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.