Table 1 The calculation formula of rock mechanics parameters.

Poisson’s ratio,\(\:\nu\:\)

\(\:\nu\:=\frac{0.5\times\:{\left(\varDelta\:{t}_{s}/\varDelta\:{t}_{p}\right)}^{2}-1}{{\left(\varDelta\:{t}_{s}/\varDelta\:{t}_{p}\right)}^{2}-1}\)

Shear modulus, G

\(\:G={\rho\:}_{b}/{\left(\varDelta\:{t}_{s}\right)}^{2}\times\:9.29\times\:{10}^{4}\)

Young’ modulus, E

\(\:E=G\cdot\:\frac{3{\left(\varDelta\:{t}_{s}\right)}^{2}-4{\left(\varDelta\:{t}_{p}\right)}^{2}}{{\left(\varDelta\:{t}_{s}\right)}^{2}-{\left(\varDelta\:{t}_{p}\right)}^{2}}\)

Bulk modulus, K

\(\:K=G\cdot\:\frac{3{\left(\varDelta\:{t}_{s}\right)}^{2}-4{\left(\varDelta\:{t}_{p}\right)}^{2}}{3{\left(\varDelta\:{t}_{p}\right)}^{2}}\)

Biot coefficient,\(\:\alpha\:\)

\(\:\alpha\:=1-\frac{{\rho\:}_{b}\left(3{v}_{p}^{2}-4{v}_{s}^{2}\right)}{{\rho\:}_{ma}\left(3{v}_{map}^{2}-4{v}_{mas}^{2}\right)}\)