Abstract:  We attempt to resolve two conflicting pieces of information: a USGS report showing that parts of the Coachella Valley topography are sinking at the same time that GPS data shows these areas are rising.  In the process we learn some math and some Earth science.

Some Background

The Desert Sun newspaper front-page article of 10/16/00 titled Report: Parts of valley sinking--Effects of dropping aquifer beginning to show in region claimed that "The ground is subsiding in portions of Palm Desert, Indian Wells and unincorporated county land near La Quinta, which could result in property damage if a decades-old practice of over pumping the Coachella Valley Groundwater Basin isn’t reversed, according to a new U.S. Geological Survey report," and goes on to say "The aquifer, an underground layer of porous rock, sand or other matter that contains water, is estimated by the CVWD to have dropped at an average rate of 1.5 feet per year for the last 30 years [...] Sneed’s study shows that the elevation of the ground is dropping at the rate of 1.25 inches per year in a near two-square mile area in Palm Desert north of College of the Desert. At that rate, the worst in the Coachella Valley, the homes and businesses in that area would see the ground level drop more than a full foot during a 10 year period."  The USGS geologist is quoted as saying, "the technique -- called Interferometric Synthetic Aperture Radar -- has only a plus or minus error rating of one-quarter inch per year."

Searching the Internet under "Interferometric Synthetic Aperatur Radar" turns up the following:

the article The Use of Synthetic Aperture Radar Interferometry to Measure Seismic Displacements of the Landers Earthquake  by Simon Tanner who is apparently studying Msc Remote Sensing at University College London.  The abstract of Tanner's essay states: "Interferometric Synthetic Aperture Radar is a relatively new technique using two or more radar images in order to show change on the earth's surface over time. It can be used to measure the co- and post-seismic deformations created by earthquakes, and this paper will address the techniques used in the monitoring of the Landers Earthquake, an event that occurred in 1992.  Through the use of interferograms and techniques such as the phase gradient it was possible to see how up to 20 fringes were created each representing 14mm of displacement radiating from the fault lines covering a distance of about 70km."

Tanner's paper references other interesting papers, including Small-Scale Deformations Associated with the 1992 Landers, California Earthquake mapped by synthetic aperture radar interferometry Phase Gradients by Evelyn J. Price and David T. Sandwell of the Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, La Jolla, CA.

The USDA-ARS (US Department of Agriculture  - Agricultural Research Service) web site of the Southwest Watershed Research Center WSM: Spatial Analysis of Hydrology and Watershed Management

The Federation of American Scientists (FAS) has an article, Interferometric Synthetic Aperture Radar (IFSAR) Shuttle Radar Topography Mission (SRTM)

This last web site contains links to some relavent articles including Mapping the Earth, Swath by Swath by WARREN E. LEARY of the New York Times.

NASA's EOCAP-SAR (Earth Observations Commercial Applications Program - Synthetic Aperture Radar)

Crustal Strain and Topography from Synthetic Aperture Radar Interferometry, has a very nice interferogram of the Hector Mine earthquake region.

SAR Interferometry and Surface Change Detection has the best explanation of the SAR that I've been able to find: II. BASIC PRINCIPLES OF SAR INTERFEROMETRY.

ADVANCED COMPUTING TECHNOLOGY APPLICATIONS FOR SAR INTERFEROMETRY AND IMAGING SCIENCE has a nice interferogram of a volcano in Russia.

Sandia National Laboratory has a nice article, What is Synthetic Aperture Radar?

The mathematics of this can get pretty complicated (see, for instance, A Statistical Description of Polarimetric and Interferometric Synthetic Aperture Radar, in Procedings of Mathematical and Physical Sciences, Volume 449, Issue 1937, (6/8/95)).

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