An Introduction to Seismic Refraction Theory and Application
1. What is Seismic Refraction?
One can study subsurface velocity and
layer interface structure by
analyzing the first arrival times of P-waves
compressional waves) at the surface of the earth. This
termed seismic refraction. Applications of subsurface imaging
locating buried archeological sites, assessing subsurface
hazards, defining aquifer geometry, and exploring for fossil fuel
other natural resources.
2. Seismic P-Wave Behavior
P-waves traveling through rock are
analogous to sound waves traveling
through air. The speed a P-wave propagates
through a medium depends on
the physical properties (i.e. rigidity, density,
saturation) and degree
of homogeneity of the rock. Spherical wave fronts
emanate from a
source, as well as ray paths. Ray paths travel normal to the
wave surface. For seismic refraction discussion, it is useful
imagine seismic waves as ray paths.
a ray encounters an inhomogeneity in its travels, for example a
contact with another rock, the incident ray transforms into
several new rays.
A reflected wave enters and exits at the same angle
measured to the normal of
the boundary - angle of incidence equals angle
Snell's Law, a ray path is dependent on the wave velocities through
layers. For refraction seismology, the critical angle is the
angle value to understand. If angle (r) equals 90
degrees, then the refracted
wave propagates along the boundary
interface. One can solve for the critical
angle (ic) by calculating
inverse sine of (V1/V2). As the critically
refracted wave propagates
along the boundary, according to Huygen's Theory of
primary critically refracted wave acts as a source for new
wave fronts and ray paths. These secondary ray paths exit at
3. A Simple Refraction Model: Two Horizontal Layers
In the ideal
world (of engineering), refraction seismology is most easily
through a horizontal two layer model.
waves are generated from a source (sledge hammer). Geophone
seismic signals received along the survey profile.
Since P-waves travel at
the fastest speeds, the first seismic signal
received by a geophone
represents the P-wave arrival. Five P-waves are
of interest in refraction
seismology: direct, diving, reflected, head,
refracted. The direct wave
propagates along the atmosphere-upper layer
1 boundary. A transmitted wave
through layer 2 is termed a diving wave.
A reflected wave enters with the
same angle of incidence as exit angle.
If the critical angle is achieved, the
critically refracted head wave
travels along the layer 1-layer 2 interface.
Refracted waves propagate
from the interface, with exit angles equal to the
With arrival time data collected, arrival times for
P-waves are noted or
computed from the seismographs. Arrival times can be
represented on a
travel-time graph or T-X plot, that is P-wave arrival times
milliseconds) verses distance (geophone location).
are we trying to calculate? Of interest are velocities of P-wave
through layers 1 and 2, and also thickness of layer 1. To
values, a healthy combination of equations and
interpretation from the T-X
plot is required.
Analysis of the direct wave yields V1. On the profile
view, notice that
the wave arrives at a geophone located a known horizontal
the source. Thus, V1 should equal geophone-source distance
P-wave arrival time for a given geophone. On the T-X plot, the
wave is represented by an interpolated line for arrival time
passing through the origin. The slope of this interpolated line is
over distance, or the inverse of velocity. The slope of lines on
T-X plot is termed slowness.
Another interpolated line can be
observed on the T-X plot, a line
representing the refracted wave. The
distance between the source and
first geophone to receive the refracted wave
is termed critical
distance. Cross-over distance is defined as the position
refracted wave overtakes the direct wave.
A common analogy
to the cross-over phenomenon are the travels of a
cyclist and motorist.
Imagine a cyclist and motorist depart from the
Fall AGU meeting in San
Francisco. Both are traveling to a field
excursion north of the Golden Gate
Bridge in the Marin Headlands. The
cyclist decides to pedal along the bike
path situated on the bay shore.
With regards to distance to the Marin
Headlands, the bike path distance
is much less than highway distance. The
cyclist can pedal at a constant
rate of 15 miles per hour. Think of the
cyclist as a direct wave.
Meanwhile, the motorist (e.g. refracted wave) must
deal with numerous
one-way streets and earthquake-retrofit construction,
traveling at a
snail's pace of 5 miles per hour. Eventually the motorist
finds the on
ramp onto Highway 101 and heads north for the Golden Gate Bridge
brisk 55 mph. Since the motorist is traveling at a significant
the cyclist can only wave to the motorist as the car speeds past
cyclist on the bridge. The motorist must wait several tens of
at the outcrop of Franciscan melange before the cyclist arrives at
designated field trip meeting place.
In this example, the
cross-over distance occurred at the southern end of
the Golden Gate Bridge.
The speed of the cyclist (15 mph) represents
the P-wave velocity of layer 1.
Highway speed for the motorist (55 mph)
would represent the P-wave velocity
for layer 2. Back to the T-X
From the slowness of the direct
and refracted wave, velocities in layers
1 and 2 can be calculated. To
determine depth of layer 1 (Z1), the time
intercept (ti) of the refracted
wave must be noted. Kearey & Brooks
(1984) derive and summarize the
equations necessary to calculate V1, V2,
4. Two Layer Dipping Model
When discussing dipping layers, one wants
to quantify the amount of dip.
For a simple case of two dipping layers,
seismic refraction can be
utilized to calculated dip of the layers. For a
given survey profile,
sources must be located at the beginning of the profile
and at the end of the profile (reverse shot).
arrival times for both forward and reverse shots can be plotted on
plot. From the Principle of Reciprocity, time required for a ray
along the forward and reverse shot should be the same, since
the ray pathways
are the same. From the T-X plot, V1 and V2 velocities
for forward and reverse
shots can be calculated, as well as the
time-intercepts for forward and
reverse refracted waves.
Kearey & Brooks (1984), the following equations yield layer 1
normal to the interface at the forward source (Zforward) and
(Zreverse). Small delta represents the dip of layer-1
5. Horizontal Multi-Layer Model
Why only stop with interpretation of
two horizontal layers?
of layer velocities and thicknesses for multi-layers requires
many equations chock full of algebra and trigonometry.
Please refer to Kearey
& Brooks(1984), Fowler (1990), or Burger (1996)
for these equations.
Interpretation of T-X plots remains the same.
Each layer yields an
interpolated refracted wave slowness, and time
intercept used to calculate
6. Problems and Limitations
The preceding models assume planar
boundary interfaces. Conformable
sequences of sedimentary rock may form
planar boundaries. However,
erosion and uplift easily produce irregular
boundary contacts. More
sophisticated algorithms can process refraction
surveys where irregular
interfaces might be expected.
and source energy limit the depth penetration of the
Typically, a profile can only detect features at a
depth of one-fifth survey
length. Thus, refraction imaging of the Moho
would require profile lengths of
over one hundred kilometers; an
unreasonable experiment. Larger sources could
be utilized for greater
depth detection, but certain sources (e.g.
explosives) may cause
problems in urban areas.
Refraction depends on
layers to increase in velocity with depth. In the
hidden slow layer senario,
a buried layer is overlain by a faster
layer. No critical refraction will
occur along the boundary interface.
Thus, refraction will not detect the slow
layer. All is not lost since
reflection seismology could detect the slower
Seismograms require careful analysis to pick first arrival times
layers. If a thin layer produces first arrivals which cannot easily
identified on a seismogram, the layer may never be identified.
another layer may be misinterpreted as incorporating the hidden
As a result, layer thicknesses may increase.
7. References Cited
These sources offer excellent discussion of
theory, derivation of
formulas, and practical examples of refraction
Burger, H.R. 1996. Exploration Geophysics of the Shallow
Prentice Hall. 489 pp.
Fowler, C.M.R. 1990. The Solid
Earth - An Introduction to Global
Geophysics. Cambridge University Press. 472
Kearey, P. & Brooks, M. 1984. An Introduction to
Exploration. Blackwell Scientific Publications. 296 pp.
8. Refraction Seismology Links
For a more rigorous discussion of
refraction and reflection seismology,
visit An Introduction to
Check out equipment and seismic refraction
applications in industry at
Lithoprobe is a
Canadian program to study North American continental crust using
seismology as one of many exploration methods.
If you have any comments
or questions, please email me, Eric Cannon, at firstname.lastname@example.org