One of the unique characteristics of Synthetic Aperture Radar (SAR) satellite remote sensing is that at smaller frequencies, the SAR signal can penetrate sand under dry conditions. The electromagnetic (EM) wave penetration in soil depends upon a parameter called the “relative permittivity”, which is actually a “complex” quantity, with real and imaginary parts. The real part is called “dielectric constant” and the imaginary part is called “loss factor.” The study of penetration of EM waves in materials is based on some mathematics and physics, which we will not discuss here (relax!). These theoretical foundations are mostly covered in any undergrad / grad course or relevant book on EM waves.

Anyway, to cut a long story short, scientists define the “penetration depth” of EM wave in any material as (beware, scientific jargon coming up): “the distance at which the power density of the electromagnetic wave drops to *1/e *of its value at the immediate sub-surface.” Here, *e* is the base of the natural logarithm, with a value of *2.72*, and therefore *1/e* has a value of *0.37*. So, in more layman terms, we can think of penetration depth as follows: If the incoming EM wave has a power density of *1* units at the surface, then the depth at which it is reduced to *0.37* units, is the penetration depth.

Under certain approximations, such as uniform material properties with depth, the penetration depth *d *can be defined mathematically as:

This equation is very interesting; a quick analysis shows us the following:

- Larger wavelength (smaller frequency) means more EM wave penetration
- EM wave penetration increases as dielectric constant dielectric constant increases
- EM wave penetration decreases as loss factor increases

So, to penetrate any material, the frequency should be small, the dielectric constant should be large, and the loss factor should be small. As moisture content in an object increases, the loss factor generally increases. Therefore, penetration depth decreases with increase in moisture content: More water molecules cause more EM wave observation at the microwave frequencies. Incidentally, this is the same principle on which the microwave oven works.

Summarizing the above passage in the context of soil surfaces, we can now state: Low-frequency SAR signals can penetrate in dry soil. In the case of very dry and arid regions, e.g. Sahara desert, low-frequency SAR signals can penetrate sand down to a depth of a few meters. In the figure below is a simulation of penetration depth with respect to volumetric moisture content in sand, at L-band frequencies.

I hope this blog post serves as a good introduction to the material penetration properties of SAR, which works for not only soil, but also for forests and snow / ice studies, among others.

In my next post, I will describe a research study we have conducted to detect a paleochannel in the Cholistan Desert in Pakistan using both SAR and optical remote sensing data.

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