Mainshock Ratio Module:
Analytical Development and Application
Modelling Approach and Caveats
The method relies on comparing ratios based on counts of the numbers of quakes occurring at different magnitude levels during the final year or two preceding mainshocks.. However, it is important to note that, in the absence of other models, these ratios do not necessarily indicate that a mainshock is imminent. There are specific caveats: the approach does not apply to large foreshocks, aftershocks, or events associated with them. Such occurrences must be avoided when calculating ratios for mainshock prediction. For example, Cape Mendocino’s M 7.0 data (Figure 1) were derived from only the previous nine months to exclude a major foreshock.
Model Requirements and Consistency
This module serves as the standard against which future events must be assessed if realistic forecasts are to be made. Notably, the slope for Californian events remained largely unchanged even after incorporating data from other regions worldwide. Detailed records of these zones yet to be made available in a future submission.
Overview of the Mainshock Ratio Module
In early 2025, the author identified strong correlations between the frequency of earthquakes at different magnitude levels across large regions globally (Figure 2). This observation led to further research into how event ratios relate to the magnitude of impending mainshocks. The resulting linear correlation (Figure 1) provides an independent estimate for the size of a forthcoming mainshock, which serves as a check on other forecasting methods. The equation for this linear correlation is:
Y = 4.599 + 27.38X
where X is the derived ratio and Y is the resolution of the equation.
The “Mainshock Ratio Module” assesses ratios between different magnitude levels, for a relatively short period of less than two years preceding a likely forthcoming mainshock, whereas the principal “Mainshock Analytical Module”, described in another chapter, analyses the largest yearly events since the previous mainshock to develop a forecasting model.
The principal function of this Mainshock Ratio Module, discussed here, is to determine from using this modelling whether a region's earthquake activity at specific magnitude levels is sufficient to support—or at least make possible—a forecast of a particular mainshock. However, a specific ratio does not guarantee that a mainshock will occur; it only indicates the possibility.
Development and Application
Figure 2 illustrates the strong correlation between M 5 and M 6 events globally from 1993 to 2024. Subsequent investigations into correlations between different magnitude levels revealed how these relationships shift relative to the size of a forthcoming mainshock, resulting in the highly significant linear correlation shown in Figure 1. The ratios used are based on comparing counts of M 3/2, 4/3, 5/4, etc., while disregarding obvious spurious results: for example, counts of 3/2 do not always provide a realistic answer to clusters of small quakes like ‘earthquake swarms’.
Similarly, ratios should approximate to realistic regional values and ideally, from the equation for Figure 1, they will provide support showing that the magnitude forecast for the next mainshock is indeed possible in the expected period.
For example, now in mid-April 2026, the author has forecast that a M 7.2 is imminent in Southern California, and has found that counts of M 4/3 and M 5/4 both give results forecasting a M 7.2, based on events since Jan 1, 2025, within a 1,000 km radius of an offshore centre: Lat 30.7035 Lon -116.391.
The linear model was refined using the author’s version of a Bootstrap-Method*, working backwards to pinpoint the parameter responsible for most of the previous scatter of points about the line in Figure 1. For earthquakes, this was solely the size of the individual search zones, which now define a future standard for each zone, to be specified separately.
Data for most zones are drawn from areas of at least 500 km radius over one to two years, with several caveats. Large foreshocks and aftershocks from previous mainshocks must be avoided—sometimes requiring data from periods of only six to nine months. Spurious results may occur if ratios yield a magnitude 10 or any magnitude foreign to the region. These anomalies are under investigation, but the separate Mainshock Analytical Module provides a robust benchmark for the expected size of a mainshock (not its timing). Checking current ratios allows assessment of whether the relative abundances of earthquakes at specific magnitude levels can support the forecast magnitude of a forthcoming mainshock in the same period of time that other modules have indicated.
Specific zones are yet to be detailed on an attached data sheet. The module’s final formulation was completed in the last week of June 2025.
*https://www.sciencedirect.com/topics/engineering/bootstrap-method
Page updated April 18 , 2026.