Earthquake Sound Travel and Pseudo-Dionysius of Tell-Mahre

In the Chronicle of Zuqnin, Pseudo-Dionysius of Tell Mahre reports on the sound of a distant earthquake the night before the earthquake which struck Manbij (aka Mabbug). In an English translation of Part 4 by Harrak (1999:177-178) we can read:

[747-748] The year one thousand and fifty nine:

... A tremor took place during the night, and something like the noise of a roaring bull was heard from a great distance.

While earthquake sound perception depends on a number of factors, it is feasible that a large earthquake, for example from the northern end of the Sea of Galilee, could have been heard ~450 km. away in Manbij (aka Mabbug). Tosi et al (2012) developed a relationship for earthquake perceptibility by examining a survey of ~70,0000 respondents in Italy from smaller magnitude earthquakes (M 5.0-5.5). The input variables are magnitude and distance. In the calculator below, this relationship predicts that ~20% of a population would notice an M 7.0 earthquake at a distance of 450 km. However, it is likely that this relationship underestimates perceptibility for larger magnitude earthquakes (e.g. M 7.0). In this eyewitness account from the 1994 M 6.7 Northridge earthquake, a respondent describes earthquake sounds which woke them up ~115 km. from the epicenter. Because Earthquake sound perception depends on a number of factors, it is difficult to predict so the only conclusion that can be made is that the report by Pseudo-Dionysius of Tell Mahre that a distant earthquake perhaps 450 km. away was heard as a rumble the night before is a credible one. Earthquake researcher Patrizia Tobi contributed the following comments (personal communication, 2021) regarding the perception of earthquake sounds.

In my paper the results are based on many earthquakes and the phenomenon may appear continuous, but in reality the earthquake sound is very variable and does not depend only on the intensity of the ground motion. For example, the study of infrasound showed that waves propagating through the atmosphere are produced by earthquakes through 3 distinct mechanisms: direct generation from seismic waves below the station, propagation of the sound wave produced in the epicenter region by strong ground motion, and radiation from a secondary source such as a high mountain. This implies that the soil composition, rock type, and topography of each site cannot be neglected. These factors, added to others that affect sound propagation in the atmosphere, such as pressure and temperature variations, make the problem very complicated to model.

Calculator - Earthquake perception at distance - Tosi et al (2012)

Source - Tosi et al (2012) - based on a study of earthquakes and fitted for Local Magnitudes between 5.0 and 5.5

The Higher Magnitude Adjustment is a thought experiment to extend the equation of Tosi et al (2012) to higher magnitude (and therefore louder) earthquakes. If, for example, the eyewitness testimony from the 1994 M 6.7 Northridge earthquake indicates an earthquake loud enough to wake someone up at a distance of 115 km. from the epicenter, we can assign a perceptibility of 100% at this distance and create a calibration point. An addition of 51% would need to be added to the result of Tosi et al (2012)'s equation to achieve 100% perceptibility. Adding this 51% to the perceptibility of one of the Sabbatical Year Earthquakes results in a perceptibility of ~72% for an M 7 earthquake where the nearest fault break was at the north end of the Sea of Galilee ~450 km. away. Without the Higher Magnitude Adjustment, perceptibility is ~21%. Thus we can likely constrain perceptibility to between 21% and 72%. In other words, between 21% and 72% of the people in Manbij (aka Mabbug) likely did experience a rumble from the Sabbatical Year earthquake the night before a large earthquake is reported to have collapsed a church in Manbij (aka Mabbug)

Variable	Input	Units	Notes
Distance to epicenter		km.
Local Magnitude		unitless
Higher Magnitude Adjustment		unitless
Variable	Output	Units	Notes
Perceptibility		%	Percentage of people who hear the rumble

Calculate   

Experimental Calculator - Earthquake Sound - Tosi et al (2000)

Source - Tosi et al (2000)

Variable	Input	Units	Notes
Mw			Moment Magnitude
ρ		g/cc	Crust Density
r		km.	Source Distance
α		km./s	P wave Velocity in the crust (?) - Typical values are 5-8 km./s
RP			Radiation Pattern of the P-wave
tr		sec.	Rise time
f		Hz.	Frequency
Cϴ		?	Transmission Coefficient of the compressional wave in the passage ground-air, function of the angle of incidence ϴ - value needed
ρa		kg/m3	Air density
V		m/s	Speed of sound in air
Variable	Output	Units	Notes
Mo		N-m	Seismic Moment
U		µ?	Ground Displacement
Uf		µ?	Ground Displacement at frequency
P		µbar	Pressure
PdB		dB	Pressure

Calculate   

Notes

Theoretical Model of Earthquake Sound

Tosi et al (2000)

Units

1 Pa = 1 N/m2
1 dyne is the force required to accelerate 1 gram 1 cm/s2
1 N = 100,000 dynes
1 bar = 10^6 dynes/cm2

References

Articles and Books

Artru et al (2004) Acoustic waves generated from seismic surface waves: propagation properties determined from Doppler sounding observations and normal-mode modelling

Brune, J. N. (1970). "Tectonic stress and the spectra of seismic shear waves from earthquakes." Journal of Geophysical Research (1896-1977) 75(26): 4997-5009.

Davison, C. (1938), Earthquake sounds, Bull. Seismol. Soc. Am., 28, 147-161.

Gold, T., and S. Soter (1979), Brontides: Natural explosive noises, Science, 204, 371-375

Hill, D. P., F. G. Fisher, K. M. Lahr, and J. M. Coakley (1976), Earthquake sounds generated by body-wave ground motion, Bull. Seismol. Soc. Am., 66, 1159-1172.

Le Pichon, A., J. Guilbert, A. Vega, M. Games, and N. Brachet (2002), Ground-coupled air waves and diffracted infrasound firm the Arequipa earthquake of June 23, 2001, Geophys. Res. Lett., 29(18), 1886

Michael, A. J. Earthquake Sounds at the Encyclopedia of Solid Earth Geophysics

Mikumo, T. (1968), Atmospheric pressure waves and tectonic deformation associated with the Alaskan earthquake of March 28,1964, J. Geophys. Res., 73, 2009-2025

Sbarra, P., et al. (2014). "How Observer Conditions Impact Earthquake Perception." Seismological Research Letters 85: 306-313.

Sylvander, M., and D. G. Mogos (2005), The sounds of small earthquakes: Quantitative results from a study of regional macroseismic bulletins, Bull. Seismol. Soc. Am., 95, 1510-1515

Sylvander, M., C. Ponsolles, S. Benahmed, and J.-F. Fels (2007), Seismo-acoustic recordings of small earthquakes in the Pyrenees: Experimental results, Bull. Seismol. Soc. Am., 97, 294-304

Thouvenot, F. and M. Bouchon (2008). What is the Lowest Magnitude Threshold at Which an Earthquake can be Felt or Heard, or Objects Thrown into the Air?: 313-326.

Tosi, P., et al. (2000). "Spatial patterns of earthquake sounds and seismic source geometry." Geophysical Research Letters 27(17): 2749-2752.

Tosi, P., et al. (2012). "Earthquake sound perception." Geophysical Research Letters 39.

Young, J. M., and G. E. Greene (1982), Anomalous infrasound generated by the Alaskan earthquake of 28 March 1964, J. Acoust. Soc. Am., 71, 334-339

Websites, Audio, and Video

Google Scholar Page for Patrizia Tosi

Catalog of Earthquake-Related Sounds Compiled by Karl V. Steinbrugge - Recording #21 has sounds recorded 250 km. away from the epicenter 1983 M 7.7 earthquake.

Eyewitness testimony about Earthquake sound ~115 km. from the epicenter of the 1994 M 6.7 Northridge Quake

Earthquake reports from the 1813 New Madrid earthquakes (M = 7.2-8.20