Tikalon Blog by Dev Gualtieri

Threshold Earthquakes

June 17, 2019

Earthquakes are rare in Northern New Jersey, the home of Tikalon. That's why I decided that there was something wrong with the wheels of my office chair when I was shaken from my spreadsheet-induced stupor in the afternoon of August 23, 2011. While I was examining the chair, the doors of my filing cabinet began to shake and I felt the Earth move. These were the effects of the 5.8 magnitude Virginia earthquake whose epicenter was 300 miles distant.

The epicenter of the August 23, 2011, Virginia earthquake, marked by the star, was at 37° 56' 10" North Latitude, 77° 55' 59" West Longitude, about 300 miles from Tikalon's Northern New Jersey home.

(Base map from the United States Geological Survey, modified using Inkscape. Click for larger image.)

While this earthquake was potentially felt by about a quarter of the US population, principally because the affected region is heavily populated, this earthquake was more of a nuisance than a disaster. There were no fatalities, and the damage is estimated to be less than $300 million. That's a consequence of the earthquake's having the relatively low magnitude of 5.8.

Earthquake magnitudes are calculated using the moment magnitude scale, an improvement of the Richter magnitude scale that was commonly used in the 20th century. The moment magnitude, M_w is calculated as

M_w = 2/3 log₁₀(M₀) - 10.7

where M₀ is the seismic moment in units of dyne-cm (10⁻⁷ N-m). The scaling factor of 2/3 and the offset of 10.7 are selected to make values on the moment magnitude scale closely conform to those on the Richter magnitude scale.

Since the moment magnitude scale is a logarithmic scale, a change in value of a single unit signals a considerable increase in an earthquake's damage potential. This is demonstrated in recent history by the 2011 Tōhoku earthquake and its resultant tsunami. That 9.0 magnitude quake killed more than 10,000 people, and it also resulted in the Fukushima Daiichi nuclear disaster when the tsunami interrupted power to the reactor cooling systems and caused reactor core meltdowns.

Physicist, Richard Feynman, so aptly said, "There's plenty of room at the bottom." Below the devastation of a 9.0 magnitude earthquake and the annoyance of a 5.0 magnitude earthquake are a multitude of lesser earthquakes, many of which are not felt by humans and just barely register on sensitive seismometers. Earthquake magnitudes follow a power law distribution in which smaller earthquakes occur much more often than larger earthquakes. There are about a million earthquakes at magnitude 2.5 and below that are not felt but happen each year.[1] On February 2, 2009, a magnitude-3.0 earthquake occurred with an epicenter just seven miles from Tikalon's home, and it passed unnoticed.

Major earthquakes in Morris County, New Jersey

Cataloged earthquakes in Tikalon's Morris County, New Jersey, home.

All these earthquakes are less than 3.4 magnitude.

New Jersey State Geological Survey image.)

This seismics background is so large that seismic isolation is required to allow the proper functioning of the Laser Interferometer Gravitational-Wave Observatory (LIGO) that's designed to detect the very faint vibrations of space produced by gravitational waves. Multiple levels of isolation are needed to allow LIGO's detection sensitivity of 10^-19 meter. For comparison, the ground slip for a magnitude 9 earthquake is several tens of meters.

Earthquake affects are found at considerable distances from the epicenter. While the mechanical effects of earthquakes propagate at the speed of sound, the a href="https://en.wikipedia.org/wiki/Gravitation">gravity effects travel at the speed of light. Acceleration from gravity change were observed in China and South Korea immediately after the Tohoku earthquake.[2] This leads to the idea that gravity signals can be used as an rapid-warning that earthquakes have begun.[3] While such a rapid warning would be welcome, scientists have struggled to find an effective indicator that an earthquake is pending long before the event, and I've detailed historical approaches in an earlier article (Earthquake Prediction, February 18, 2011).

In 1989, Stanford University electrical engineer, Antony Fraser-Smith, made the chance observation that the Loma Prieta earthquake produced high intensity ULF radio signals in the days prior to the quake.[4] Three hours before this earthquake, the ULF signal was 20-30 times larger than the typical signal level.[4] Correlation of low frequency electromagnetic activity and seismic activity has been documented in satellite observations.[5-7]

While all prediction methods based on a single effect have proven ineffective, there's the idea that a combination of observations might yield earthquake prediction using pattern recognition. This method was pioneered by Russian mathematical physicist and seismologist, Vladimir Keilis-Borok (1921-2013). While earthquake swarms are thought to be one possible indicator of an impending destructive earthquake, their predictive strength is just as weak as any other single indicator.[7-8] More data on background seismicity might still be helpful for the pattern recognition approach.

Seismogram of the 1906 San Francisco earthquake, as recorded in Gottingen, Germany.

Half a world away - Seismogram of the 1906 San Francisco earthquake, as recorded in Göttingen, Germany. (image via the USGS website.)

A team of geoscientists from the California Institute of Technology (Pasadena, California), Los Alamos National Laboratory (Los Alamos, New Mexico), and the Scripps Institution of Oceanography (La Jolla, California) have just published a study of the occurrence of tiny earthquakes that occurred over a recent 10-year period in Southern California.[10-14] Their data were collected from about 400 seismic sensors. From 2008 to 2017, they detected 1.81 million such tiny earthquakes in that region, a ten-fold increase in number over previous measurements. This detection was made despite seismic interference from environmental noise sources such as road vehicles, building construction, and ocean waves.[10-13]

This Mining Seismic Wavefields research project began in 2016 to examine the entire continuous dataset of the Southern California Seismic Network.[12] The data analysis was enabled by a computer cluster of 200 graphics processing units housed at Caltech for tens of thousands of hours of initial data screening followed by hundreds of thousands of hours of computation on other computers.[11,13] The method used to overcome the low signal-to-noise ratio was template matching in which the data were selected based on waveforms of known earthquakes.[10-11] Template matching works best when cross-correlations can be made between sensors located within 2 miles of each other.[11]

The essential problem that template matching solves is to distinguish such small earthquakes from the background noise.[12] This was only possible through a machine-learning system trained with millions of examples of both real earthquake signals and other vibrations.[12] Says Caltech's Zachary Ross, lead author of the study, "It's not that we didn't know these small earthquakes were occurring. The problem is that they can be very difficult to spot amid all of the noise."[11] Borrowing waveform analysis techniques from audio signal processing, the team developed an algorithm called FAST (Fingerprinting and Similarity Thresholding).[12]

The analysis revealed that there are about 495 earthquakes daily across Southern California, and these occur at an average interval of about three minutes.[11] The previous estimate was that earthquakes occur about 30 minutes apart.[11] This 10-fold increase in number arises from the study's detection of earthquakes in the -2.0 to 1.7 range.[11]

Seismic swarm activity associated with the Cahuilla earthquake in Southern California's Anza Valley.

Template matching shows the swarm of small earthquakes from 2016-2017 in greater detail with the color of each seismic event indicating its depth.

The gradient of depth indicates the shallow-to-deep slant of the fault that was not apparent from earlier data.

(Still image from a California Institute of Technology YouTube Video.[14] Click for larger image.)

The expanded earthquake catalog reveals foreshocks of major earthquakes that were previously undetected and the evolution of swarms of earthquakes.[11] This analysis technique could also be used to study slow slip that progresses over a time period of months to years, and it might also be useful for earthquake prediction.[12-13] This research was funded by the National Science Foundation and the United States Geological Survey.[11]

Threshold Earthquakes

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