Compute a source moment without predicting local shaking

1. Define the evidence and convention

Scalar seismic moment combines rigidity, ruptured fault area and mean displacement: M0=μAD. It captures source deformation on a fault. Moment magnitude maps this large dimensional quantity onto a logarithmic scale; it is not obtained by averaging arbitrary local shaking intensities.

2. Connect mechanism and model

The supplied rupture has width 15 km, length a and slip b, with rigidity 30 GPa. Convert both area dimensions to meters and rigidity to pascals before multiplication. For M0 in N m, Mw=(2/3)(log10 M0−9.1). A commonly printed constant 16.1 instead uses dyne-cm; mixing that constant with SI moment produces a major error.

Moment and radiated seismic energy have related source physics but are not the same quantity, even though their SI dimensional units can look similar. Doubling area or slip doubles moment and adds (2/3)log10 2≈0.200687 to magnitude. It does not double magnitude or establish how much energy was radiated.

Intensity describes effects or shaking at a location and depends on distance, wave propagation, ground conditions and structures. A single earthquake has one estimated source magnitude for a given method/version but many spatially varying intensities. No source calculation here predicts a site’s safety, loss or next earthquake.

3. Reconstruct the worked packet

Length 20 km, width 15 km and slip 1 m give area 300 million m² and moment 9×10^18 N m. Mw≈6.56950. Doubling slip to 2 m raises magnitude by about 0.200687, not by a factor of two.

4. Predict and investigate

Predict first: Does doubling slip double moment magnitude or only the underlying moment?

Convert dimensions explicitly, vary area and slip separately, and compare moment ratios with magnitude differences. Explain which independent observations are needed to assess local shaking rather than source size.

5. Test a changed case

Apply the evidence to a changed case

For length 40 km and slip 1 m at the same width/rigidity, what is moment and the magnitude change from the worked example?

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Moment is 1.8×10^19 N m, twice the baseline, so Mw≈6.77018 and the change is about 0.200687. No local intensity follows uniquely.

6. Retain a defensible evidence notebook

Preserve first predictions, map orientation, intermediate calculations, units, assumptions and alternatives. These maps, numerical packets and diagrams are original invented instructional cases, not surveyed sites or current hazard forecasts. Independent practical review and genuinely unfamiliar evidence remain separate learner gates.

Mechanism reference, checked 30 October 2026. Original prose, diagrams and numerical exercises. No physical loading, pressurization or field hazard exposure is requested.