Geophysical Methods — Worked Examples

A flat horizontal two-layer interpretation has a direct line through (0 m, 0 ms) and (16 m, 40 ms), and a head line through (30 m, 75 ms) and (80 m, 95 ms). Find both velocities and the extrapolated head-line intercept.

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For a horizontal homogeneous two-layer model, $V_1=400\text{ m/s}$, $V_2=2500\text{ m/s}$ and crossover $x_c=30.0\text{ m}$. Find interface depth. The first-arrival curves are shown below.

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A horizontal model has $V_1=500\text{ m/s}$, $V_2=1000\text{ m/s}$ and depth 12.0 m. The receiver is 55.0 m from the source. Find critical angle, minimum head-path offset, crossover and the first arrival.

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A proposed conventional two-layer refraction interpretation assigns $V_1=1500\text{ m/s}$ and $V_2=900\text{ m/s}$. Can its critical-angle and crossover-depth formulas be used to infer the deeper boundary?

A surface Wenner array has A, M, N and B at 0, 5, 10 and 15 m. Injected current is 100 mA and $V_M-V_N=200\text{ mV}$ with the stated polarity. Calculate apparent resistivity.

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A synthetic Wenner record lists $a=5.00\text{ m}$, $I=0\text{ mA}$ and $\Delta V=200\text{ mV}$. A second record has both current and voltage zero. What should the apparent-resistivity calculator report?

In the stated homogeneous low-loss model, relative permittivity is 9.00 and a zero-offset two-way reflection time is 40.0 ns. Use the declared rounded $c=0.300\text{ m/ns}$ to infer vertical depth.

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A synthetic point is 3.00 m deep. A coincident transmitter/receiver is 4.00 m laterally from directly above it. In a homogeneous medium with $v=0.100\text{ m/ns}$, find two-way time and the depth error from treating that return as vertical.

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A planned 3 m excavation crosses saline clay. GPR shows poor penetration and no identifiable utility return. Existing utility records are incomplete. What conclusion is supported?

A crosshole shear-wave test has an independently verified source–receiver distance of 8.00 m at the measurement depth. The corrected shear arrival is 25.0 ms after the source trigger. Calculate path-average velocity.

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A surface source lies directly above a vertical receiver hole. Corrected shear arrivals are 40.0 ms at 10.0 m and 65.0 ms at 15.0 m, using a consistent trigger. Assume the relevant path is vertical. Find interval velocity between the receivers.

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The upper 30 m consists of 5.00 m at 150 m/s, 10.0 m at 300 m/s and 15.0 m at 600 m/s. Calculate $V_{s30}$ and compare with the thickness-weighted arithmetic average.

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A highway-cut survey reports a P-wave velocity of 3200 m/s. No equipment-specific rippability chart, discontinuity survey, weathering information or trial excavation is supplied. Must the entire cut be drilled and blasted?

A synthetic resistivity inversion in limestone shows a 10000 Ω·m anomaly in a 200 Ω·m background. Sparse boreholes do not intersect it. What does this establish about a proposed foundation?