Transient heat flow in a stratified medium

The equation of heat conduction is solved for a horizontally stratified medium initially at constant temperature and subject to a step-function surface temperature change. The problem is solved by Laplace transformation and by applying a concept of further stratifications of the medium into unitary layers of constant ratio of thickness to the square root of thermal diffusivity. The solution takes the form of an infinite sum of complementary error functions, with coefficients given by recursion relations, is suitable for numerical applications and offers an attractive alternative to harmonic and quasi transient approaches in calculating the penetration of transient surface temperature variations into a layered medium. Use of the theorem of superposition yields a general expression for an arbitrary surface temperature function. The utility of the theory is illustrated by modelling examples of palaeoclimatically induced subsurface temperature and heat flow perturbations.     

The origin of oceanic plagiogranites from the karmoy ophiolite,western Norway

Both field relationships and geochemical characteristics indicate two suites of plagiogranitic and related rocks coexisting in the higher parts of the Karmoy ophiolite of western Norway. The plutonic zone of this ophiolite can be subdivided into three complexes; the East-Karmoy Igneous Complex, the Visnes High Level Complex and the Veavagen Igneous Complex and plagiogranitic rocks are well developed in the first two of these.Within the East-Karmoy Igneous Complex, plagiogranites are associated with high temperature, pre-basic dyke, shear zones. Rare earth element modelling indicates that these plagiogranites were derived by anatexis of amphibolite (hydrated diabase) assuming a starting material consisting of 40% hornblende and 60% plagioclase and that batch melting occurred within the stability field of hornblende.In comparison, plagiogranite occurs in a number of bodies in the upper part of the Visnes High Level Complex and forms a sandwich horizon together with biotite diorites and epidosites between a roof assemblage of dykes, microgabbros and magnetite gabbros, and a floor assemblage of layered and non-layered gabbros. The R.E.E. modelling of the petrogenesis of this series of plagiogranites indicates that they were derived by filter pressing of a differentiated interstitial liquid to the vari-textured gabbros, although the distribution of highly hygromagmatophile elements such as K, Rb, Ba, etc. cannot be explained satisfactorily by this model alone. Depletion in these elements appears to be an autometasomatic effect.     

Airborne VLF Measurements and Variations of Ground Conductivity: A Tutorial

Airborne very low frequency (VLF) data are routinely collected by national agencies and commercial companies together with other passive geophysical measurements of the static magnetic field and radiometric data. The purpose of this paper is to demonstrate that both standard three-component VLF and tensor VLF (TVLF) data contain a lot of useful quantitative and qualitative information about the electrical conductivity distribution in the upper few hundred meters of the crystalline basement. We first give a new derivation of the fundamental transfer functions (the tipper) used in the TVLF technique. We then show that the tipper can be estimated from simultaneous measurements of the wave magnetic fields from at least two transmitters with somewhat different frequencies, and present a simple model by which the maximum error introduced by the difference in frequencies can be found. Single transmitter scalar VLF maps emphasise those conductive structures that have dominant strikes in the direction of the transmitter. Multiple transmitter transfer functions are dependent only upon the underlying conductivity structure. Two dimensional structures can be quantitatively modelled by modern inversion methods developed originally for deep electromagnetic magnetotelluric (MT) soundings. In such cases three-component VLF measurements can be modelled easily upon appropriate rotation of the co-ordinate system to “strike” co-ordinates. Single frequency transfer functions (tippers) have real and imaginary parts that carry information on not only lateral contrasts in conductivity, as usually stated in text books, but, taken together, they provide a robust tool for determining the background conductivity level away from distinct conductors, and they can also be used to discriminate between deep and shallow conductors. Based upon simulations using multi-frequency data, it can be concluded that such a new development would dramatically increase the resolving power of airborne VLF measurements.     

Palaeomagnetic distortion modelling and possible recovery by inversion

A robust finite-element technique is presented for computation of both the internal demagnetization effects and magnetic terrain effects in bodies with arbitrary shape and arbitrary susceptibility distribution. This method facilitates a flexible analysis of the palaeomagnetic deflection problem. Tests on geologically realistic settings of highly magnetic rocks demonstrate that deflections of several degrees may occur even for relatively simple two-dimensional models. Similarly, the magnetic intensity may well be biased by 5-15% by demagnetization effects. The present paper focuses on deflections and intensity variations inside the magnetized body, where we find a systematic shallowing of inclination for bodies with a horizontal elongation. Because the bodies sampled at a typical palaeomagnetic site will have a dominant direction of elongation, the magnetic deflection effect will tend to impose a systematic bias which doesn’t average out. An inversion-based procedure for elimination of the deflection effect is presented. It requires that the magnetic body is quite homogeneous and that its surface geometry is known, as may be the case for historical lava flows. Tests demonstrate that in order to recover both ambient palaeofield direction and the effective susceptibility at blocking temperature it is necessary to sample near strong topographic elements in the magnetic body. Since the surface geometry rarely is known it is proposed as an alternative to inversion that an effective susceptibility is assessed and a horizontal slab correction is applied for samples taken far from topographical features. When shape geometry is unknown and no correction applied, palaeomagnetic conclusions must take into account the possible bias from internal demagnetization and magnetic terrain effects.     

New paleomagnetic pole and magnetostratigraphy of Faroe Islands flood volcanics, North Atlantic igneous province

A paleomagnetic sampling was carried out along four sections (altogether 86 lava flows, 548 samples) in the North Atlantic Igneous Province outcropping in Faroe Islands, Denmark. The four polarity zones in the 700-m-thick exposed part of the Faroes lower formation can be correlated with the geomagnetic polarity time scale as C26n-C25r-C25n-C24r. The seven lava flows erupted during C25n indicate a very low eruption rate in the upper part of the Faroes lower formation of ∼1/70 kyr. The Faroes middle and upper formations (composite thickness ∼2300 m) are all reversely magnetized corresponding to C24r. The eruption rate at the onset of middle formation volcanism was very high as evidenced by several thick lava sequences recording essentially spot readings of the paleomagnetic field. The shift in eruption rate between the Faroes lower and middle formations and evidence that onset of the Faroes middle formation volcanism took place in C24r are of particular importance, placing onset of middle formation volcanism in close temporal relation to North Atlantic continental break-up and the late Paleocene thermal maximum. After grouping flows recording the same field directions, we obtained 43 independent readings of the paleomagnetic field, yielding a paleomagnetic pole with coordinates 71.4°N, 154.7°E (A₉₅=6.0°, K=14, N=43); age 55-58 Ma. The pole is supported by a positive reversal test. Paleosecular variation, estimated as the angular standard deviation of the virtual geomagnetic pole distribution 21.7°+3.9°/−2.8°, is close to expected for the given age and paleolatitude. Our new Faroes paleomagnetic pole is statistically different from the majority of previously published poles from the British and Faroes igneous provinces, and we suggest that these older data should be used with care.     

Data-moderate assessments of Cape monkfish Lophius vomerinus and west coast sole Austroglossus microlepis in Namibian waters

There is global interest in providing scientific advice on optimal harvesting of all commercially exploited fish stocks. Nevertheless, many commercially important stocks lack analytical assessments. Therefore, we evaluate a data-moderate stock assessment method: the stochastic surplus production model in continuous time (SPiCT). The method was applied to two Namibian stocks: (i) the data-rich Cape monkfish Lophius vomerinus, where results are compared to a new data-rich assessment using a state–space assessment model (SAM); and (ii) the data-moderate west coast sole Austroglossus microlepis, which is an important bycatch species in the Cape monkfish fishery, but currently unassessed. The information available to the data-moderate assessment is total commercial catch, commercial catch per unit effort (CPUE), and survey CPUE. SPiCT and SAM gave largely consistent estimates of relative fishing mortality (F/F_MSY) and relative exploitable biomass (B/B_MSY) for the Cape monkfish stock, although with some discrepancies. Differences in the biomass estimates between the two assessments suggest that further investigation is required to understand the cause, and that some caution is necessary when considering the biomass of the stock. SPiCT shows that the west coast sole may be overexploited, although the confidence bounds were too wide for a firm conclusion. Similarity in the estimates of F/F_MSY for Cape monkfish in recent years, using SPiCT relative to SAM, likewise indicates the suitability of SPiCT for managing west coast sole.