2.1 Introduction

Figure 2.1. Geometrics 826 cesium vapor magnetometer in action at LANL waste disposal site. The Manhattan Project-era site has been covered with a clay cap and asphalt.Watch a video clip of the magnetometer in action: Quicktime or Real

The geophysical signal in Figure 1.5 is magnetic data recorded with a cesium vapor magnetometer. It was carried across a buried 1940s pit containing Manhattan Project waste at Los Alamos National Laboratory (LANL) (Figure 2.1).

You don’t have to be a geophysicist to guess that the large variations in the magnetic field in Figure 1.5 (repeated below as Figure 2.2a) are detecting buried magnetic material. This is an important finding in itself. We will probably never know exactly what is buried in the pit since records are lacking and the site will likely never be unearthed. However, digital analysis may contribute to better estimating the location and extent of some of the buried objects.

SAGE SAYS:

Amplitude usually means the maximum value (the magnitude) of a signal. In the context here, it’s used to mean the continuous, time-varying (or space-varying) values of signal strength. Don’t let this confuse you.

The magnetic field graph (Figure 2.2a) appears to be a continuous variation of signal strength with distance. Actually, both the signal amplitude and the distance were digitized during the recording. But, in this case the vertical amplitude sampling (also referred to as the sampling precision or amplitude quantization ) and the horizontal sampling interval (or sampling rate ) are so detailed that lines joining the points give the impression of a continuous signal. Geophysical data such as magnetic field variations or seismic waves are continuous in nature; as mentioned above, for these data to be useful for modern computer processing, modeling, and interpretation, the information must be available in digital form. For example, discrete values are needed for both the vertical and horizontal values of the magnetic example (Figure 2.2a) from LANL. This leads to four combinations:

  1. Continuous amplitude values and continuous space (or time) values.
  2. Continuous amplitude values and discrete space (or time) samples.
  3. Discrete amplitude samples and continuous space (or time) values.
  4. Discrete amplitude samples and discrete space (or time) samples.

These combinations are illustrated sequentially in Figures 2.2a, b, c, and d, respectively.

Figure 2.2. Four combinations of LANL total magnetic field amplitude versus distance: a) continuous amplitude and distance, b) continuous amplitude versus 100 discrete distance samples, c) 8 discrete amplitude levels versus continuous distance, and d) 8 amplitude levels versus 50 discrete distance samples.

...you might not be aware of the severity of the sampling problems since you usually don't have the "luxury" of knowing the correct, continuous result. The LANL magnetic recording in Figure 2.2a looks (to the eye) like the completely continuous combination a (above). We have used 100 discrete distance samples to present combination b in Figure 2.2b. To illustrate combinations c and d we have undersampled the amplitude (to 8 levels) and distance in d to 50 samples (Figures 2.2c and 2.2d). Figure 2.2d illustrates the way that most geophysical data are digitally recorded, i.e., discrete in both amplitude and space (or time). Serious distortion is obvious in both Figures 2.2c and 2.2d. You would be in big trouble if your recorded data looked like these examples. Yet, you might not be aware of the severity of the sampling problems since you usually don’t have the "luxury" of knowing the correct, continuous result. Understanding the potentially devastating consequences of improper sampling and how to properly record data are the subjects of this section. The vertical amplitude sampling and the horizontal sampling in space or time will be treated separately.