Modeling techniques commonly exhibit errors of 3 to 10 percent or more in the calculation of apparent resistivities over earth models for which analytic solutions are easily available. A singularity occurs in the solution of any elliptic partial differential equation for which the forcing function is not smooth. The inability to adequately represent in discrete space a discontinuous function (in this case, the delta function describing the introduction of current at a point) commonly results in numerical error near the source of a modeled singularity.Inspection of an integrated finite-difference method for modeling the de resistivity geophysical technique indicates much of the error encountered is of singular origin. A procedure is herein detailed by which the singularity is mathematically removed from the modeling process and reintroduced as a last step, thus preventing it from contributing to the numerical error. Using this procedure, the average error in apparent resistivity values for a model of a polar-dipole traverse over a nonconducting sphere is reduced by 40 percent. For a dipole-dipole traverse of a two-layer model the error decreases by 75 percent, and in the case of a Wenner profile of a model of a vertically faulted earth, the average error is diminished by 90 percent.

Rocks that were once present in the deep continental crust can be found in surface exposure as xenoliths, as parts of high-grade metamorph{c and plutonic terrains, and as obducted lower crustal cross sections. A review of magnetic and mineralogic studies of samples representing all such occurrences shows that magnetite is the only magnetic phase present in significant amounts in these rocks. Thermodynamic considerations indicate that Tipoor magnetite is the expected magnetic oxide under equilibrium conditions that exist i n the lower crust, regardless of the primary magmatic composition of the spinel phase. Furthermore, it seems unlikely that serpentinites with metal alloys contribute significantly to the magnetization of the•lower crust or mantle. Thus magnetite in the deep-crust is the most likely candidate for the soq•ce of the long-wavelength magnetic anomalies observed in regional aeromagnetic and satellite magnetometer surveys. If so, the entire crust sho'utd be magnetic in most continental areas, including shields. In areas of high heat flow the bottom of the magnetic crust may lie considerably above the Moho. Pre-orogenic tectonics and metamorphism in western Tethys ophiolites, Ofioliti, 9, 245-278, 1984. Andersen, D. J., and D. H. Lindsley, New (and final) models for the Ti-magnetite/ilmenite geothermometer and oxygen barometer, Eos Trans. AGU, 66, 416, 1985. Berckhemer, H., Direct evidence for the composition of the lower crust and the MOHO, Tectonophysics, 8, 97-105, 1969. Bohlen, S. R. and E. J. Esserie, Feldspar and oxide thermometry of granulites in the 6520 Frost and Sh•ve: Magnetic Mineralogy of the Continental Crust Adirondack Highlands, Contrib. Mineral.

Curie point and lattice parameter measurements were made on 57 titanomaghemite samples produced from sintered titanomagnetites with x (mole fraction ulvospinel) values of 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. Oxidation was carried out in various atmospheres at temperatures as low as 113°C for durations of about 24 hours. The oxidation process was successful in producing homogeneous titanomaghemites with z (oxidation parameter) values between 0.0 and 1.0. Spinels with z < 0.6 are generally single phase, but the necessity of using temperatures greater than 300°C to produce strongly oxidized phases resulted in spinel oxidation in the presence of a rhombohedral phase. Curie temperature and lattice constant data are significantly different from results presented by Ozima and Sakamoto (1971), Readman and O'Reilly (1972), and Nishitani (1979). Although some of these differences may be due to unmixing (inversion), most of them apparently result from differences in techniques of titanomaghemite preparation and oxidation.

Peak area analyses of room temperature Mössbauer spectra of synthetic titanomagnetites permit a direct test of the cation distribution models proposed for this series. The analyses were confined to samples containing 80 mole % or more magnetite. These samples have an average cation distribution very close to that described by Akimoto's model, but the spectra suggest that most of the titanium resides in small clusters of titanium‐rich (x ≃ 0.6) composition surrounded by a matrix of almost pure magnetite. The size and composition of the clusters may be affected by the method of sample preparation, and this effect could explain the scatter in saturation magnetization measurements of titanomagnetites made by others. Theoretical considerations of the behavior of small polarons indicate that it is impossible to freeze a high‐temperature cation distribution by quenching because of rapid electron transfer.

Seventeen samples from the Malenco serpentinite in the Swiss Alps, representing systematic prograde metamorphic conditions from prehnite‐pumpellyite to upper amphibolite, are moderately to strongly magnetic (average susceptibility of 6.61×10−2 SI units) due predominantly to the presence of a magnetite‐rich spinel. Some greenschist facies samples contain the metal alloy awaruite (Ni3Fe); these contain in addition much greater amounts of magnetite. Small amounts of pyrrhotite in about half the samples complete the contributions to the total magnetization. Susceptibilities generally decrease with increasing metamorphic grade because of the production of increasing amounts of chromerich spinel which dilutes the magnetite component. These results indicate that significant magnetic anomalies should be generated in suture zones containing metamorphosed serpentinite and in areas where serpentinite is being actively subducted.