Seismic Refraction Surveying

Applied Seismology

Earthquake Seismology

Recordings of distant or local earthquakes are used to infer earth structure and faulting characteristics.

Applied Seismology

A signal, similar to a sound pulse, is transmitted into the Earth. The signal recorded at the surface can be used to infer subsurface properties. There are two main classes of survey:



History of Seismology

Exploration seismic methods developed from early work on earthquakes:




Seismic Refraction

Seismic Reflection



Stress and Strain

A force applied to the surface of a solid body creates internal forces within the body:

Triaxial Stress

Stresses act along three orthogonal axes, perpendicular to faces of solid, e.g. stretching a bar:


Forces act equally in all directions perpendicular to faces of body, e.g. pressure on a cube in water:

Strain Associated with Seismic Waves

Inside a uniform solid, two types of strain can propagate as waves:

Axial Stress

Stresses act in one direction only, e.g. if sides of bar fixed:


Shear Stress

Stresses act parallel to face of solid, e.g. pushing along a table:



Hooke’s Law

Hooke’s Law essentially states that stress is proportional to strain.

Constant of proportionality is called the modulus, and is ratio of stress to strain, e.g. Young’s modulus in triaxial strain.


Seismic Body Waves

Seismic waves are pulses of strain energy that propagate in a solid. Two types of seismic wave can exist inside a uniform solid:

A) P waves (Primary, Compressional, Push-Pull)

Motion of particles in the solid is in direction of wave propagation.

B) S waves (Secondary, Shear, Shake)

Particle motion is in plane perpendicular to direction of propagation.

Seismic Surface Waves

No stresses act on the Earth's surface (Free surface), and two types of surface wave can exist

A) Rayleigh waves

B. Love waves

Occur when a free surface and a deeper interface are present, and the shear wave velocity is lower in the top layer.

Seismic Wave Velocities

The speed of seismic waves is related to the elastic properties of solid, i.e. how easy it is to strain the rock for a given stress.

Speed of wave propagation is NOT speed at which particles move in solid ( ~ 0.01 m/s ).

Constraints on Seismic Velocity

Seismic velocities vary with mineral content, lithology, porosity, pore fluid saturation, pore pressure, and to some extent temperature.

Igneous/Metamorphic Rocks

In igneous rocks with minimal porosity, seismic velocity increases with increasing mafic mineral content.

Sedimentary Rocks

In sedimentary rocks, effects of porosity and grain cementation are more important, and seismic velocity relationships are complex.

Various empirical relationships have been estimated from either measurements on cores or field observations:

1) P wave velocity as function of age and depth


where Z is depth in km and T is geological age in millions of years (Faust, 1951).

2) Time-average equation

where f is porosity, Vf and Vm are P wave velocities of pore fluid and rock matrix respectively (Wyllie, 1958).

Nafe-Drake Curve

An important empirical relation exists between P wave velocity and density.

Waves and Rays

In a homogeneous, isotropic medium, a seismic wave propagates away from its source at the same speed in every direction.

Huygen’s Principle

Every point on a wavefront can be considered a secondary source of spherical waves, and the position of the wavefront after a given time is the envelope of these secondary wavefronts.

Reflection and Refraction at Oblique Incidence

When a P wave is incident on a boundary, at which elastic properties change, two reflected waves (one P, one S) and two transmitted waves (one P, one S) are generated.

Angles of transmission and reflection of the S waves are less than the P waves.

Snell’s Law

Exact angles of transmission and reflection are given by:

p is known as the ray parameter.

Critical Angles

There are two critical angles corresponding to when transmitted P and S waves emerge at 90°.

Amplitude of Reflected and Transmitted Waves

At oblique incidence, energy transformed between P and S waves at an interface.

Amplitudes of reflected and transmitted waves vary with angle of incidence in a complicated wave given by Zoeppritz equations.


P wave reflection amplitude can increase at top of gas sand.

Wave Incident on Low Velocity Layer (No critical point)

Wave Incident on High Velocity Layer (P and S critical point)

Normal Incidence Reflection Amplitudes

When angle of incidence is zero, amplitudes of reflected and transmitted waves simplify to the expressions below.

Reflection Coefficient:

Transmission Coefficient:

where Z is the acoustic (P wave) impedance of the layer, and is given by Z = Vr, where V is the P wave velocity and r the density.


Critical Refraction

When seismic velocity increases at an interface (V2>V1), and the angle of incidence is increased from zero, the transmitted P wave will eventually emerge at 90°.

Head Waves

The interaction of this wave with the interface produces secondary sources that produce an upgoing wavefront, known as a head wave, by Huygen’s principle.

The ray associated with this head wave emerges from the interface at the critical angle.


This phenomenon is the basis of the refraction surveying method.







Reflection by Huygen’s Principle

When a plane wavefront is incident on a plane boundary, each point of the boundary acts as a secondary source. The superposition of these secondary waves creates the reflection.

Diffraction by Huygen’s Principle

If interface truncates abruptly, then secondary waves do not cancel at the edge, and a diffraction is observed.

Seismic Field Record

Dynamite shot recorded using a 120-channel recording spread

Seismic Refraction Surveying

Refraction surveys use the process of critical refraction to infer interface depths and layer velocities.

Critical refraction requires an increase in velocity with depth. If not, then there is no critical; refraction: Hidden layer problem.


For a shallow survey, 12-24 vertical 30 Hz geophones would be laid out to record a hammer or shotgun shot.

First Arrival Picking

In most refraction analysis, we only use the travel times of the first arrival on each recorded seismogram.

As velocity increases at an interface, critical refraction will become first arrival at some source-receiver offset.

First Break Picking

The onset of the first seismic wave, the first break, on each seismogram is identified and its arrival time picked.

Example of first break picking on Strataview field monitor

Travel Time Curves

Analysis of seismic refraction data is primarily based on interpretation of critical refraction travel times.

Plots of seismic arrival times vs. source-receiver offset are called travel time curves.


Travel time curves for three arrivals shown previously:

Critical Distance

Offset at which critical refraction first appears.

Crossover Distance

Offset at which critical refraction becomes first arrival.

Field Surveying

Usually we analyse P wave refraction data, but S wave data occasionally recorded

Land Surveys

Typically 12 or 24 geophones are laid out to record a shot along a cable, with takeouts to which geophones can be connected.

Marine Surveys

Shot firing and seismograph recording systems are housed on a boat.

Two options for receivers:

A) Bottom-cable:

B) Sonobouys

Interpretation of Refraction Traveltime Data

After completion of a refraction survey first arrival times are picked from seismograms and plotted as traveltime curves

Interpretation objective is to infer interface depths and layer velocities

Data interpretation requires making assumption about layering in subsurface: look at shape and number of different first arrivals.


Analysis based on considering critical refraction raypaths through subsurface.

[There are more sophisticated approaches to handle non-uniform velocity and 3-D layering.]








Planar Interfaces: Two Layers

For critical refraction at top of second layer, total travel time from source S to receiver G is given by:

Hypoteneuse and horizontal side of end 90o-triangle are:

and respectively.

So, as two end triangles are the same:

At critical angle, Snell’s law becomes:

Substituting for V1/ V2, and using cos2q + sin2q = 1:

This equation represents a straight line of slope 1/V2 and intercept

Interpretation of Two Layer Case

From traveltimes of direct arrival and critical refraction, we can find velocities of two layers and depth to interface:

1.  Velocity of layer 1 given by slope of direct arrival

2.  Velocity of layer 2 given by slope of critical refraction

3.  Estimate ti from plot and solve for Z:

Depth from Crossover Distance

At crossover point, traveltime of direct and refraction are equal:

Solve for Z to get:

[Depth to interface is always less than half the crossover distance]


Planar Interfaces: Three Layer Case

In same way as for 2-layer case, can consider triangles at ends of raypath, to get expression for traveltime.

After simplification as before:

The cosine functions can be expressed in terms of velocities using Snell’s law along raypath of the critical refraction:

Again traveltime equation is a straight line, with slope 1/V3 and intercept time t2.


q1 is NOT the critical angle for refraction at the first interface.

It is an angle of incidence along a completely different raypath!


Interpretation of Three Layer Case

In three layer case, the arrivals are:

1.  Direct arrival in first layer

2.  Critical refraction at top of seconds layer

3.  Critical refraction at top of third layer

Because, intercept time of traveltime curve from third layer is a function of the two overlying layer thicknesses, we must solve for these first.

Use a layer-stripping approach:

1.  Solve two-layer case using direct arrival and critical refraction from second layer to get thickness of first layer.

2.  Solve for thickness of second layer using all three velocities and thickness of first layer just calculated.



Planar Interfaces: Multi-Layer Case

For a subsurface of many plane horizontal layers, the planar interface travel time equation can be generalised to:

where qi is the angle of incidence at the ith interface, which lies at depth Zi at the base of a layer of velocity Vi.


Proceeds by a layer-stripping approach, solving two-layer, three-layer, four-layer etc. cases in turn.


Dipping Planar Interfaces

When a refractor dips, the slope of the traveltime curve does not represent the "true" layer velocity:

To determine both the layer velocity and the interface dip, forward and reverse refraction profiles must be acquired.

Note: Travel times are equal in forward and reverse directions for switched, reciprocal, source/receiver positions.

Dipping Planar Interface: Two Layer Case

Geometry is same as flat 2-layer case, but rotated through
a, with extra time delay at D. So traveltime is:

Formulae for up/downdip times are (not proved here):

where Vu/ Vd and tu/ td are the apparent refractor velocities and intercept times.


Can now solve for dip, depth and velocities:

1) Adding and subtracting, we can solve for interface dip a and critical angle qC:


[V1 is known from direct arrival, and Vu and Vd are estimated from the refraction traveltime curves]

2) Can find layer 2 velocity from Snell’s law:

1.  Can get slant interface depth from intercept times, and convert to vertical depth at source position:


Faulted Planar Interface

If refractor faulted, then there will be a sharp offset in the travel time curve:


Can estimate throw on fault from offset in curves, i.e. difference between two intercept times, from simple formula:



Interpretation of Realistic Traveltime Data

With field data it is necessary to examine traveltime curves carefully to decide on best method to use:

Surface Topography Intervening Velocity Anomaly

Refractor Topography Refractor Velocity Variation

Delay Times

For irregular traveltime curves, e.g. due to bedrock topography or glacial fill, much analysis is based on delay times.

Total Delay Time

Difference in traveltime along actual raypath and projection of raypath along refracting interface:


Total delay time is delay time at shot plus delay time at geophone:

For small dips, can assume x=xI and:

Refractor Depth from Delay Time

If velocities of both layers are known, then refractor depth at point A can be calculated from delay time at point A:

Using RH triangle to get lengths in terms of z:

Using Snell’s law to express angles in terms of velocities:


So refractor depth at A is:

Varying Interface & Refractor Velocity: Plus-Minus Method

Hagedoorn’s Plus-Minus method used for more complex cases:


Delay time at G given by:

which can be found from observed data.

Plus and Minus Terms

Using previous figure can write down forward/ reverse traveltimes:

Minus Term

Used to determine laterally varying refractor velocity, i.e. V2(x):

Plus Term

Determines refractor depth at a location from delay time there:

So from delay time formula for depth, depth at G given by:


Plot of Minus Term

A. Composite traveltime distance plots for four different shots

B. Plot of Minus Terms: note lateral changes in refractor velocity

Hidden Layer Problem

Layers may not be detected by first arrival analysis:

A. Velocity inversion produces no critical refraction from layer 2

B. Insufficient velocity contrast makes refraction difficult to identify

C.Refraction from thin layer does not become first arrival

D.Geophone spacing too large to identify second refraction

Seismic Refraction Energy Sources

Source for a seismic survey source has to be chosen bearing in mind the possible signal attenuation that can occur, often a function of the geology.



There are many different seismic refraction sources, but the most important are:

On land:

sledge hammer, weight drop, shotgun (shallow work)

dynamite (crustal studies)

At sea:

airgun (oil exploration, crustal studies)








Land Seismic Sources: Mechanical

Sledge Hammer

A sledge hammer is struck against a metal plate:

Inertial switch on hammer triggers data recording on impact.

Accelerated weight–drop

Mechanical system, using compressed air or thick elastic slings, forces weight onto baseplate with greater force

Land Seismic Sources: Explosive

Buffalo Gun

Metal pipe inserted up to 1 m into the ground, and a blank shotgun cartridge fired.

Exploding gases from gun impact ground and generate the seismic pulse.


Shot holes up to 30 m are drilled, and loaded with dynamite, which usually comes in 0.5 m plastic cylinders that can be screwed together.

Marine Seismic Sources: Airgun

Airguns are most common seismic source used at sea.

Essentially, an airgun is a cylinder that is filled with compressed air, and then releases the air into the water.

The sudden release of air creates a sharp pressure impulse in the water.

Airgun Bubble Oscillation

1.  Air bubble from airgun expands until pressure of surrounding water overcomes its expansion, and forces it to contract.

2.  Bubble then collapses, compressing the air until the air pressure exceeds the water pressure, and the bubble can expand again.

3.  Expansion and collapse continues as bubble rises to surface, giving oscillatory signal characteristic of single airgun.

Land Sensor: The Geophone

Geophone is essentially only type of sensor used on land.

A geophone comprises a coil suspended from springs inside a magnet.

When the ground vibrates in response to a passing seismic wave, the coil moves inside the magnet, producing a voltage, and thus a current, in the coil by induction.

Principle of Geophone

Geophone Damping

As geophone coil moves inside magnet, current induced in coil produces a magnetic field that opposes, i.e. damps, the movement of the coil.

Natural Frequency

Natural frequency and damping affect the range of frequencies the geophone can record:

Marine Sensor: The Hydrophone

Hydrophones used to detect the pressure variations in water due to a passing seismic wave.

A hydrophone comprises two piezoelectric ceramic discs cemented to a sealed hollow canister.


Recording Instruments

Electrical output from geophone, i.e. voltage, is digitised by recording instrumentation and written onto tape or disk.

Data are viewed on monitor records in field to check quality.

Many different type of recording instrument available.

Example (Strataview, Geometrics)

Face of a Strataview seismograph commonly used in shallow seismic work, and able to record up to 24 channels.

Recording Channel

Channel refers to electrical input to recording system. Might be from a single geophone as in engineering work, or a group of 9 geophones, common in oil exploration.

Application to Assessment of Rock Quality

Seismic refraction most commonly employed where velocities increase suddenly with depth, e.g. determining depth to bedrock.

From the estimated layer velocities estimates of rock strength and excavation difficulty can be made.

Rippability for various common rocks:




Application to Landfill Investigation 1

Seismic methods rarely used in landfills, because seismic waves are often attenuated in the unconsolidated materials.

Fault analysis used to find quarry height from offset in intercepts


Application to Landfill Investigation 2

Integrity of clay cap from refraction velocities


Application to Tectonics: Structure of Ocean Crust

Fracture zones comprise active transform faults located between the ends of spreading segments on a midocean ridge, plus their lateral extension

Fracture zones contain some of the most rugged topography on Earth

Crustal thickness can be measured by firing explosive shots over seafloor deployed ocean-bottom

Reversed Refraction Profiles over Normal Ocean Crust

Reversed Refraction Profiles along Fracture Zone

Plane Layer Solution for Normal Ocean Crust


Plane Layer Solution for Normal Fracture Zone Crust


Fracture zone crust is thin and has low velocities due to fracturing and hydrothermal circulation


Refraction Profile Orthogonal to Fracture Zone

Raytracing for Large Lateral Velocity Variations