Chikorita Magnitude

The Chikorita Magnitude is a measure of the strength of earthquakes developed by USER: CHIKORITAROBLOXHURRICANES and presented in this landmark 2022 article, where he called it "Chikorita Magnitude". It is unrevised as of now.

Formula

Variable Definitions

${\displaystyle A=}$Downdip rupture length in miles

${\displaystyle B=}$Rupture area in square miles

${\displaystyle C=}$Surface rupture length in miles

${\displaystyle D = }$Subsurface rupture length in miles

${\displaystyle E =}$Average displacement in feet

${\displaystyle F = }$Fault slip rate in inches per year

Helper Variable Definitions

$${\displaystyle M_{a}=\frac{\ln\left(\frac{128A}{11}\right)}{\ln\left(2\right)}}$$

$${\displaystyle M_{b}=-\frac{\ln\left(\frac{500246412961}{4586471424000000B}\right)}{-\ln\left(29\right)+\ln\left(5\right)+\ln\left(3\right)+4\ln\left(2\right)}}$$

$${\displaystyle M_{c}=-\frac{\ln\left(\frac{1953125}{4586471424C}\right)}{-\ln\left(5\right)+\ln\left(3\right)+3\ln\left(2\right)}}$$$${\displaystyle M_{d}=\frac{\ln\left(\frac{8192D}{15}\right)}{2\ln\left(2\right)}}$$$${\displaystyle M_{e}=-\frac{\ln\left(\frac{5764801}{105046700288E}\right)}{\ln\left(17\right)-\ln\left(7\right)+\ln\left(2\right)}}$$$${\displaystyle M_{f}=-\frac{\ln\left(\frac{815730721}{10485760000000000F}\right)}{-\ln\left(13\right)+\ln\left(5\right)+4\ln\left(2\right)}}$$To calculate Chikorita Magnitude...

$${\displaystyle M_{chikorita}=\frac{M_{a}+M_{b}+M_{c}+M_{d}+M_{e}+M_{f}}{6}}$$Raw version:

$${\displaystyle M_{chikorita}=\frac{-\frac{\ln\left(\frac{815730721}{10485760000000000F}\right)}{-\ln\left(13\right)+\ln\left(5\right)+4\ln\left(2\right)}-\frac{\ln\left(\frac{5764801}{105046700288E}\right)}{\ln\left(17\right)-\ln\left(7\right)+\ln\left(2\right)}+\frac{\ln\left(\frac{8192D}{15}\right)}{2\ln\left(2\right)}-\frac{\ln\left(\frac{1953125}{4586471424C}\right)}{-\ln\left(5\right)+\ln\left(3\right)+3\ln\left(2\right)}-\frac{\ln\left(\frac{500246412961}{4586471424000000B}\right)}{-\ln\left(29\right)+\ln\left(5\right)+\ln\left(3\right)+4\ln\left(2\right)}+\frac{\ln\left(\frac{128A}{11}\right)}{\ln\left(2\right)}}{6}}$$Derivation

The scale is derived by exponential interpolation between the properties of the earthquake at seismic moment magnitudes 7 and 8. The results are then averaged using a equally weighted arithmetic mean.

Properties:

• The original unrevised Chikorita Magnitude has the most certainty of all the seismic moment magnitudes, even when a equal uncertainty exists for at least one variable.
• However, the Chikorita Magnitude assumes each of the weights is equally weighted, which might not be true for some earthquakes.

Possible Revisions:

It is possible that the scale could be revised by the following:

Let ${\displaystyle \sum _{n=1}^{6}\lambda _{n}=1,\lambda _{i}\geq 0\operatorname {for} 1\leq i\leq 6,i\in \mathbb {Z} }$, then ${\displaystyle M_{chikorita}=\sum _{n=1}^{6}\lambda _{n}M_{n}}$ (weighted mean).

Properties of Revised Scale:

• M_chikorita is bounded between the smallest possible magnitude and the largest possible magnitude.
  • Because of those bounds, it narrows the range of possible seismic moment magnitudes.
  • However, if uncertainty exists in at least one of those variables, the range could widen.