Seismic Moment Tensor Components Calculator
Calculate seismic moment tensor components with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Calculator
Adjust values & calculate0/180 = strike-slip, 90 = thrust, -90 = normal fault
Formula
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.
Last reviewed: December 2025
Worked Examples
Example 1: Strike-Slip Fault (San Andreas Type)
Example 2: Thrust Fault Event
Background & Theory
The Seismic Moment Tensor Components Calculator applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) โ 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0โ12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1โ10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5โ7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 ร exp(โMgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.
History
The history behind the Seismic Moment Tensor Components Calculator traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity โ foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.
Frequently Asked Questions
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.
What inputs do I need to use Seismic Moment Tensor Components Calculator accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting โ for example, a weight measurement in kilograms, a distance in metres, or a dollar amount โ and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy