Seismic Moment Tensor Components Calculator
Calculate seismic moment tensor components with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Formula
Mij = M0 * f(strike, dip, rake) | Mw = (2/3)(log10(M0) - 9.1)
Moment tensor components are calculated from scalar seismic moment M0 and fault geometry (strike, dip, rake) using the Aki & Richards formulation. Moment magnitude Mw relates to M0 via the Hanks-Kanamori relation.
Worked Examples
Example 1: Strike-Slip Fault (San Andreas Type)
Problem: Calculate moment tensor for M0 = 1.0e18 N*m, strike = 320, dip = 90, rake = 180 (right-lateral strike-slip).
Solution: Using Aki & Richards formulation:\nMxx = -M0*(sin(90)cos(180)sin(640) + sin(180)sin(180)sin^2(320))\nWith pure strike-slip on vertical fault, dominant Mxy component\nMw = (2/3)*(log10(1e18) - 9.1) = (2/3)*(18 - 9.1) = 5.93
Result: Mw = 5.93, dominant Mxy component
Example 2: Thrust Fault Event
Problem: Calculate moment tensor for M0 = 5.0e20 N*m, strike = 45, dip = 30, rake = 90 (pure thrust).
Solution: Pure thrust (rake=90) on a 30-degree dip fault\nMzz = M0*sin(60)*sin(90) = 4.33e20\nMw = (2/3)*(log10(5e20) - 9.1) = (2/3)*(20.7 - 9.1) = 7.73
Result: Mw = 7.73, large Mzz component
Frequently Asked Questions
What is a seismic moment tensor?
A seismic moment tensor is a 3x3 symmetric matrix that completely describes the equivalent body forces at an earthquake source. It encodes information about the fault orientation (strike and dip), the slip direction (rake), and the size of the earthquake (scalar seismic moment). The six independent components of the tensor can be decomposed into an isotropic part (volume change), a compensated linear vector dipole (CLVD), and a double-couple component representing shear faulting.
How is moment magnitude related to scalar seismic moment?
Moment magnitude Mw is derived from the scalar seismic moment M0 using the Hanks-Kanamori relation: Mw = (2/3)(log10(M0) - 9.1), where M0 is in Newton-meters. This scale was developed to provide a physically meaningful and non-saturating magnitude measure. Unlike the Richter scale which saturates for large earthquakes, moment magnitude accurately reflects the total energy of any size earthquake because it is directly tied to the physical fault parameters through M0 = rigidity * area * slip.
Why is the trace of a double-couple moment tensor zero?
The trace (sum of diagonal elements Mxx + Myy + Mzz) of a pure double-couple moment tensor is always zero because earthquake faulting is a shear process with no net volume change. A non-zero trace would indicate an isotropic (explosive or implosive) component, which occurs in volcanic or mining-induced events. Monitoring networks use the trace as a diagnostic: nuclear explosions produce large positive isotropic components, while pure tectonic earthquakes have traces very close to zero.
What is the difference between Richter and moment magnitude scales?
The Richter scale (ML) measures local magnitude using seismograph amplitude but becomes inaccurate above magnitude 7. The moment magnitude scale (Mw) measures total energy released and works for all earthquake sizes. Each whole number increase represents about 31.6 times more energy. Modern seismology primarily uses Mw.
Is Seismic Moment Tensor Components Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.
How accurate are the results from Seismic Moment Tensor Components Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.