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.


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