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Epicentral Location Algorithms

References
References

Ambraseys, N. N. (1985). Intensity-attenuation and magnitude-intensity relationships for northwest European earthquakes . Earthquake Engineering & Structural Dynamics, 13(5), 733–778.

Bakun, W.H., & Wentworth, C.M. (1997). Estimating earthquake location and magnitude from seismic intensity data. Bulletin of the Seismological Society of America, 87(6), 1502–1521.
➔ Bakun and Wentworth method (BW97): Inverts observed intensities to locate epicenters and magnitudes by minimizing a cost function.

Bakun, W.H. (2006). Estimating locations and magnitudes of earthquakes in southern California from modified Mercalli intensities. Bulletin of the Seismological Society of America, 96(4A), 1278–1295.
➔ Application of BW97 with refinements to southern California.

Galli, P., & Galadini, F. (2003). Surface faulting during historical earthquakes in Italy: a review and a new case study. Earth-Science Reviews, 62(3-4), 73–94.
➔ Highlights multiple cases where earthquakes attributed to single epicenters were actually multi-segment ruptures.

Gasperini, P., Bernardini, F., Valensise, G., & Boschi, E. (1999). The attenuation of seismic intensity in Italy: A bilinear shape model with regional dependence . Bulletin of the Seismological Society of America, 89(4), 1184–1198.

Gasperini, P., Vannucci, G., Tripone, D., Boschi, E. (2010) The Location and Sizing of Historical Earthquakes Using the Attenuation of Macroseismic Intensity with Distance , Bulletin of the Seismological Society of America 100 (5A), 2035–2066.

Johnston, A.C. (1996). Seismic moment assessment of earthquakes in stable continental regions — III. New Madrid 1811–1812, Charleston 1886 and Lisbon 1755. Geophysical Journal International, 126(2), 314–344.
➔ Focuses heavily on moment-area relationships to assess rupture length and position for historical quakes.

Mäntyniemi, P., Tatevossian, R.E., and Tatevossian, T.N. (2014) Uncertain historical earthquakes and seismic hazard: theoretical and practical considerations, Geomatics, Natural Hazards and Risk, 5:1, 1-6

Mäntyniemi, P., Tatevossian, R. E., and Vakarchuk, R. N. (2017) On the Epicenter Determination of Historical Earthquakes Attested to by Sparse Intensity Data Sets, Bulletin of the Seismological Society of America, Vol. 107, No. 3, pp. –, June 2017

Montaldo, V., Rovida, A., D'Amico, V., & Locati, M. (2021). On the relocation of historical earthquakes in Italy using parametric and intensity data. Annals of Geophysics, 64(4).
➔ Recent methodological paper that discusses different strategies to relocate old earthquakes based on macroseismic parameters.

Musson, R.M.W. (1998). Intensity-based seismic risk assessment. Soil Dynamics and Earthquake Engineering, 17(1), 25–36.
➔ Discusses macroseismic field modeling including epicenter estimation.

Sieberg, A. (1932a). Erdbebengeographie. Borntraeger.

Sirovich, L. (1996) A Simple Algorithm for Tracing Synthetic Isoseismals, Bulletin of the Seismological Society of America 86 (4), 1019–1027.

Zohar, M. and Marco, S. (2012) Re-estimating the epicenter of the 1927 Jericho earthquake using spatial distributionof intensity data, Journal of Applied Geophysics 82 (2012) 19-29
➔ Pinpoints an epicentral region based on a grid of points, an attenuation relationship, and a table of IDPs. Demonstrated on data from 1927 Jericho Quake.

Notes

ChatGPT Summaries

Ambraseys (1985)

  • summarized by ChatGPT version 4o, 26 May 2025
Ambraseys (1985) developed an attenuation-based technique to estimate epicentral locations and focal depths for historical earthquakes in Northwest Europe using macroseismic intensity data. Building on Kovesligethy's and Sponheuer's methods, the approach uses a point-source radiation model where intensity decreases logarithmically with distance from the source, modified by energy absorption (α) and geometric spreading (n).

The intensity difference ΔI = I₀ - Iᵢ is modeled as a function of distance, source depth (h), and attenuation coefficients, through the equation:

ΔI = b · log[(Rᵢ / h)ⁿ · exp(α(Rᵢ - h))]

Least-squares regression is used to fit observed isoseismal radii and intensities, minimizing residuals to infer best-fit values of focal depth, geometric and anelastic attenuation, and intensity factor (b·n). Solutions require at least 3–4 isoseismals. Instrumental depth data, if available, can help decouple parameters. This model was applied to 270 well-documented events across the British Isles, France, Belgium, and the Netherlands, with corrections made for overestimated felt areas in older catalogs.

Notes

Bonus: Particularly Useful if You're Looking for "Line Epicenters" in Practice Bakun (2006) sometimes produces a probability density strip along a fault rather than a sharp point.