In this dissertation, different space marching implementations of the Mollification method are introduced to numerically recover the temperature and heat flux histories on a bounded two-dimensional rectangular body when the initial sample data are collected on one side of the body. We combined the mollification method with a singular perturbation scheme to obtain a stable algorithm. A reliable set of parameter values is experimentally determined by numerical tests to guarantee the accuracy and stability of the algorithm.
The Richmond Group (Late Ordovician) in the tristate region of southwestern Ohio, north-central Kentucky, and southeastern Indiana consists of a succession of clastic and carbonate sediments deposited on a prograding intracratonic ramp and distal clastic fan. Six regional depositional facies have been delineated during a detailed examination of cores, outcrops, and geophysical logs across a 325 by 350 km study area. The facies, informally designated Facies A through F, are assigned to depositional environments consisting of: a shale-dominated shale distal intracratonic ramp; mixed carbonate and shale proximal intracratonic ramp; shallow subtidal to supratidal intracratonic ramp, and shallow-water, distal clastic wedge; based on their sedimentologic and paleontologic characteristics. Regional cross sections of these facies indicate that the distal clastic wedge prograded from the east and that the intracratonic ramp prograded from the south. In addition, isopach maps indicate that the depocenter of the basin was located southeastern Indiana and southwestern Ohio.
The Coalinga, California region contains massive amounts of diapirically emplaced deposits of serpentinite. The largest deposit, the New Idria Formation, forms the core of the Joaquin Ridge Anticline and outcrops over an elliptically-shaped 48-square mile area in a mountainous area 17 miles northwest of Coalinga and 15 miles west of the California Aqueduct constructed along the western margin of the San Joaquin Valley. The serpentinite deposit is in faulted diapiric contact with Cretaceous-aged sandstones and shales and became emergent approximately 17 to 20 million years ago in the Miocene era. Eroded asbestos-bearing sediment from this ultramafic deposit has been incorporated in late-Miocene and younger sedimentary formations in the central San Joaquin Valley region.
The Miamitown shale has been considered an enigmatic unit in the upper part of an Edenian-Maysvillian sequence. A new look at Cincinnatian sequences reveals that this unit is actually an integral part of a complex sequence architecture. Three fourth-order sequences at the base of the Upper Ordovician in the Cincinnati area are formally named in stratigraphic order: (1) the Brent Sequence, comprising the Edenian Kope Formation; (2) the Riedlin Sequence comprising the Maysvillian Fairview, Miamitown and Bellevue formations; and (3) the Stonelick Sequence comprising the Maysvillian Corryville and Mt Auburn formations. A detailed study of the Riedlin Sequence in outcrops, cores and well logs between Cincinnati, Ohio, Ft Wayne, Indiana, and Indianapolis, Indiana, (13,000 km$\sp2$), reveals stacking patterns within the Riedlin Sequence that are comparable to those of a type-2 sequence. This interpretation contrasts with previous interpretations wherein Cincinnatian third- and fourth-order cycles are dominated by highstand systems tracts with thin or absent lowstand and transgressive deposits, or where these cycles are interpreted as parasequences or parasequence sets rather than sequences. The Miamitown Shale provides a testing ground for a new integrated cyclic, lithologic, and quantitative faunal method of correlating meter-scale fifth-order cycles. This has been accomplished within the 12 m interval surrounding the Miamitown Shale in the upper part of the Riedlin Sequence. First, using lithologic criteria alone, six shale-to-limestone cycles bounded by flooding surfaces were delineated and correlated between seven 12 m outcrop sections within a 30 km radius. Unusual fossil occurrences constrained correlations of cycles 3 & 4, and the presence of a dalmanellid, Heterorthina fairmountensis, showed that the flooding surface above cycle 3 lay 10 cm below the lithologic contact. Quantitatively-defined faunal clusters constrained correlations between all cycles, and revealed a major transition at the top of cycle 2, again below the lithologic contact. Finally, depth gradient fluctuations interpreted from ordination of faunal data suggest that the major transition at the top of cycle 2 is a transgressive surface, and that the middle part of cycle 3 includes the interval of maximum depth.