Velocity of shear waves

Input(s)

G: Shear Modulus $(\mathrm{Pa})$

$\rho$: Density $\left(\mathrm{kg} / \mathrm{m}^{3}\right)$

Output(s)

$V_{s}$: Velocity of Shear Waves $(\mathrm{m} / \mathrm{s})$

Formula(s)

$$ \mathrm{V}_{\mathrm{s}}=\left(\frac{\mathrm{G}}{\rho}\right)^{0.5} $$

Reference(s)

Bassiouni, Z., 1994, Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4. Chapter 3, Page: 46.

$11.81 \quad V_{p}$ and $V_{s}$ calculation (Eberhart-Phillips)

Input(s)

$\emptyset$: Porosity (fraction)

C: Clay Content (fraction)

$\sigma$: Effective Stress (psi)

Output(s)

$V_{p}$: Velocity of Compressional Waves $(\mathrm{ft} / \mathrm{s})$

$V_{s}$: Shear Waves $(\mathrm{ft} / \mathrm{s})$

Formula(s)

$$ \begin{aligned} & \mathrm{V}_{\mathrm{p}}=5.77-6.94 * \emptyset-1.73 *\left(\mathrm{C}^{0.5}\right)+0.446 *\left(\sigma-(-1) * \mathrm{e}^{(-1) * 16.7 * \sigma}\right) \\ & \mathrm{V}_{\mathrm{s}}=3.7-4.94 * \emptyset-1.57 *\left(\mathrm{C}^{0.5}\right)+0.361 *\left(\sigma-(-1) * \mathrm{e}^{(-1) * 16.7 * \sigma}\right) \end{aligned} $$

Reference(s)

Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 53.

$11.82 \quad V_{p}$ and $V_{s}$ calculation (geomechanical model)

Input(s)

$\mathrm{K}$: Bulk Modulus (psi)

G: Shear Modulus (psi)

$\rho$: Density (ppg)

Output(s)

$V_{p}$: Velocity of Compressional Waves $(\mathrm{ft} / \mathrm{s})$

$V_{s}$: Shear Waves $(\mathrm{ft} / \mathrm{s})$

Formula(s)

$$ \begin{gathered} \mathrm{V}_{\mathrm{p}}=\left(\frac{\mathrm{K}+\frac{4_{*} \mathrm{G}}{3}}{\rho}\right)^{0.5} \\ \mathrm{~V}_{\mathrm{s}}=\left(\frac{\mathrm{G}}{\rho}\right)^{0.5} \end{gathered} $$

Reference(s)

Mark D. Zoback, Reservoir Geomechanics, Cambridge University Press, UK, Page: 63.