Forming Hypotheses About the Chances of an Earthquake

  One can study the USGS Ridgecrest area earthquake data and try to come up with some hypotheses about factors indicating the likelihood of the occurrence of an earthquake. The horizontal axis is the day of the year (doy).

When we compare this data with JPL's Horizons Lunar data we encounter some factors that seem to correlate well with the occurrence of the M6.4 and M7.1 and we get a number of coincidental events such as the relative force acting on the Earth's surface, the declination of the Moon and the Moon-Earth-Sun angle (∠M-E-S). The ratio of the average range of the Moon and its value at some time can be represent by the dimensionless factor φ and ϕ² is a measure of the relative force acting on a portion of the Earth's surface. The relative force was near a maximum at the time of the two earthquakes.

The sine of the Moon's declination and the cosine of M-E-S angle were also near maximums.

The product of the first and third factors might be used to indicate the lunar perigee and syzygy alignment which tells us when there will be a Supermoon. The product of the first and second is a measure of the relative torque acting on the Earth's equatorial bulge. If we combine all three factors we also get a good agreement of their maximum with the time of the two earthquakes.

If we look at this indicator over the entire year we see that it was near a global maximum at the times of the two earthquakes.

It will be interesting to see what the plots of the earthquake data look like over the next couple of months or so.

Supplemental (Jul 19): Replaced the histogram above with one that included some missing days at the end. One can modify the definitions of the indices to let them represent relative quantities better such as replacing sin(dec) with μ=sin(dec)/sin(ι) where ι=23.473 deg is the inclination of the ecliptic. This makes the combined indicator a little more meaningful.

The doy of the indicator peaks can be converted into calendar dates.

It should be noted that one cannot accurately evaluate the indices based on a small sample of data over a short period of time. The peaks of the indices are likely to diverge as the time increases since there are different periods associated with each index. We may be able to determine which of the indices best match the pattern of earthquake activity over time.