# Lecture formulas and optional calculation reference

Subject: Disaster Management

Exam: M2

Reader: https://deep-learning-study-room.vercel.app/dm/#m2/formulas/facts/formula-sheet

Canonical: https://deep-learning-study-room.vercel.app/read/dm/m2/formulas/facts--formula-sheet/

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.

[Open the complete explanation and solved examples →](https://deep-learning-study-room.vercel.app/read/dm/m2/read/earthquakes--logarithms/)

## Approximate energy ratio



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



Uses the common approximate magnitude–energy relation.

[Open the complete explanation and solved examples →](https://deep-learning-study-room.vercel.app/read/dm/m2/read/earthquakes--logarithms/)

## Seismic moment



$$
M_0=\mu A D
$$



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

[Open the complete explanation and solved examples →](https://deep-learning-study-room.vercel.app/read/dm/m2/read/earthquakes--moment/)

## 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.

[Open the complete explanation and solved examples →](https://deep-learning-study-room.vercel.app/read/dm/m2/read/earthquakes--moment/)

## 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.

[Open the complete explanation and solved examples →](https://deep-learning-study-room.vercel.app/read/dm/m2/read/floods--runoff/)

## 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.

[Open the complete explanation and solved examples →](https://deep-learning-study-room.vercel.app/read/dm/m2/read/floods--channel-flow/)

## 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.