Time between the initiation of the pulse and the first arrival acoustic energy at the receiver

Input(s)

$d_{h}$: Borehole Diameter (in.)

$d_{t}$: Tool Diameter (in.)

$L_{s}$: Spacing $(\mathrm{ft})$

$l_{c}$: Displaced Distance $(\mathrm{ft})$

v: Formation Compressional Velocity ( $\mu \mathrm{s} / \mathrm{ft})$

$v_{m}$: Mud Compressional Velocity $(\mu \mathrm{s} / \mathrm{ft})$

Output(s)

$t_{l o g}$: Time Between Initiation of the Pulse and First Arrival Acoustic Energy at the Receiver ( $\mu \mathrm{s} / \mathrm{ft}$ )

Formula(s)

$$ \mathrm{t}_{\log }=\left(\frac{\mathrm{L}_{\mathrm{s}}}{\mathrm{v}}\right)+\left(\frac{\mathrm{d}_{\mathrm{h}}-\left(\mathrm{d}_{\mathrm{t}}+2 * \mathrm{l}_{\mathrm{c}}\right)}{\mathrm{v}_{\mathrm{m}}}\right) * \operatorname{sqrt}\left(1-\left(\frac{\mathrm{v}_{\mathrm{m}}}{\mathrm{v}}\right)^{2}\right) $$

Reference(s)

Bassiouni, Z., 1994, Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4. Chapter 10, Page: 189.