B Value Standard Error Shi Bolt Formula
Shi & Bolt (1982) b-value uncertainty, simplified for unit-variance magnitude residuals: σ_b = 2.30·b²/√(N−1); supply magnitude residuals for the full Σ(Mᵢ−M̄)² form.
Description
Shi & Bolt (1982) b-value uncertainty, simplified for unit-variance magnitude residuals: σ_b = 2.30·b²/√(N−1); supply magnitude residuals for the full Σ(Mᵢ−M̄)² form.
B Value Standard Error Shi Bolt Formula is a focused tool for the following task. Shi & Bolt (1982) b-value uncertainty, simplified for unit-variance magnitude residuals: σ_b = 2.30·b²/√(N−1); supply magnitude residuals for the full Σ(Mᵢ−M̄)² form. It reports σ_b, σ% from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use B Value Standard Error Shi Bolt Formula
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.
- b
- Required number. Fitted b-value.
- N
- Required integer. Events used in the fit.
The cited overview of Seismic magnitude scales supplies background for the terminology and domain context used by this tool.1
How B Value Standard Error Shi Bolt Formula works
Shi & Bolt (1982) b-value uncertainty, simplified for unit-variance magnitude residuals: σ_b = 2.30·b²/√(N−1); supply magnitude residuals for the full Σ(Mᵢ−M̄)² form. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- σ_b
- Returned number. One-sigma uncertainty on b.
- σ% (%)
- Returned number in %. Relative uncertainty.
Limitations and assumptions
- 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.
- b must be at least 0.
- N must be at least 2.
- Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.
Alternative or Complementary approaches
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.
References
-
Seismic magnitude scales — Wikipedia contributors
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