The magnetotelluric inverse problem

The magnetotelluric inverse problem is reviewed, addressing the following mathematical questions: (a)Existence of solutions: A satisfactory theory is now available to determine whether or not a given finite collection of response data is consistent with any one-dimensional conductivity profile. (b)Uniqueness: With practical data, consisting of a finite set of imprecise observations, infinitely many solutions exist if one does. (c)Construction: Several numerically stable procedures have been given which it can be proved will construct a conductivity profile in accord with incomplete data, whenever a solution exists. (d)Inference: No sound mathematical theory has yet been developed enabling us to draw firm, geophysically useful conclusions about the complete class of satisfactory models. Examples illustrating these ideas are given, based in the main on the COPROD data series.     

SYNOPTIC CONTROL OF REGIONAL TEMPERATURE TRENDS IN THE COTERMINOUS UNITED STATES BETWEEN 1949 AND 1981

Regional patterns of January and mean annual temperature change between 1949 and 1981 are compared with regional changes in January precipitation totals and related to upper-level atmospheric circulation. During cold periods, cooling is concentrated in the eastern United States and is associated with a southward shift in the zone of maximum precipitation in the eastern United States (reflecting the mean position of the polar front jet), and with a strengthening of meridional flow aloft. During this same period, enhanced meridionality yields an increase in temperatures in the Pacific Northwest, associated with amplification of the mean long wave ridge over the Rocky Mountains. Warm periods in the eastern United States, conversely, correlate with a stronger zonal flow aloft (resulting in cooler, wetter conditions in the Pacific Northwest). Accordingly, temporal variation in regional temperature trends may be more readily interpreted as responses to synoptic controls which yield departures of opposite sign in locales influenced by ridges vs. troughs, rather than as a reflection of uniform, progressive hemispheric or global temperature change.     

Influence of Casing Materials on Trace-Level Chemicals in Well Water

Four well casing materials — polyvinyl chloride (PVC), polytetrafluoroethylene (PTFE), and stainless steel 304 (SS 304) and 316 (SS 316) — were examined to determine their suitability for monitoring inorganic and organic constituents in well water.
The inorganic study used a factorial design to test the effect of concentration of mixed metals (arsenic [As], chromium [Cr], lead [Pb], and cadmium [Cd]), pH, and organic carbon. Sample times were 0.5, 4, 8, 24, and 72 hours. Except for slow loss of Pb, PTFE well casings had no significant effect on the concentration of metals in solution. For the other casings, changes in analyte concentration often exceeded 10 percent in eight hours or less and, thus, could bias analyses of samples taken from wells constructed with these materials. Specifically, PVC casings sorbed Pb and leached Cd; SS 316 casings sorbed As and Pb and leached Cd; and SS 304 casings sorbed As, Cr, and Pb and leached Cd. Both stainless steel casing materials showed markedly poorer performance than the PVC casings.
The well casings were also tested for sorption/desorption of 10 organic substances from the following classes: chlorinated alkehes, chlorinated aromatics, nitroaromatics and nitramines. Sample times were 0, 1, 8, 24, and 72 hours, seven days, and six weeks. There were no detectable losses of analytes in any of the sample solutions containing stainless steel well casings. Significant loss of some analytes was observed in sample solutions containing plastic casings, although losses were always more rapid with the PTFE casings than with PVC. Chlorinated organic substances were lost most rapidly. For samples containing PTFE casings, losses of some of these compounds were rapid enough (>10 percent in eight hours) to be of concern for ground water monitoring. Losses of hydrophobic organic constituents in samples containing PTFE casings were correlated with the compound's octanol/water partition coefficient.     

Thermal Treatment of Eight CVOC Source Zones to Near Nondetect Concentrations

In situ thermal desorption (ISTD) was used for the treatment of eight separate source zones containing chlorinated solvents in a tight loess (silt/clay) above the water table. The source areas were as much as 365 m (1200 feet) apart. A target volume of 38,200 m³ (49,950 cubic yards) of subsurface material to a depth of 9.1 m (30 feet) was treated in a period of 177 days. Energy was delivered through 367 thermal conduction heater borings, and vapors were extracted from 68 vertical vacuum wells. A vapor extraction and capture system, including a surface cover and vertical vacuum wells next to heater borings, provided for effective pneumatic control and capture of the chlorinated volatile organic compound (CVOC) vapors. A central treatment system, based on condensation and granular activated carbon filtration, was used to treat the vapors. Approximately 5675 kg (12,500 pounds) of contaminants was recovered in the extracted vapors. Forty-seven soil samples were used to document remedial performance. Based on these, the concentrations of the target contaminants were reduced to below the target remedial goals in all eight areas, typically with concentrations below 0.01 mg/kg in locations that had had CVOC concentrations higher than 1000 mg/kg. Turn-key costs for the thermal remediation were $3.9 million, and the unit treatment cost, including all utilities, was $103 per cubic meter treated ($79 per cubic yard).     

Making sound inferences from geomagnetic sounding

We examine the nonlinear inverse problem of electromagnetic induction to recover electrical conductivity. As this is an ill-posed problem based on inaccurate data, there is a critical need to find the reliable features of the models of electrical conductivity. We present a method for obtaining bounds on Earth’s average conductivity that all conductivity profiles must obey. Our method is based completely on optimization theory for an all-at-once approach to inverting frequency-domain electromagnetic data. The forward modeling equations are constraints in an optimization problem solving for the electric fields and the conductivity simultaneously. There is no regularization required to solve the problem. The computational framework easily allows additional inequality constraints to be imposed, allowing us to further narrow the bounds. We draw conclusions from a global geomagnetic depth sounding data set and compare with laboratory results, inferring temperature and water content through published Boltzmann-Arrhenius conductivity models. If the upper mantle is assumed to be volatile free we find it has an average temperature of 1409-1539 ° C. For the top 1000 km of the lower mantle, we find an average temperature of 1849-2008 ° C. These are in agreement with generally accepted mantle temperatures. Our conclusions about water content of the transition zone disagree with previous research. With our bounds on conductivity, we calculate a transition zone consisting entirely of Wadsleyite has <0.27  wt.% water and as we add in a fraction of Ringwoodite, the upper bound on water content decreases proportionally. This water content is less than the 0.4 wt.% water required for melt or pooling at the 410 km seismic discontinuity.