Geophysical Methods

Learning Objectives

  • Explain how geophysical measurements respond to subsurface physical-property contrasts.
  • Compare seismic refraction, electrical resistivity, and ground-penetrating radar.
  • Describe surface-wave and borehole seismic methods for velocity profiling.
  • Select and validate a geophysical method without treating an interpretation as unique ground truth.

Role and Limits of Geophysics

Geophysical method

An indirect investigation method that measures a physical response and uses a model to infer subsurface properties or boundaries.

Engineering Use

Geophysics can extend spatial coverage, identify contrasts or anomalies, and help connect direct exploration points. The measured response is not itself a unique lithology or engineering property. Interpretation depends on survey geometry, expected contrast, noise, resolution, assumptions, and suitable calibration or ground truth.

Near-Surface Geophysical Methods

Seismic Refraction

First-Arrival Refraction

Seismic refraction interprets first-arrival travel times from direct and refracted seismic waves recorded by surface geophones. A critically refracted head wave can constrain an interface when the lower refractor has higher seismic velocity than the overlying material and the survey geometry supports that interpretation. A lower-velocity layer beneath a faster layer can be hidden from conventional first-arrival refraction.

Refraction Rays and Blind Zones

Original synthetic horizontal two-layer case: V1=500 m/s, V2=1000 m/s and depth 12 m give a 30° critical angle from the normal. Both upper-layer legs have the same angle. The separate inversion sketch illustrates a conventional first-arrival limitation.

A head wave travels along a faster lower refractor and returns to geophones, while a velocity inversion may create a blind zone

Two-Layer Travel Times

Flat surface, horizontal interface and homogeneous isotropic layers; lower velocity must exceed upper velocity for a head wave.

sin⁡ic=V1V2,tdirect=xV1,thead=ti+xV2,ti=2hcos⁡icV1\sin i_c=\frac{V_1}{V_2},\qquad t_{\text{direct}}=\frac{x}{V_1},\qquad t_{\text{head}}=t_i+\frac{x}{V_2},\qquad t_i=\frac{2h\cos i_c}{V_1}

Variables

SymbolDescriptionUnit
V1,V2V_1,V_2Upper- and lower-layer velocities of the same wave type; V2 must exceed V1m/s
ici_cCritical incidence angle measured from the interface normaldegrees or radians, used consistently
x,hx,hHorizontal receiver offset and upper-layer thicknessm
tit_iExtrapolated head-line intercept, not a measured first arrival at zero offsets
tdirect,theadt_{\text{direct}},t_{\text{head}}Travel times for the direct and physically available head pathss

Critical Offset, Crossover and Depth

A head path can exist before it becomes the first arrival. Do not exchange these two distances.

xmin⁡=2htan⁡ic,xc=2hV2+V1V2−V1,h=xc2V2−V1V2+V1x_{\min}=2h\tan i_c,\qquad x_c=2h\sqrt{\frac{V_2+V_1}{V_2-V_1}},\qquad h=\frac{x_c}{2}\sqrt{\frac{V_2-V_1}{V_2+V_1}}

Variables

SymbolDescriptionUnit
xmin⁡x_{\min}Minimum offset for the critical head path to have a nonnegative interface segmentm
xcx_cCrossover offset where direct and head travel times are equalm
hhInferred interface depth only under the stated two-layer assumptionsm

Read the Time–Distance Axes

For time on the vertical axis and offset on the horizontal axis, velocity is the inverse line slope: V=Δx/ΔtV=\Delta x/\Delta t. Convert milliseconds to seconds before reporting m/s. The head-wave expression applies only at x≥xmin⁡x\ge x_{\min}; a line extrapolated to smaller offsets is not a physical head path. At xcx_c the two arrivals coincide; beyond it the faster lower-layer path arrives first in this model.

If V2≤V1V_2\le V_1, this head-wave interpretation is unavailable. A missing second first-arrival segment may also reflect insufficient spread, weak contrast, a hidden layer or poor data. It does not prove an infinitely deep soil deposit or the absence of rock. A measured velocity does not uniquely supply lithology, intact strength or rippability. Excavation assessment also needs structure, weathering, equipment and site evidence; no universal velocity threshold mandates blasting.

Two-layer refraction and first arrivals

Concept and model scope

Change velocities, depth and receiver offset to distinguish an existing head path from a head wave that arrives first.

Model and limits: Synthetic horizontal homogeneous layers and flat surface. V1: 200–2000 m/s; V2: 300–6000 m/s; depth: 1–50 m; offset and plotted survey: 0–120 m. Angles are measured from the interface normal. Velocity contrast is not a density or lithology diagnosis. No amplitude, hidden-layer inversion or excavation prediction.

Controls
400 m/s

Upper velocity V1

Wave velocity in the upper layer. Increasing V1 changes direct time and the critical angle; V2 must exceed V1 for this head-wave model.

Range: 200–2000 m/s. Step: 100 m/s.

2500 m/s

Lower velocity V2

Wave velocity in the lower layer, not a material label. Equal or lower V2 holds the head-wave model while retaining direct arrivals.

Range: 300–6000 m/s. Step: 100 m/s.

12 m

Interface depth

Positive thickness of the homogeneous upper layer. Greater depth increases intercept, critical offset and crossover distance.

Range: 1–50 m. Step: 1 m.

60 m

Receiver offset

Horizontal distance from the source. A head path begins at the critical offset; it overtakes the direct arrival only at the larger crossover distance.

Range: 0–120 m. Step: 1 m.

The head wave arrives first at this offset. This is a synthetic model, not a material identification.

Source at 0 m · receiver at 60 m · interface 12 m below surface. Scene x/y scales are equal.
Direct and physically available critical head-wave pathsBoth axes use five drawing units per metre. The surface and horizontal interface remain references at zero receiver offset. Blue head path is drawn only when its horizontal interface segment is nonnegative.

Dashed brown: direct · solid blue: available head path · dashed grey: model interface.

Travel time: 0–300.0 ms upwards · offset: 0–120 m rightwards.
Direct, head and first-arrival travel timesSolid blue is the first-arrival lower envelope. Brown dashes show direct time, grey dots show existing head-wave time. No head line is extrapolated below its critical offset. Crossover may lie outside this 120 metre survey.
0306090120

Solid blue: first arrival · brown dashes: direct · grey dots: head time.

Direct / available head time
150.000 ms / 83.227 ms
First arrival
Head wave · 83.227 ms
Critical angle / minimum head-path offset
9.207° / 3.890 m
Crossover distance
28.203 m

Electrical Resistivity

Resistivity Response

Current is injected through current electrodes and voltage is measured at potential electrodes. Apparent resistivity depends on electrode geometry and the distribution of material properties within a broad sensitivity volume. Lithology, pore structure, saturation, pore-water chemistry, temperature, and buried infrastructure can all affect the response; a resistivity anomaly is not a unique material identification.

Four-Electrode Resistivity Array

The shaded region is conceptual; array spacing and material contrasts control the measurement response.

Current electrodes A and B inject current while potential electrodes M and N measure voltage over a subsurface sensitivity volume

Wenner Apparent Resistivity

Surface electrodes in the order A–M–N–B, with equal adjacent spacing a and a consistent current/voltage polarity.

ρa=KΔVI,K=2πa\rho_a=K\frac{\Delta V}{I},\qquad K=2\pi a

Variables

SymbolDescriptionUnit
ρa\rho_aEquivalent homogeneous-half-space apparent resistivity for this arrayΩ·m
a,Ka,KAdjacent electrode spacing and Wenner geometry factorm
ΔV\Delta VPotential at M minus potential at N for current injected at A and returned at BV
IIInjected current, nonzero for the quotientA

Geometry and Units Are Part of the Measurement

For point current at a flat homogeneous half-space surface, potential varies as ρI/(2πr)\rho I/(2\pi r). Combining the source and return contributions at equally spaced M and N gives ΔV=ρI/(2πa)\Delta V=\rho I/(2\pi a) and the Wenner factor above. In heterogeneous ground, the same conversion reports an apparent value rather than one layer's uniquely identified resistivity.

The numerical ratio mV/mA equals V/A, which is resistance in ohms; multiplying by a geometry factor in metres gives Ω·m. Zero current makes the quotient undefined even if voltage is also zero. Spacing does not give one exact investigation depth. Clay, salinity, saturation and other contrasts can produce overlapping responses; an anomaly's colour does not prove a cavity or contaminant.

Ground-Penetrating Radar

Radar Reflection and Attenuation

GPR transmits high-frequency electromagnetic energy and records reflections from boundaries with contrasting dielectric properties. Two-way travel time must be related to depth using an appropriate velocity estimate. Conductive ground can attenuate the signal and reduce useful depth; frequency, moisture, target geometry, and site noise also matter. GPR is a useful utility or shallow-feature tool where conditions permit, not a universal locating method.

GPR Reflection and Signal Loss

Original qualitative paths, not to scale. The fading transmitted path enters the conductive zone; it is not a calculated detection threshold. Site calibration and direct utility verification may be needed.

A GPR pulse reflects from a dielectric boundary while conductive ground attenuates energy

GPR Velocity and Two-Way Travel

Homogeneous low-loss nonmagnetic dielectric, coincident transmitter/receiver and a point reflector; use compatible distance and time units.

v≈cεr,t(s)=2z2+s2v,z=vt(0)2v\approx\frac{c}{\sqrt{\varepsilon_r}},\qquad t(s)=\frac{2\sqrt{z^2+s^2}}{v},\qquad z=\frac{vt(0)}{2}

Variables

SymbolDescriptionUnit
ccRounded teaching light speed used consistently in these models and exercises0.300 m/ns
εr\varepsilon_rAssumed relative permittivity of the homogeneous materialdimensionless
vvRadar velocity under the stated dielectric approximationm/ns
z,sz,sVertical point depth and signed lateral antenna offset from directly above itm
t(s)t(s)Two-way travel time along the retraced source-to-point pathns

A Radargram Is a Time Record

A point-like target can produce a hyperbola because slant range increases away from its apex. With time increasing downward, the apex has the smallest time. Treating an offset return as vertical gives z2+s2\sqrt{z^2+s^2} rather than the true depth zz. A hyperbola is not uniquely a metallic pipe; geometry, velocity calibration, processing and confirmation matter.

Conductive ground can hide a target; no return is not clearance. A planar return does not uniquely identify a metal sheet, and a resistive anomaly does not uniquely prove an air-filled cave. Use appropriate locating and confirmation procedures for design-critical or excavation decisions. The simulation below calculates geometry, not signal strength, detectability or safe utility clearance.

Electrical and radar measurement models

Concept and model scope

Compare apparent resistivity from a real array geometry with GPR two-way travel time from a known synthetic point. Change the method to use its own measurements and assumptions.

Model and limits: Wenner: surface AMNB with equal spacing, one voltage/current polarity; a=1–20 m, I=0–200 mA, ΔV=0–1000 mV. GPR: homogeneous, nonmagnetic low-loss dielectric and coincident transmitter/receiver, rounded teaching c=0.300 m/ns; depth=0–10 m, εr=1–36, scan offset=−10–10 m. No inversion, material identity, detection guarantee or utility clearance.

Controls

Measurement model

Concept and model scope

Wenner uses an electrical array's measured current and voltage with its geometry factor. GPR uses a chosen synthetic point, dielectric velocity and a retraced two-way path. Switching changes the engineering measurement, not a generic learning mode.

5 m

Electrode spacing

Equal A–M, M–N and N–B spacing. The geometry factor is 2πa; a is not a unique investigation depth.

Range: 1–20 m. Step: 1 m.

100 mA

Injected current

Positive current for the selected AMNB polarity. Zero current leaves ΔV/I undefined, including when voltage is also zero.

Range: 0–200 mA. Step: 10 mA.

200 mV

Measured voltage

Potential difference for the stated electrode polarity. mV/mA has the same numerical ratio as V/A. These synthetic measurements do not identify a material.

Range: 0–1000 mV. Step: 10 mV.

Apparent resistivity is an array response. Different ground models can produce similar measurements.

AMNB array on a fixed 0–60 m axis. Current: A to B · voltage: M minus N.
Equal-spacing Wenner electrode positionsAll positions use ten drawing units per metre on one fixed horizontal axis. This surface layout does not assign a depth or a unique sensitivity boundary.
015304560

A = 0 m · M = 5 m · N = 10 m · B = 15 m.

Geometry K = 2πa
31.416 m
Measured ΔV/I
2.000 Ω
Apparent resistivity ρa = KΔV/I
62.832 Ω·m
Array interpretation
No unique material or excavation decision.

Seismic Velocity Methods

Multichannel Analysis of Surface Waves

MASW and Shear-Wave Velocity

MASW records dispersive surface waves on a receiver array, estimates a dispersion relationship, and inverts that relationship for a shear-wave velocity (VsV_s) profile. The dispersion curve is measured or processed; the resulting depth profile is model-dependent and non-unique without suitable constraints. Use code-based site classification only with the governing code edition, procedure, and required data.

MASW: Dispersion to Vs Profile

The curve and layered profile are synthetic teaching sketches; they are not measured data or a unique inversion.

A receiver array records surface waves, a dispersion curve is interpreted, and inversion yields a model-dependent Vs profile

Cross-Hole and Down-Hole Testing

Borehole Seismic Travel Paths

Cross-hole testing places a source and receiver in separate boreholes at corresponding depths to measure travel time between them. Down-hole testing uses a surface source and a receiver at successive depths in a borehole. Both require suitable borehole geometry, coupling, orientation, and interpretation to estimate in-situ wave velocities.

Travel-Time Velocity and Vs30

Use verified path lengths and compatible arrival picks. Vs30 requires the complete upper 30 m profile and is a travel-time average.

V=Lt,Vinterval=ΔLΔt,Vs30=30∑idi/Vs,i,∑idi=30 mV=\frac{L}{t},\qquad V_{\text{interval}}=\frac{\Delta L}{\Delta t},\qquad V_{s30}=\frac{30}{\sum_i d_i/V_{s,i}},\quad \sum_i d_i=30\text{ m}

Variables

SymbolDescriptionUnit
L,ΔLL,\Delta LActual total or interval path length under the adopted propagation modelm
t,Δtt,\Delta tCorrected total or interval travel time with a consistent triggers
di,Vs,id_i,V_{s,i}Layer thickness and corresponding shear-wave velocity over the full upper 30 mm and m/s
Vs30V_{s30}Time-averaged shear velocity, distinct from an arithmetic mean or a value at 30 mm/s

Keep Geometry and Classification Assumptions

Cross-hole spacing is the actual source–receiver distance at depth, which can differ from collar spacing if holes deviate. Down-hole travel from an offset surface source is slant travel, and can refract; a vertical-depth difference is not automatically a path-length difference. Coupling, orientation, trigger corrections and arrival identification affect inferred velocity. Do not diagnose homogeneity from a single ratio.

Vs30V_{s30} does not by itself prescribe a code class, design load or amount of reinforcement. Apply the governing edition and its complete criteria, including special conditions and data coverage. A profile shorter than 30 m cannot simply be labelled a measured Vs30V_{s30}.

Cross-Hole and Down-Hole Layouts

The paths are schematic; borehole spacing and test procedures determine whether measured times support the intended velocity estimate.

Cross-hole travel is measured between receivers at matching depths while down-hole travel uses a surface source and borehole receiver

Other Geophysical Methods

Reflection, Gravity, and Magnetic Methods

  • Seismic reflection: interprets reflected wave travel times to map subsurface interfaces; method design, depth, resolution, and noise differ from shallow refraction.
  • Gravity: measures spatial changes in gravitational acceleration associated with subsurface density contrasts after appropriate corrections and interpretation.
  • Magnetic surveying: measures variations in the magnetic field related to magnetic susceptibility and remanence contrasts.

Each method has a target-property sensitivity rather than a unique material label. Survey design and interpretation must match the scale and decision question.

Method Selection and Validation

Geophysical Method Selection and Validation

Select geophysical methods by the target property, expected contrast, depth and resolution needs, site conditions, and noise. Interpretations remain indirect until checked against suitable ground truth.

Use one or more complementary methods only when their sensitivities address the project question. Document acquisition limits and inversion uncertainty. If direct checks or project information needs remain unresolved, hold design-critical conclusions and revise the investigation.

Geophysical Method Selection and ValidationSelect geophysical methods by the target property, expected contrast, depth and resolution needs, site conditions, and noise. Interpretations remain indirect until checked against suitable ground truth.. Use one or more complementary methods only when their sensitivities address the project question. Document acquisition limits and inversion uncertainty. If direct checks or project information needs remain unresolved, hold design-critical conclusions and revise the investigation.. Start → Define target property and decision question; Define target property and decision question → Assess contrast, depth, resolution, access, and noise; Assess contrast, depth, resolution, access, and noise → Method sensitivity fits target and site?; Method sensitivity fits target and site? — Yes → Acquire data with controls and quality checks; Method sensitivity fits target and site? — No → Hold: revise target, array, or method plan; Acquire data with controls and quality checks → Interpret response within method assumptions; Interpret response within method assumptions → Plan and complete targeted direct checks; Suitable direct ground truth available? — Yes → Integrated model meets information needs?; Plan and complete targeted direct checks → Suitable direct ground truth available?; Suitable direct ground truth available? — No → Hold: direct confirmation unavailable; retain uncertainty; Integrated model meets information needs? — Yes → Report interpretation, uncertainty, and limits; Integrated model meets information needs? — No → Hold: reassess model or acquisition plan; Report interpretation, uncertainty, and limits → End

Start → Define target property and decision question; Define target property and decision question → Assess contrast, depth, resolution, access, and noise; Assess contrast, depth, resolution, access, and noise → Method sensitivity fits target and site?; Method sensitivity fits target and site? — Yes → Acquire data with controls and quality checks; Method sensitivity fits target and site? — No → Hold: revise target, array, or method plan; Acquire data with controls and quality checks → Interpret response within method assumptions; Interpret response within method assumptions → Plan and complete targeted direct checks; Suitable direct ground truth available? — Yes → Integrated model meets information needs?; Plan and complete targeted direct checks → Suitable direct ground truth available?; Suitable direct ground truth available? — No → Hold: direct confirmation unavailable; retain uncertainty; Integrated model meets information needs? — Yes → Report interpretation, uncertainty, and limits; Integrated model meets information needs? — No → Hold: reassess model or acquisition plan; Report interpretation, uncertainty, and limits → End

  • Start: terminator
  • Define target property and decision question: process
  • Assess contrast, depth, resolution, access, and noise: process
  • Method sensitivity fits target and site?: decision
  • Hold: revise target, array, or method plan: terminator
  • Acquire data with controls and quality checks: process
  • Interpret response within method assumptions: process
  • Suitable direct ground truth available?: decision
  • Plan and complete targeted direct checks: process
  • Hold: direct confirmation unavailable; retain uncertainty: terminator
  • Integrated model meets information needs?: decision
  • Report interpretation, uncertainty, and limits: document
  • Hold: reassess model or acquisition plan: terminator
  • End: terminator

Interpretation Requires Ground Truth

Do not use a geophysical section as though every boundary were directly observed. Record the method’s sensitivity, resolution, assumptions, uncertainty, and calibration evidence; use direct exploration or other independent data where the decision requires material identification or design parameters.

Key Takeaways
  • Geophysical methods measure physical responses and infer properties through models.
  • Refraction depends on velocity structure and may not reveal a hidden low-velocity layer.
  • Resistivity and GPR responses are affected by multiple material and environmental factors.
  • MASW inversion and other geophysical interpretations are model-dependent and non-unique.
  • Select methods for the target and site, then validate interpretations with suitable direct evidence.

References