Geophysics

Vertical Resolution

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"

Seismic 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.

Rayleigh Criterion 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

shallow earth, upper 10 meters depth : 1000 m/s, 100 Hz, wavelength = 10 m
deep earth, 5000 meters depth: 5000 m/s, 20 Hz, wavelength= 250 m

Assumptions: seismic signal has one frequency and that seismic waves travel at one velocity and there is the level of background seismic noise is negligible

However, with 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 depths.
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])

Vertical resolution decreases with the distance traveled (hence depth) by the ray because attenuation robs the signal of the higher frequency components more readily.

Horizontal Resolution and the First Fresnel Zone ([Yilmaz, 1988 p. 470,71)

Horizontal resolution refers to how close two reflecting points can be situated horizontally, and yet be recognized as two separate points rather than one.

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 concepts:

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.