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9 results for “magnitude”

Formulae (9)

|\vec{a}\times\vec{b}| = |a||b|\sin\theta

Magnitude of the vector perpendicular to two vectors.

|\vec{v}| = \sqrt{v_1^2 + v_2^2 + v_3^2}

Length of a vector.

\|\mathbf{v}\| = \sqrt{\sum v_i^2}

Length of a vector.

\cos\theta = \frac{\mathbf{a}\cdot\mathbf{b}}{\|a\|\|b\|}

Angle from the dot product and magnitudes.

m - M = 5\log_{10}(d) - 5

Relates apparent and absolute magnitude to distance.

M = \log_{10}\frac{A}{A_0}

Earthquake magnitude from seismograph amplitude.

\log_{10} E = 4.8 + 1.5\,M

Energy released by a quake of Richter magnitude M.

M_w = \tfrac{2}{3}\log_{10} M_0 - 10.7

Modern magnitude from the seismic moment of a quake.

\log_{10}E = 4.8 + 1.5M

Approximate energy released by an earthquake.