Modern Modeling Determines Magnitudes of Historic Earthquakes

Researchers used a modeling approach to study the magnitudes of California’s largest historical earthquakes, finding that the 1906 San Francisco quake was magnitude-7.9.

By Lauren Milideo, Ph.D., science writer (@lwritesscience)

Citation: Milideo, L., 2021, Modern Modeling Determines Magnitudes of Historic Earthquakes, Temblor,

On Dec. 15, 2020, California lightly shook some of its residents when a pair of earthquakes struck near the town of Morgan Hill, south of the San Francisco Bay area. Scientists quickly got a handle on the quakes’ magnitudes via an extensive system of on-the-ground seismographic equipment, as well as real-time reports from the public, noting the intensity of shaking they’d experienced moments after the rumbling subsided. Planning for these quakes — and the bigger ones that will strike California in the future — depends on knowledge of past, historic earthquake magnitudes and their shaking intensities to understand future quakes. But without modern equipment – and without Californians volunteering information about whether they “felt it” — how can we know these historic quakes’ magnitudes? Newspaper accounts and other records can give scientists some idea, but do not substitute for measurements or data-informed estimates.

New research explores how scientists can approximate the magnitude of California’s three biggest historic earthquakes. The idea for the study took shape following the 2019 Ridgecrest, California, earthquake sequence, says lead author and U.S. Geological Survey (USGS) geophysicist Susan Hough. As reports poured into the USGS “Did You Feel It?” system from the widely felt event, scientists including Hough and her colleagues noted a strong correlation between crowdsourced reports of what Californians reported on the ground and instrument-measured data. After making this observation, Hough says, “I thought, can you close the loop for historical earthquakes?”

Closing the loop

The team looked at the three largest known historical California earthquakes: the 1857 Fort Tejon earthquake, the 1872 Owens Valley earthquake and the 1906 San Francisco earthquake. To determine each earthquake’s magnitude, the researchers applied a method based on ground-motion models. This approach includes three pieces of information: magnitude of the quake itself, intensity of shaking at various locations determined from historical accounts using equations developed for this purpose, and distance of these locations from the earthquake’s epicenter. In the cases of California’s historical earthquakes, researchers knew approximately where the quakes had occurred and had at least some information about ground shaking intensity gleaned from previously studied historical newspaper reports. They used these two pieces of the puzzle — distance from the epicenter and degree of shaking intensity — to determine the third: the earthquake’s magnitude.

Black and white photo of damaged city buildings
Damage from the 1906 San Francisco earthquake. Credit: Chadwick, H. D., National Archives and Recordings Administration, public domain


The team needed to determine what magnitude would not only best fit the shaking intensity data they had, but also align with the degree of shaking experienced relative to distance from the quakes’ epicenters. Building on previously published models, Hough and her colleagues used these data to create a range of possible magnitude values for each quake and then looked at which value most closely matched other known parameters, such as geological data for the location, for each event. The team particularly used information derived from the California Historical Intensity Mapping Project.

Constraining the magnitude for the 1857 Fort Tejon quake proved challenging, as little recorded information was available regarding the earthquake’s intensity. Despite similar difficulties, the team determined that the 1872 Owens Valley earthquake was likely between magnitude 7.7 and 7.8. For the 1906 quake, Hough’s team used data gathered in the California Historical Intensity Mapping Project to arrive at an estimated magnitude 7.9, which lines up with previous approximations of the quake’s magnitude that had utilized the sparse instrumental and geodetic data available at the time.

Confirming the equations

To inform hazard maps, seismologists have developed equations to “predict what the shaking will be for a given magnitude and distance,” says Hough. “It’s encouraging that the equations seem to be quite good,” matching what other studies have found using seismological and geodetic data, “for even the biggest earthquakes that we expect in California,” she says.

The three studied earthquakes, despite the uncertainty about their exact size, are important not only historically, but also for current and future residents of California. “The prehistoric earthquakes are the biggest ones in the record and therefore the hazard models are totally driven by these rare events,” says Christie Rowe, an earthquake geologist at McGill University who was not involved with the research. She adds that California’s very brief record of earthquakes measured with modern equipment and methods leaves researchers and planners heavily dependent on just these three huge quakes.

The challenge with creating hazard maps, Hough says, is that although we know earthquakes on the scale of magnitude 7.9 are possible in California, we do not have any such earthquakes that were measured by modern instruments to inform the maps.

“This paper is really important,” says Rowe, “because what they’ve done is go back and apply modern [equations] that relate earthquake-radiated energy to the shaking that was actually experienced and apply that to these prehistoric earthquakes.”

This study “puts a ribbon around 7.9 as a magnitude for this very important [1906] earthquake,” says Hough. “It says that those equations are pretty good — they work all the way up to the biggest earthquakes we expect to see in California.”

Further Reading

Hough, S.E, Page, M., Salditch, L., Gallahue, M.M., Lucas, M.C., Neely, J.S., & Stein, S. (2020). Revisiting California’s Past Great Earthquakes and Long-Term Earthquake Rate. Bulletin of the Seismology Society of America.