Velocity of shear waves

Input(s)

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

ρ\rho: Density (kg/m3)\left(\mathrm{kg} / \mathrm{m}^{3}\right)

Output(s)

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

Formula(s)

Vs=(Gρ)0.5\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.

11.81Vp11.81 \quad V_{p} and VsV_{s} calculation (Eberhart-Phillips)

Input(s)

\emptyset: Porosity (fraction)

C: Clay Content (fraction)

σ\sigma: Effective Stress (psi)

Output(s)

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

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

Formula(s)

Vp=5.776.941.73(C0.5)+0.446(σ(1)e(1)16.7σ)Vs=3.74.941.57(C0.5)+0.361(σ(1)e(1)16.7σ)\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.

11.82Vp11.82 \quad V_{p} and VsV_{s} calculation (geomechanical model)

Input(s)

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

G: Shear Modulus (psi)

ρ\rho: Density (ppg)

Output(s)

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

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

Formula(s)

Vp=(K+4G3ρ)0.5 Vs=(Gρ)0.5\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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