Disaster Management · M2 · formulas

Lecture formulas and optional calculation reference

Definitions and formulas

Read the meaning, then use the worked examples

These are formulas discussed or explained alongside the lectures, not a list of confirmed numerical questions. The approximate energy relation is a USGS extension. The available 12 TEE papers contain no numerical substitution questions.

Magnitude difference

\frac{A_2}{A_1}=10^{M_2-M_1}

Compares seismic-wave amplitudes on a comparable logarithmic scale; it is not the energy ratio.

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Approximate energy ratio

\frac{E_2}{E_1}\approx10^{1.5(M_2-M_1)}

Uses the common approximate magnitude–energy relation.

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Seismic moment

M_0=\mu A D

Rigidity × rupture area × average slip. Use compatible SI units to obtain N·m.

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Moment magnitude, SI

M_w=\frac{2}{3}(\log_{10}M_0-9.1)

Here the numerical value of M₀ is in N·m. Do not substitute dyne·cm into this version.

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Rational runoff method

Q=0.27778CIA

Q in m³/s, rainfall intensity I in mm/h, catchment area A in km², dimensionless C. It estimates peak runoff under the method’s assumptions.

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Channel discharge

Q=A_c v

Flow cross-section A_c in m² × mean velocity v in m/s gives Q in m³/s. A_c is not the catchment area above.

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Conversions used in the calculations

1\,\mathrm{km}=1000\,\mathrm m,\qquad1\,\mathrm{km^2}=10^6\,\mathrm{m^2}

1\,\mathrm{ha}=10^4\,\mathrm{m^2},\qquad1\,\mathrm h=3600\,\mathrm s

1\,\mathrm{N\,m}=10^7\,\mathrm{dyne\,cm}

Yaad rakho: Pehle units match; phir formula; phir calculation. Same A symbol ka meaning har formula mein same nahi hota.