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Moment Magnitude & Seismic Energy Calculator

The Moment Magnitude scale (Mw) is the standard logarithmic scale used by seismologists to measure total earthquake size and fault rupture work.

Earthquake moment magnitude rating (typically 1.0 to 9.5).

Calculated Result
1.995e+15 Joules

Radiated Seismic Energy

Seismic Moment (M₀)

3.981e+19 N·m

TNT Explosive Equivalent

476.9 kilotons TNT

Energy vs. Magnitude 5.0

1000.0x

Calculation Breakdown

  1. log₁₀(M₀) = 1.5 · Mw + 9.13.981e+19 N·m
  2. log₁₀(E_s) = 4.8 + 1.5 · Mw1.995e+15 J
  3. TNT_kt = E_s / (4.184 × 10¹² J)476.9 kt

What Is the Moment Magnitude & Seismic Energy Calculator?

Moment Magnitude (Mw) measures total mechanical work done during an earthquake fault slip.

Unlike the older local Richter scale (ML), Mw does not saturate for huge mega-thrust earthquakes.

How Does the Moment Magnitude & Seismic Energy Calculator Work?

Calculates physical seismic moment M0 in Newton-meters.

Evaluates radiated wave energy using the empirical Gutenberg-Richter relation.

Converts Joules to equivalent TNT explosive yield in kilotons.

Moment Magnitude & Seismic Energy Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

M_0 = 10^{1.5 M_w + 9.1} \text{ N}\cdot\text{m}, \quad \log_{10}(E_s) = 4.8 + 1.5 M_w, \quad E_s = 10^{4.8 + 1.5 M_w} \text{ J}

Hanks-Kanamori formulation linking moment magnitude to physical rock fracture work and radiated acoustic energy.

How to Use the Moment Magnitude & Seismic Energy Calculator

  1. Enter the Moment Magnitude Mw value.

Step-by-Step Example Calculation

Magnitude 7.0 Major Earthquake

Input Values:

momentMagnitudeMw:7
Worked Steps: Significant tectonic plate boundary fault rupture event.

Understanding Your Result

Seismic moment M0 reflects physical fault rupture area and slip distance.

Radiated energy represents the destructive acoustic shock waves radiating through the Earth crust.

Factors That Affect the Result

  • Fault slip area and displacement: Megathrust faults rupturing hundreds of kilometers generate magnitudes above 8.5.
  • Rock rigidity: Deeper lithospheric faults in stiffer rock radiate higher energy per square meter of slip.

When Should You Use This Calculator?

  • Seismological research, structural seismic hazard mitigation, and disaster risk assessment.
  • Comparing earthquake energy release across historical seismic events.

Assumptions & Limitations

  • Radiated energy represents approximately 1% to 10% of total strain energy; the remainder dissipates as frictional heat.
  • Standard scaling assumes average crustal shear modulus.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Hanks-Kanamori relationship is universally standardized across the USGS and global seismological networks.

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