Seismic refraction

S-wave refraction

S-wave refraction evaluates the shear wave generated by the seismic source located at a known distance from the array. The wave is generated by horizontally striking an object on the ground surface to induce the shear wave. Since the shear wave is the second fastest wave, it is sometimes referred to as the secondary wave. When compared to the compression wave, the shear wave is approximately one-half (but may vary significantly from this estimate) the velocity depending on the medium.

Two horizontal layers

i_c0 - critical angle
V₀ - velocity of the first layer
V₁ - velocity of the second layer
h₀ - thickness of the first layer
T0₁ - intercept

${\displaystyle i_{c_0}=asin\left(\frac{V_0}{V_1}\right)}$

${\displaystyle T=\frac{2h_{0}cos(i_{c_0})}{V_0}+\frac{X}{V_1}=T{0}_1+\frac{X}{V_1}}$

${\displaystyle h_0=\frac{T{0}_1{V}_0}{2cos(i_c)}}$

${\displaystyle h_0=\frac{X_{cros{s}_1}}{2}\sqrt{\frac{V_1-V_0}{V_1+V_0}}}$

Several horizontal layers

${\displaystyle h_n=\frac{V_n}{cos(i_n)}\left(\frac{T{0}_{n+1}}{2}-\sum _{j=0}^{n-1}{h}_j\sqrt{\frac{1}{V_j^2}-\frac{1}{V_{j+1}^2}}\right)}$

Inversion methods

• The General Reciprocal method
• The Plus minus method
• Refraction inversion modeling (refraction tomography)
• Monte Carlo simulation
• Genetic algorithms

Applications

Seismic refraction has been successfully applied to tailings characterisation through P- and S-wave travel time tomographic inversions.