Use this seismology calculation to reproduce a stated convention, screen observations, or compare scenarios whose units, coordinate conventions, catalog selection, and model assumptions are known.

n_i

Required list. Event counts per magnitude bin.

M₀

Optional number. Central magnitude of the first bin.

ΔM

Optional number. Bin width.

The cited overview of Seismic magnitude scales supplies background for the terminology and domain context used by this tool.^[1]

Mc from the maximum-curvature (mode) of the binned frequency-magnitude distribution. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Mc

Returned number. Magnitude of the modal bin.

n_max

Returned number. Count in the modal bin.

• Earth structure, source geometry, path effects, site response, instrument response, catalog completeness, uncertainty, and the fitted range can dominate the accuracy of simplified seismic calculations.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

For analysis or hazard decisions, retain uncertainty and provenance and compare the result with waveform processing, calibrated regional models, and guidance from qualified seismologists or the responsible agency.

• Magnitude Frequency Entropy Shannon Calculator

  Shannon entropy H = −Σ p·log₂p over magnitude-bin probabilities.

• Network Detection Threshold Coverage Calculator

  Illustrative magnitude-of-completeness screening relation M_min ≈ 1.5 + log₁₀(r/km) using a detection radius of 1.5 times station spacing; it is not a calibrated network threshold.

• Antialias Filter Corner Nyquist Checker

  Check that a low-pass corner sits safely below the Nyquist frequency of the sample rate.