Induction in arbitrarily shaped oceans—III. Oceans of finite conductivity

Summary. Approximate methods of solution for induction in arbitrarily shaped oceans, derived earlier for 'oceans of infinite conductivity, are extended to cover cases where the oceans are of finite conductivity. The method enables the magnetic potential to be evaluated without undue effort. It is further shown how these ideas link up with integro-differential formulations involving either the oceanic electric current density or its associated current function. The problem of uniqueness of solution when there are two or more land masses is finally considered.     

Induction in arbitrarily shaped oceans — IV. Sq for a simple case

Summary. World curves are presented of electric currents induced in electrically insulated oceans by Sq using a perfectly conducting sphere to simulate the underlying mantle. The curves are valid everywhere away from those coastal regions at which the sea bed rises steeply. In such cases an edge correction may be needed. The numerical computations are for periods of 6, 8, 12 and 24 hr and comparison is made with results obtained by others for a 24-hr period. Circulation conditions around the island are ignored in this note.     

Induction in a thin sheet of variable conductance at the surface of a stratified earth – II. Three-dimensional theory

Summary. The algorithm of Dawson & Weaver for modelling electromagnetic induction effects in a thin sheet at the surface of a uniform earth is modified to permit the use of a layered earth model. The theory is developed in Fourier space in terms of the toroidal and poloidal transfer functions instead of with the Green's function approach which was used by Dawson & Weaver. The integral equation for the surface electric field and most of the integral formulae for the derived field components are the same as before, except for the inclusion of additional integral the kernel of which has to be calculated numerically with the aid of fast Hankel transforms. The accuracy of the results is tested by comparing solutions with those obtained from a related 2-D algorithm and finally an example of 3-D modelling is presented.     

Electromagnetic response of an arbitrarily shaped three-dimensional conductor in a layered earth—numerical results

Summary. In an earlier work, mathematical formulation on computing the electromagnetic response of an arbitrarily shaped three-dimensional inhomogeneity in a layered earth had been worked out using an integral equation technique. The method has been used to show its efficacy by computing numerical results. Introducing suitable changes of variables the secondary contributions to Green's dyadic are put in the form of convolution integrals and are computed using a digital linear filtering scheme. The matrix equation is solved for the unknown electric fields in the inhomogeneity. The scattered fields are then calculated at the surface of the Earth using the appropriate Green's dyadic. The performance of the computations has been shown by comparing the numerical results with those obtained by analogue modelling as well as by other numerical schemes. The use of digital linear filtering saves an enormous amount of computer time.
The effects of varying excitation-frequency, conductivity of the host medium and that of the overburden have been studied in detail for a horizontal loop system traversing over a two-layered earth with a prismatic inhomogeneity situated in the lower conducting half space.     

Detecting arbitrarily shaped clusters in origin-destination flows using ant colony optimization

An origin-destination (OD) flow can be defined as the movement of objects between two locations. These movements must be determined for a range of purposes, and strong interactions can be visually represented via clustering of OD flows. Identification of such clusters may be useful in urban planning, traffic planning and logistics management research. However, few methods can identify arbitrarily shaped flow clusters. Here, we present a spatial scan statistical approach based on ant colony optimization (ACO) for detecting arbitrarily shaped clusters of OD flows (AntScan_flow). In this study, an OD flow cluster is defined as a regional pair with significant log likelihood ratio (LLR), and the ACO is employed to detect the clusters with maximum LLRs in the search space. Simulation experiments based on AntScan_flow and SaTScan_flow show that AntScan_flow yields better performance based on accuracy but requires a large computational demand. Finally, a case study of the morning commuting flows of Beijing residents was conducted. The AntScan_flow results show that the regions associated with moderate- and long-distance commuting OD flow clusters are highly consistent with subway lines and highways in the city. Additionally, the regions of short-distance commuting OD flow clusters are more likely to exhibit ‘residential-area to work-area’ patterns.     

Rapid computation of magnetic anomalies with demagnetization included, for arbitrarily shaped magnetic bodies

Summary. The potential function ø for a magnetic body of susceptibility μ in a medium of susceptibility μ* satisfies the integral equation
Here Φ* is the potential function for the region without the heterogeneity and R is the distance from the point of observation to the point on the surface, s , of the body. δΦ /δn is the normal derivative, in the direction of the outward normal. The equation allows for the effects of demagnetization. For numerical purposes the surfaces can be divided into N facets over which δΦ/δ n is a constant. The unknown quantities δΦ/δn_j can be found from the system of equations defined by:
The prime on the summation sign denotes that the summation does not include the i th element. The magnetic field in the direction of the unit vector P( P ₁, P ₂, P₃ ) is given by:      

A long-term Arctic snow depth record from Abisko, northern Sweden, 1913–2004

A newly digitized record of snow depth from the Abisko Scientific Research Station in northern Sweden covers the period 1913-present. Mean snow depths were taken from paper records of measurements made on a profile comprising 10 permanent stakes. This long-term record yields snow depths consistent with two other shorter term Abisko records: measurements made at another 10-stake profile (1974-present) and at a single stake (1956-present). The measurement interval is variable, ranging from daily to monthly, and there are no data for about half of the winter months in the period 1930-1956. To fill the gaps, we use a simple snowpack model driven by concurrent temperature and precipitation measurements at Abisko. Model snow depths are similar to observed; differences between the two records are comparable to those between profile and single stake measurements. For both model and observed snow depth records, the most statistically significant trend is in winter mean snow depths, amounting to an increase of about 2 cm or 5 % of the mean per decade over the whole measurement period, and 10% per decade since the 1930-40s, but all seasonal means of snow depth show positive trends on the longest timescales. However, the start, end, and length of the snow season do not show any statistically significant long-term trends. Finally, the relation between the Arctic Oscillation index and Abisko temperature, precipitation and snow depth is positive and highly significant, with the best correlations for winter.     

The effects of the atmosphere and oceans on the Earth's wobble — I. Theory

Summary The theory of wobble excitation for a non-rigid earth is extended to include the effects of the earth's fluid core and of the rotationally induced pole tide in the ocean. The response of the solid earth and oceans to atmospheric loading is also considered. The oceans are shown to be affected by changes in the gravitational potential which accompany atmospheric pressure disturbances and by the load-induced deformation of the solid earth. These various improvements affect the excitation equations by about 10 per cent. Atmospheric and oceanic excitation can be computed using either an angular momentum or a torque approach. We use the dynamical equations for a thin fluid to relate these two methods and to develop a more general, combined approach. Finally, geostrophic winds and currents are shown to be potentially important sources of wobble excitation, in contrast to what is generally believed.     

LISPB – IV. Crustal structure of Northern Britain

Summary. This paper presents those results from the 1974 Lithospheric Seismic Profile in Britain (LISPB) which relate to the compressional velocity structure of the crust and uppermost mantle beneath Northern Britain. A combination of interpretation techniques suitable for modelling laterally inhomogeneous media, including two-dimensional ray-tracing and time-term analysis, has resulted in a detailed seismic cross-section across the Caledonian orogenic belt. The main features of this section are a possible horizontal discontinuity in the Pre-Caledonian'basement, a change in the relationship between the lower crust and the uppermost mantle from north to south and a considerable thickening of the crust beneath the Caledonian fold belt. These results place considerable constraints upon tectonic models for the evolution of the Caledonides in particular in their implication of differing crustal structures north and south of the Southern Uplands and their indication of the primary significance of the Southern Uplands Fault.