One of the most common questions made by people
to me about reflection seismology is on the level of detail that I
can see. The answer to this seemingly easily answered question
first requires that we have a clear definition of "resolution"
is the ability to distinguish separate features; the minimum
distance between 2 features so that the two can be defined
separately rather than as one. Normally we think of resolution in
the vertical sense, but there is also a limit to the horizontal
width of an object that we can interpret from seismic data.
The seismic "measure" is a wavelength.
In order for two nearby reflective interfaces to be distinguished
well, they have to be about 1/4 wavelength in thickness (Rayleigh
Criterion). This is also the thickness where interpretation
criteria change (AAPG Explorere, Geophysical Corner). For
smaller thicknesses than 1/4 wavlength we rely on the amplitude to
judge the bed thickness. For thicknesses larger than 1/4 wavelength
we can use the wave shape to judge the bed thickness.
e.g. Velocity =
frequency x wavelength
upper 10 meters depth : 1000 m/s, 100 Hz, wavelength = 10
deep earth, 5000 meters depth: 5000 m/s, 20 Hz, wavelength=
signal has one frequency and that seismic waves travel at one
velocity and there is the level of background seismic noise is
additional calculations we may be able to discern bed thicknesses,
for example that are as small as 1/8 of the dominant wavelength in
the signal (Widess, 1973). When the thickness of a bed is at
about 1/8 of the dominant wavelength, constructive interference of
those reflections from the top and the bottom of the bed build up
the amplitude to large values.
There is a practical
limitation in generating high frequencies that can penetrate large
The earth acts as a natural filter removing the higher frequencies
more readily than the lower frequencies.
In effect the deeper the source of reflections, the lower the
frequencies we can receive from those depths and therefore the lower
resolution we appear to have from great depths such as the middle
crust. Often we presume that the lower crust is more homogeneous but
that can be a human perception borne by poor resolution.
One could argue that
we could simply increase the power of our source so that high
frequencies could travel farther without being attenuated. However,
larger power sources tend to produce lower frequencies.
(Figure 7.31, p. 218[ Sheriff, 1995 #1510])
decreases with the distance traveled (hence depth) by the ray
because attenuation robs the signal of the higher frequency
components more readily.
resolution refers to how close two reflecting points can be situated
horizontally, and yet be recognized as two separate points rather
If we only think of rays then we never have any problems with resolving the lateral
extent of features because a ray is infinitely thin, has infinite frequencies, and
can detect all changes. We will deal with the concept of rays
versus waves later in the semester.
However, the effect
we see in real normal incidence data is explained better by wave
To begin, a reflection is not energy from just
one point beneath us. A reflection is energy that bounces back at us from a region.
As waveforms are really non-planar, reflections from a surface are returned from
over a region and over an interval of time. Signal that comes in at about the same
time may not be separated into temporally short individual components. So, we
predict that reflections
that can be considered as almost but not quite coincident in time
interfere with each other.
The area that produces the reflection is known as the First Fresnel Zone: the reflecting
zone in the subsurface insonified by the first quarter of a
wavelength. If the wavelength is large then the zone over which the
reflected returns come from is larger and the resolution is lower.
Horizontal resolution depends on the frequency and velocity.
For equations: See handouts from AAPG Explorer
and in-class notes.
Case Study: Sheriff's case
study in the AAPG Explorer shows that reflections in normal
incidence data sets collect energy over a finite area whose size
depends on the First Fresnel Zone. Reflected energy within
this footprint contributes constructively to build a wiggle in the
data set. Reflected energy from outside the footprint cancels
out in the data set.. For this reason we the physical edge of
objects that have sharp lateral terminations does not coincide
directly with the amplitude drop-off in the data.