)
where
with few exceptions, macroseismic data for the historical period are scanty and the magnitudes that can be calculated from eq. (1) are rather uncertain. They suggested in such cases to use the magnitude estimate to
group earthquakes into three broad categories
Source -
Wells and Coppersmith (1994)
Variable | Input | Units | Notes |
---|---|---|---|
cm. | Strike-Slip displacement | ||
cm. | Strike-Slip displacement | ||
Variable | Output - not considering a Site Effect | Units | Notes |
unitless | Moment Magnitude for Avg. Displacement | ||
unitless | Moment Magnitude for Max. Displacement |
Source - Wells and Coppersmith (1994)
Variable | Input | Units | Notes |
---|---|---|---|
cm. | |||
cm. | |||
Variable | Output - not considering a Site Effect | Units | Notes |
unitless | Moment Magnitude for Avg. Displacement | ||
unitless | Moment Magnitude for Max. Displacement |
Source - Wells and Coppersmith (1994)
Variable | Input | Units | Notes |
---|---|---|---|
cm. | Seismic slip on the ramps | ||
cm. | Seismic slip on the ramps | ||
Variable | Output - not considering a Site Effect | Units | Notes |
unitless | Moment Magnitude for Avg. Displacement | ||
unitless | Moment Magnitude for Max. Displacement |
Variable | Input | Units | Notes |
---|---|---|---|
km. | Rupture Length | ||
Variable | Output - not considering a Site Effect | Units | Notes |
unitless | Moment Magnitude |
Variable | Input | Units | Notes |
---|---|---|---|
km. | Rupture Length | ||
Variable | Output - not considering a Site Effect | Units | Notes |
unitless | Moment Magnitude |
Variable | Input | Units | Notes |
---|---|---|---|
km. | Fault Break | ||
Variable | Output - not considering a Site Effect | Units | Notes |
unitless | Moment Magnitude |
Variable | Input | Units | Notes |
---|---|---|---|
km. | Rupture Length | ||
Variable | Output - not considering a Site Effect | Units | Notes |
unitless | Moment Magnitude from Ambraseys (1988) (developed for the Middle East) |
||
unitless | Moment Magnitude from Bonilla and Lienkaemper (1984) | ||
unitless | Surface Magnitude from Ambraseys and Jackson (1998) Eqn. 2 | ||
unitless | Surface Magnitude from Ambraseys and Jackson (1998) Eqn. 3 | ||
unitless | Moment Magnitude from Ambraseys and Jackson (1998) Eqn. 11 |
Variable | Input | Units | Variable Name |
---|---|---|---|
km. | Mean isoseismal radius for a given Intensity I | ||
unitless | The given Intensity | ||
unitless | p=0 for mean values. p=1 for 84 percentile values (Ambraseys, 1992) | ||
Variable | Output | Units | Notes |
unitless | Surface Magnitude |
Variable | Input | Units | Notes |
---|---|---|---|
km. | |||
km. | |||
Variable | Output | Units | Notes |
unitless | Moment Magnitude computed using Wesnousky (2008) | ||
unitless | Moment Magnitude computed using Hanks and Bakun (2008) | ||
km.^{2} |
Ambraseys, N. [1988] “Magnitude-fault length relationships for earthquakes in the
Middle East,” ed. Lee, W. H. History of Seismograms and Earthquakes of the World, Academic, San Diego, Calif., 309–310.
Ambraseys, N., 1992. Soil mechanics and engineering seismology Invited Lecture, Proc. 2nd Natl. Conf. Geotechn. Eng., Thessaloniki, pp. xxi–xlii.
Ambraseys, N. N., Jackson, J.A. (1998). "Faulting associated with historical and recent
earthquakes in the Eastern Mediterranean region." Geophysical Journal International 133(2): 390-406.
Bonilla, Mark and Lienkaemper [1984], In: Bullen, K. E. and Bolt, B. A. An Introduction to the Theory of Seismology (1993), 4th ed., Cambridge.
Darawcheh, R., et al. (2000). "THE 9 JULY 551 AD BEIRUT EARTHQUAKE, EASTERN MEDITERRANEAN REGION." Journal of Earthquake Engineering 4(4): 403-414.
Hanks, T. C. and W. H. Bakun (2008). "M-log A observations for recent large earthquakes." Bulletin of the Seismological Society of America 98(1): 490-494.
Wells, D. L. and K. J. Coppersmith (1994). "New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement."
Bulletin of the Seismological Society of America 84(4): 974-1002,A1001-A1004,B1001-B1011,C1001-C1049.
Wesnousky, S. (2008). "Displacement and Geometrical Characteristics of Earthquake Surface Ruptures: Issues and Implications for Seismic-Hazard
Analysis and the Process of Earthquake Rupture." Bulletin of The Seismological Society of America - BULL SEISMOL SOC AMER 98.
The value given for Intensity with site effect removed is how much you should subtract from your Intensity estimate to obtain a pre-amplification value for Intensity. For example if the output is 0.5 and you estimated an Intensity of 8, your pre-amplification Intensity is now 7.5. An Intensity estimate with the site effect removed is helpful in producing an Intensity Map that will do a better job of "triangulating" the epicentral area. If you enter a V_{S30} greater than 655 m/s you will get a positive number, indicating that the site amplifies seismic energy. If you enter a V_{S30} less than 655 m/s you will get a negative number, indicating that the site attenuates seismic energy rather than amplifying it. Intensity Reduction (I_{reduction}) is calculated based on Equation 6 from Darvasi and Agnon (2019).
V_{S30} is the average seismic shear-wave velocity from the surface to a depth of 30 meters at earthquake frequencies (below ~5 Hz.). Darvasi and Agnon (2019) estimated V_{S30} for a number of sites in Israel. If you get V_{S30} from a well log, you will need to correct for intrinsic dispersion. There is a seperate geometric dispersion correction usually applied when processing the waveforms however geometric dispersion corrections are typically applied to a borehole Flexural mode generated from a Dipole source and for Dipole sources propagating in the first 30 meters of soft sediments, modal composition is typically dominated by the Stoneley wave. Shear from Stoneley estimates are approximate at best. This is a subject not well understood and widely ignored by the Geotechnical community and/or Civil Engineers but understood by a few specialists in borehole acoustics. Other considerations will apply if you get V_{S30} value from a cross well survey or a shallow seismic survey where the primary consideration is converting shear slowness from survey frequency to Earthquake frequency. There are also ways to estimate shear slowness from SPT & CPT tests.
Variable | Input | Units | Notes |
---|---|---|---|
m/s | Enter a value of 655 for no site effect Equation comes from Darvasi and Agnon (2019) |
||
Variable | Output - Site Effect Removal | Units | Notes |
unitless | Reduce Intensity Estimate by this amount to get a pre-amplification value of Intensity |
Salamon et. al. (2010) noted that seismic amplification could occur on slopes greater than 60 degrees where the slope
height is roughly equal to one fifth of a seismic wavelength. Turning this relationship around, the frequency at which
this effect will occur is defined as follows :
f = V_{S}/(5*H)
wheref = frequency (Hz.)
V_{S} = Shear Wave Velocity (m/s)
H = slope height in meters
Source -
Salamon et. al. (2010)
Variable | Input | Units | Notes |
---|---|---|---|
m/s | Shear Wave Velocity | ||
m | Slope Height | ||
Variable | Output | Units | Notes |
Hz. | Frequency |
Variable | Input | Units | Notes |
---|---|---|---|
g | Peak Horizontal Ground Acceleration | ||
km. | Distance to earthquake producing fault | ||
unitless | Site Effect due to Topographic or Ridge Effect (set to 1 to assume no site effect) |
||
Variable | Output - Site Effect not considered | Units | Notes |
unitless | Conversion from PGA to Intensity using Wald et al (1999) | ||
unitless | Attenuation relationship of Hough and Avni (2009) used to calculate Magnitude |
||
Variable | Output - Site Effect removed | Units | Notes |
unitless | Conversion from PGA to Intensity using Wald et al (1999) | ||
unitless | Attenuation relationship of Hough and Avni (2009) used to calculate Magnitude |
Hough, S. E., and R. Avni (2009). "The 1170 and 1202 Dead Sea Rift earthquakes and
long-term magnitude distribution on the Dead Sea fault zone." Isr. J. Earth Sci. 58(3-4): 295-308.
Massa, M., et al. (2010). "An Experimental Approach for Estimating Seismic Amplification Effects at the Top of a Ridge, and
the Implication for Ground-Motion Predictions: The Case of Narni, Central Italy." Bulletin of the Seismological
Society of America 100(6): 3020-3034.
Wald, D. J., et al. (1999). "Relationships between Peak Ground Acceleration, Peak
Ground Velocity, and Modified Mercalli Intensity in California." Earthquake Spectra 15(3): 557-564.
Rodkin and Korzhenkov (2018) presented two ways to estimate Peak Ground Velocity (PGV) - the Tilt Method (my name) and the PGV estimation method (PGVEM - their name).
Structure | Height (m) | Thickness (m) | α - Critical Tilt Angle |
---|---|---|---|
Church | |||
House |
Variable | Input | Units | Notes |
---|---|---|---|
degrees | Critical Tilt Angle | ||
m | Wall Thickness | ||
Variable | Output - not considering a Site Effect | Units | Notes |
m/s | Peak Ground Velocity | ||
unitless | Intensity |
Variable | Input | Units | Notes |
---|---|---|---|
unitless | Coefficient of friction | ||
cm. | Displacement of masonry | ||
Variable | Output - not considering a Site Effect | Units | Notes |
m/s | Peak Ground Velocity | ||
unitless | Intensity |
Korzhenkov, A. M. and E. Mazor (2014). "Archaeoseismological damage patterns at the ancient ruins at Rehovot-ba-Negev, Israel."
Archaeologischer Anzeiger: 75–92-75–92.
Rodkin, M. V. and A. M. Korzhenkov (2018). "Estimation of maximum mass velocity from macroseismic data:
A new method and application to archeoseismological data." Geodesy and Geodynamics.
Wald, D. J., et al. (1999). "Relationships between Peak Ground Acceleration, Peak
Ground Velocity, and Modified Mercalli Intensity in California." Earthquake Spectra 15(3): 557-564.
Variable | Input | Units | Notes |
---|---|---|---|
unitless | |||
degrees | |||
cm. | Wechsler et al (2009) recommends a value of 5 or 10 | ||
km. | Distance to nearest earthquake producing fault | ||
Variable | Output (No Site Effect) |
Units | Notes |
g | minimum acceleration to induce slide | ||
unitless | Conversion from a_{c} to I using Wald et al (1999) | ||
unitless | Attenuation relationship of Hough and Avni (2009) used to calculate Magnitude from I and R |
||
m/s | Calculated from eqn. 2 of Wechsler et al (2009) | ||
m/s | Calculated from eqn. 3.17 of (Kramer, 1996:87) | ||
unitless | calculated from eqn. 3 of
Wechsler et al (2009) which comes from Katz and Crouvi (2007) |
||
Variable | Input | Units | Notes |
unitless | Site Effect due to Topographic or Ridge Effect (set to 1 to assume no site effect) | ||
Variable | Output (Site Effect) |
Units | Notes |
unitless | Intensity with Topographic Effect removed | ||
unitless | Magnitude with Topographic Effect removed - using Hough and Avni (2009) | ||
unitless | Moment Magnitude with Topographic Effect removed M_{W} from eqn. 3 of Wechsler et al (2009) which comes from Katz and Crouvi (2007) |
Hough, S. E., and R. Avni (2009). "The 1170 and 1202 Dead Sea Rift earthquakes and
long-term magnitude distribution on the Dead Sea fault zone." Isr. J. Earth Sci. 58(3-4): 295-308.
Jibson, R. W. (1996). "Use of landslides for paleoseismic analysis." Engineering Geology 43(4): 291-323.
Jibson, R. W., et al. (2000). "A method for producing digital probabilistic seismic landslide hazard maps." Engineering Geology 58(3): 271-289.
Katz, O. and O. Crouvi (2007). "The geotechnical effects of long human habitation (Less Than 2000 years):
Earthquake induced landslide hazard in the city of Zefat, northern Israel." Engineering Geology 95(3–4): 57-78.
Massa, M., et al. (2010). "An Experimental Approach for Estimating Seismic Amplification Effects at the Top of a Ridge, and the Implication for Ground-Motion Predictions:
The Case of Narni, Central Italy." Bulletin of the Seismological Society of America 100(6): 3020-3034.
Miles and Keefer (2001), Seismic Landslide Hazard for the City of Berkeley, California, USGS Miscellaneous Field Studies Map 2378
Newmark, N. M. (1965). "Effects of earthquakes on dams and embankments." Géotechnique 15(2): 139-160.
Wald, D. J., et al. (1999). "Relationships between Peak Ground Acceleration, Peak
Ground Velocity, and Modified Mercalli Intensity in California." Earthquake Spectra 15(3): 557-564.
Wechsler, N., et al. (2009). "Estimating location and size of historical earthquake by combining archaeology and geology in Umm-El-Qanatir, Dead Sea Transform." Natural Hazards 50(1): 27-43.
Salamon and Di Manna (2019) created a bounding envelope for landslide tsunamis based on a curated data set.
Obermeier (1996) supplied a chart which can be used to estimate PGA (Peak Ground Acceleration) of earthquake induced Sand Boils.
Variable | Input | Units | Notes |
---|---|---|---|
g | Peak Horizontal Ground Acceleration | ||
Variable | Output (No Site Effect) |
Units | Notes |
unitless | Conversion from PGA to Intensity using Wald et al (1999) |
Ishihara, K., 1985. Stability of natural deposits during earthquakes. In:
Proceedings of the 11th International Conference on Soil Mechanics and
Foundation Engineering. San Francisco, CA, USA, 1, 321–376.
Obermeier, S. F. (1996). "Use of liquefaction-induced features for paleoseismic analysis — An overview of
how seismic liquefaction features can be distinguished from other features and how their regional
distribution and properties of source sediment can be used to infer the location and strength of
Holocene paleo-earthquakes." Engineering Geology 44(1–4): 1-76.
Rateria, G. and B. W. Maurer (2022). "Evaluation and updating of Ishihara’s (1985) model for liquefaction
surface expression, with insights from machine and deep learning." Soils and Foundations 62(3): 101131.
Wald, D. J., et al. (1999). "Relationships between Peak Ground Acceleration, Peak
Ground Velocity, and Modified Mercalli Intensity in California." Earthquake Spectra 15(3): 557-564.
Variable | Input | Units | Notes |
---|---|---|---|
g | Peak Horizontal Ground Acceleration | ||
Variable | Output - Site Effect not considered | Units | Notes |
unitless | Conversion from PGA to Intensity using Wald et al (1999) |
Variable | Input | Units | Notes |
---|---|---|---|
unitless | Surface Magnitude | ||
Variable | Output | Units | Notes |
unitless | Moment Magnitude |
Darawcheh, R., et al. (2021). "Empirical relationship for assessing the near-field horizontal coseismic displacement
using GPS Seismology data." Geofísica Internacional 60: 31-50.
Scordilis, E. M. (2006). "Empirical Global Relations Converting MS and mb to Moment Magnitude." Journal of Seismology 10(2): 225-236.
Wald, D. J., et al. (1999). "Relationships between Peak Ground Acceleration, Peak
Ground Velocity, and Modified Mercalli Intensity in California." Earthquake Spectra 15(3): 557-564.