Isotherm Migration Research Articles

40Ar/39Ar constraints on the emplacement, uplift, and cooling of the Coast Plutonic Complex sill, southeastern Alaska

Research Article| July 01, 1991 40Ar/39Ar constraints on the emplacement, uplift, and cooling of the Coast Plutonic Complex sill, southeastern Alaska D. J. WOOD; D. J. WOOD 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 Search for other works by this author on: GSW Google Scholar H. H. STOWELL; H. H. STOWELL 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 Search for other works by this author on: GSW Google Scholar T. C. ONSTOTT; T. C. ONSTOTT 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 Search for other works by this author on: GSW Google Scholar L. S. HOLLISTER L. S. HOLLISTER 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 Search for other works by this author on: GSW Google Scholar Author and Article Information D. J. WOOD 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 H. H. STOWELL 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 T. C. ONSTOTT 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 L. S. HOLLISTER 1Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544 Publisher: Geological Society of America First Online: 01 Jun 2017 Online ISSN: 1943-2674 Print ISSN: 0016-7606 Geological Society of America GSA Bulletin (1991) 103 (7): 849–860. https://doi.org/10.1130/0016-7606(1991)103<0849:AACOTE>2.3.CO;2 Article history First Online: 01 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation D. J. WOOD, H. H. STOWELL, T. C. ONSTOTT, L. S. HOLLISTER; 40Ar/39Ar constraints on the emplacement, uplift, and cooling of the Coast Plutonic Complex sill, southeastern Alaska. GSA Bulletin 1991;; 103 (7): 849–860. doi: https://doi.org/10.1130/0016-7606(1991)103<0849:AACOTE>2.3.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract A >700-km-long and 5- to 15-km-wide aggregation of sill-like Tertiary plutons separates low- to medium-grade (greenschist to amphibolite facies) metamorphic rocks to the west from medium- to high-grade (upper amphibolite to granulite facies) gneisses and granitic plutons to the east along the western boundary of the Coast Plutonic Complex in southeastern Alaska and British Columbia. 40Ar/39Ar analyses of hornblende, biotite, and plagioclase samples from a sea-level traverse and a 1- to 2-km-elevation traverse across one of the sills, near Holkham Bay, southeastern Alaska, yield dates that vary systematically with position. Samples collected on the eastern margin of the sill are 3 to 6 m.y. younger than samples of the same mineral collected at the same elevation from the western margin of the sill, indicating that the western margin cooled earlier. Samples collected at sea level yield 40Ar/39Ar dates on hornblende, biotite, and plagioclase that are consistently younger than those collected at 1- and 2-km elevation. Dates from the center and eastern margin of the sill define isotherm-migration rates (km/m.y.) of 0.8-1.3 at 60-56 Ma (hornblende), 0.8-0.6 at 56-53 Ma (biotite), and 0.4 at 54-50 Ma (plagioclase). 40Ar/39Ar dates from a single sea- level sample collected 15 km farther south indicate no significant variation in dates parallel to the southeasterly strike of the sill for at least 30 km. The younger dates calculated for the east side relative to the west side and metamorphic temperatures suggest that the country rock was hotter to the east than to the west when the pluton cooled through mineral blocking temperatures. The rapid isotherm migration rates calculated from the vertically distributed samples and the suggestion of hotter country rock to the east during cooling is consistent with an interpretation that the pluton intruded during uplift of the rocks to the east. Because the relative precision of the 40Ar/39Ar technique is sufficient to detect subtle difference in the cooling ages, its application to spatially distributed samples within a homogeneous plutonic body, as in this study, may yield new insights into the timing of metamorphism, magmatism, and tectonism of young mountain belts. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

TECHNICAL NOTE UNCONDITIONALLY STABLE IMPLEMENTATION OF THE ISOTHERM MIGRATION METHOD

In this paper, we present a particularly efficient implementation of the isotherm migration method for solving melting and freeing problems in which the hopscotch difference scheme is utilized to overcome the usual time-step restriction imposed on explicit-type numerical integrators. The method is illustrated on a simple one-phase problem, and numerical results are presented.

Basin and Range style tectonics in East Africa

Geophysical and geological evidence suggest that the asthenospheric structure beneath the presently active east African rifts resembles that of the Basin and Range tectonic province of the western United States. Both regions are underlain by anomalously thin lithosphere riding on hot asthenospheric pillows that extend laterally for as much as 1500 km normal to structural trend. The continental rifts associated with these terranes do not appear to be leading to plate separation, and young oceanic rifts such as the Red Sea probably evolved from narrower, more restricted mantle thermal anomalies. Low-angle normal faults are interpreted to control the physiography and structural style in the east African rifts in a fashion analogous to that proposed for the Basin and Range. The limited horizontal extension that has occurred in east Africa, however, requires that mechanical thinning of the lithosphere must play a subsidiary role to thermal crosion from below. The upward migration of mantle isotherms has converted the base of the lithosphere to material with asthenospheric properties beneath thousands of square kilometers of crust. The presence of a broad zone of thin, warm lithosphere in both these tectonic provinces may help to distribute extensional strains over correspondingly broad regions. This in turn is expected to result in the development of numerous detachment surfaces (and corresponding surficial rifts), none of which ever completely thin the lithosphere or evolve to oceanic-style rifts.

Isotherm migration method applied to fusion problems with convective boundary conditions

A numerical technique based on the Isotherm Migration Method is presented for solving Moving Boundary Problems involving convective boundary conditions. The method is illustrated by solving sample problems in one dimension as well as in two dimensions. The comparison of present results with those of earlier authors shows an extremely good agreement.

Mathematical Modeling of Microwave Thawing by the Modified Isotherm Migration Method

ABSTRACTA mathematical model of microwave thawing of homogeneous food products is developed and solved numerically using the Modified Isotherm Migration Method. The model is used to predict thawing time and temperature profiles for microwave thawed meat cylinders at three frequencies (2450 MHz, 915 MHz, 300 MHz) and different power levels. Model and experimental results for thawing a lean beef cylinder heated at low microwave power using 2450 MHz frequency compare well. The advantage of using 915 or 300 MHz power over 2450 MHz power is shown by calculations. The results show that microwaves significantly accelerate the thawing rate. The mathematical model is explored as a tool for designing optimal microwave/convective heating protocols for rapidly thawing foods in desired temperature ranges.

Solution of a stefan problem in the theory of laser welding by the method of lines

Use of a laser beam as the source of energy for penetration welding gives rise to a long, thin cylindrical hole surrounded by molten metal. Material moves from the front to the rear of the hole as the workpiece is translated relative to the laser, by flowing around the hole. A computer program has been written which solves the equations governing a 2-dimensional steady-state mathematical model in which the only spatial variations considered are in a plane perpendicular to the axis of the hole. The program uses the method of lines applied to a reformulation of the problem suitable for solution by the isotherm migration technique. Computed results have been found to agree satisfactorily with those derived from an analytical model valid for low speeds of welding, and at higher speeds they give results similar to what is observed in practice, although lack of experimental evidence precludes a detailed quantitative comparison at present.

An efficient approach to isotherm migration method in two dimensions

Analyse numerique par deux methodes l'une implicite et l'autre explicite du mouvement de l'interface liquide-solide au cours de la solidification d'un liquide dans un prisme rectangulaire de longueur definie

Moving boundary problems in simple shapes solved by isotherm migration

AbstractThe Modified Isotherm Migration Method (MIMM) is developed for solving one‐dimensional Stefan‐type problems of multifront propagation in slabs, cylinders and spheres with a boundary condition of the third kind (radiation‐type boundary condition). The method is illustrated for all three geometries with applications to the thawing of ice and to the freezing of a 50–50 dispersion of tetradecane in water, a system in which two freezing fronts propagate simultaneously.

Progressive freezing of composites analyzed by isotherm migration methods

AbstractThe Isotherm Migration Method of numerically analyzing conduction with phase change is modified to handle surface and external resistances, appearance, and propagation of successive fronts into slabs of composite material of one or more constituents finely dispersed in a matrix, different components transforming at different temperatures. Procedures are developed for selecting temperature intervals between isotherms, initially locating isotherms by means of analytical approximations to the earliest stages, and thereafter inserting and removing isotherms as appropriate, particularly when each component gives rise to a separate front.

Analysis of Propagation of Freezing and Thawing Fronts

ABSTRACTThe modified isotherm migration method (MIMM) is used to calculate the temperature profiles and freezing (thawing) times for symmetrically cooled (heated) slabs with meat‐like thermal properties. MIMM, which is reviewed briefly is not restricted to the usual idealizations such as zero surface resistance, uniform critical temperature distribution, and infinitely large sample. Dimensional analysis is used to identify the dimensionless groups controlling freezing and thawing front propogation in slabs, cylinders, and spheres having uniform thermal properties and constant freezing temperature. The MIMM results provide a basis for evaluating the qualitative origins and the quantitative extent of the success of Plank's (1913) old model. The freezing times predicted by the moving front model used here agree with those predicted by the empirical correlation found by Cleland and Earle for the Karlsruhe test substance.

A numerical method for the calculation of traveling wave solutions of a quench front problem

A numerical method is described for the solution of the following quench front problem: Find u(x, y) and ν such that ˩˨ ˩˨x k(u) ˩˨u ˩˨x +vq(u) ˩˨u ˩˨x + ˩˨ ˩˨y k(u)=0 , ˩˨u ˩˨y y=0 =f(u) , ˩˨u ˩˨y y=1 =0 , u(−∫,y)=0 , u(+∫,y)=1 , The method is based on the idea of isotherm migration. The resulting problem is an eigenvalue problem for a system of nonlinear Cauchy-Riemann equations. The method is very efficient in comparison with previous methods for this problem.

Implicit isotherm migration: A numerical method for the two-dimensional quench front problem

The traveling wave solution induced by the quenching of an axisymmetric multi-region fuel rod is numerically determined by use of a transformed heat equation in which the dependent variable is the axial position of an isotherm. The differential equation is finite-differenced in such a way as to avoid the use of prohibitively small time steps. The result is a well structured sparse system of linear equations. Sample calculations are included.

On an implicit scheme for the isotherm migration method along orthogonal flow lines in two dimensions

Abstract In a previous paper the authors developed an explicit scheme for the numerical solution of the equations of isotherm migration along orthogonal flow lines in two space dimensions. This paper presents an implicit scheme. It is used to solve a two-dimensional one-phase Stefan problem and results are compared with those obtained by other methods.

Isotherm migration along orthogonal flow lines in two dimensions

A novel approach to the solution of transient heat flow problems in two dimensions is described. The movements of isotherms along orthogonal flow lines are tracked in successive small intervals of time by solving a locally one-dimensional IMM form of radial heat equation. The determination of the new orientation of the orthogonal system at the end of each time interval is based on geometrical considerations. The method is applied to the moving boundary problem presented by the solidification of a square prism of fluid and the results compared with those obtained by the enthalpy method.

Isotherm Migration Method in two dimensions

The Isotherm Migration Method is extended to two dimensions. The equations are formulated and a convenient finite-difference method of solution is described for a variety of initial and boundary conditions. Particular attention is devoted to Stefan problems in which phase changes occur on a moving interface. As an example the solidification of a square prism of fluid is solved in detail and the numerical results are compared with those obtained by earlier authors.

An upwelling rate for Massachusetts Bay

Contours of time series bathythermograph data taken at the Boston light vessel station over several years (1964–1971) indicate that upwelling occurs in Massachusetts Bay during most summers. Cold more saline water is noted near the bottom progressing upward through the water column. Upwelling rates for 1971 of 2.0×10−4 cm s−1 and 5×10−4 cm s−1 were computed from the upward migration of isotherms and by the equations of Yoshida (1955), respectively. The upwelling period (summer) coincides with the time of predominate southeasterly to westerly winds. A definite decrease in sea level height observed during the summer of 1971 may have been due to the offshore wind-driven transport of surface water.

Paleomagnetic zones in the Oligocene East Sooke Gabbro, Vancouver Island, British Columbia

The 39-m.y.-old East Sooke polyphase gabbro stock intrudes Late Eocene Metchosin volcanics, shows no evidence of metamorphism, and is unconformably overlain by undeformed Late Oligocene sediments. A grid of samples (36 sites, 180 cores, 360 specimens) was collected in and around its 5- × 2½-mile (8 × 4 km) outcrop area at the southernmost end of Vancouver Island. Antiparallel directions, a positive contact test, thermomagnetic curves, and so forth indicate that all phases after af demagnetization retain a characteristic magnetization residing in magnetite. The stock contains a central zone of normal polarity bounded by two reverse zones. The zones are independent of petrologic boundaries. Thus all phases were solidified above the determined Curie temperatures (505° ± 10°C). Gradational direction trends in the zones show the irregular migration of isotherms in the stock while the earth's magnetic field switched polarity at least once and probably twice. The East Sooke pole position (150.9°E, 69.5°N, δm = 6.7°, δp = 5.3°) reflects a 20° ± 7° counterclockwise twist rotation of the southern Tertiary belt relative to the rest of Vancouver Island.