Applying essentially non‐oscillatory interpolation to controlled‐source electromagnetic modelling*

Modelling and inversion of controlled‐source electromagnetic (CSEM) fields requires accurate interpolation of modelled results near strong resistivity contrasts. There, simple linear interpolation may produce large errors, whereas higher‐order interpolation may lead to oscillatory behaviour in the interpolated result. We propose to use the essentially non‐oscillatory, piecewise polynomial interpolation scheme designed for piecewise smooth functions that contains discontinuities in the function itself or in its first or higher derivatives. The scheme uses a non‐linear adaptive algorithm to select a set of interpolation points that represent the smoothest part of the function among the sets of neighbouring points. We present numerical examples to demonstrate the usefulness of the scheme. The first example shows that the essentially non‐oscillatory interpolation (ENO) scheme better captures an isolated discontinuity. In the second example, we consider the case of sampling the electric field computed by a finite‐volume CSEM code at a receiver location. In this example, the ENO interpolation performs quite well. However, the overall error is dominated by the discretization error. The other examples consider the comparison between sampling with essentially non‐oscillatory interpolation and existing interpolation schemes. In these examples, essentially non‐oscillatory interpolation provides more accurate results than standard interpolation, especially near discontinuities.     

The biogeochemical sulfur cycle in the marine boundary layer over the Northeast Pacific Ocean

The major components of the marine boundary layer biogeochemical sulfur cycle were measured simultaneously onshore and off the coast of Washington State, U.S.A. during May 1987. Seawater dimethylsulfide (DMS) concentrations on the continental shelf were strongly influenced by coastal upwelling. Concentration further offshore were typical of summer values (2.2 nmol/L) at this latitude. Although seawater DMS concentrations were high on the biologically productive continental shelf (2–12 nmol/L), this region had no measurable effect on atmospheric DMS concentrations. Atmospheric DMS concentrations (0.1–12 nmol/m³), however, were extremely dependent upon wind speed and boundary layer height. Although there appeared to be an appreciable input of non-sea-salt sulfate to the marine boundary layer from the free troposphere, the local flux of DMS from the ocean to the atmosphere was sufficient to balance the remainder of the sulfur budget.     

The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation II-the topographic-isostatic geoid

In Part I we focussed on a convergent representation of the gravitational potential generated bytopographic masses on top of the equipotential surface atMean Sea Level, thegeoid, and by those masses which compensate topography. Topographic masses have also been condensated, namely represented by a single layer. Part II extends the computation of the gravitational field of topographic-isostatic masses by a detailed analysis of itsforce field in terms ofvector-spherical harmonic functions. In addition, the discontinuous mass-condensated topographic gravitational force vector (head force) is given. Once we identify theMoho discontinuity asone interface of isostatically compensated topographical masses, we have computed the topographic potential and the gravitational potential which is generated by isostatically compensated masses atMean Sea Level, the geoid, and illustrated by various figures of geoidal undulations. In comparison to a data oriented global geoid computation ofJ. Engels (1991) the conclusion can be made that the assumption of aconstant crustal mass density, the basic condition for isostatic modeling, does not apply. Insteaddensity variations in the crust, e.g. betweenoceanic and continental crust densities, have to be introduced in order to match the global real geoid and its topographic-isostatic model. The performed analysis documents that thestandard isostatic models based upon aconstant crustal density areunreal.     

Variations in exospheric density at heights near 1100km, derived from satellite orbits

In an earlier paper, values of exospheric density were obtained from the orbit of Echo 2 for the years 1964–1965. The results indicated a semi-annual variation in density by a factor of between 2 and 3, considerably larger than predicted by existing atmospheric models.

These studies have now been extended to the beginning of 1967, using both Echo 2 and Calsphere 1, to show how the density is responding to increasing solar activity. Variations in density during 1964 have been analysed in more detail. The long-term variation associated with the solar cycle and the short-term variations associated with magnetic and solar disturbances agree with the variations expected on the basis of current models. The semi-annual variation is persisting to higher levels of solar activity, and although its amplitude is diminishing the factor of variation was still 1.6 in 1966.     

Energetic protons from the solar flare of March 24, 1966

Ten to 100 meV protons from the solar flare of March 24, 1966 were observed on the University of California scintillation counter on OGO-I. The short rise and decay times observed in the count rates of the 32 channels of pulse-height analysis show that scattering of the protons by the interplanetary field was much less important in this event than in previously observed proton flares. A diffusion theory in which D = M _r is found to be inadequate to account for the time behavior of the count rates of this event. Small fluctuations of the otherwise smooth decay phase may be due to flare protons reflected from the back of a shock front, which passed the earth on March 23.     

The OSO-1 solar neutron experiment

BF₃ counters on OSO-1 were used to look for solar neutrons by trying to observe a diurnal variation in count rate. No effect was observed and an upper limit was placed on the solar neutron flux at the earth of J _n < 2 × 10^–3 neut/cm²/sec of 10 keV < E _n < 10 meV for the period March to May 1962. No proton-producing flares occurred during this time, so the most obvious source of solar neutrons could not be studied. The emulsion experiment of Apparao et al., flown during this period, which seemed to indicate solar neutrons has probably been misinterpreted.     

A glancing incidence solar telescope for the soft x-ray region

This paper describes the instrumentation of an Aerobee rocket (NASA 4.95 GS) which was launched from White Sands Missile Range on May 20th 1966, to observe the Sun in the soft X-ray region. The experiment package, which was pointed at the sun by a control system stabilized about all three axes, carried two Wolter type I glancing incidence telescopes to photograph the sun in wavelength regions (determined by bandpass filters) between 3 and 75 Å, and two proportional counters to obtain flux data and rough spectral shapes in the regions 2–11 Å and 8–20 Å. The spatial resolution obtained was about 20 arc seconds. Limb brightening and polar darkening are very pronounced at the longer wavelengths. A tuft of emission was observed at the North Pole in addition to an arch-like structure on the NW limb. Several of the photographs are presented, and some preliminary results are discussed.     

Riometer observations in the polar caps of solar cosmic ray events during the IQSY

During the period of the IQSY, January 1964 through December 1965, the sun remained quiet, accelerating few energetic particles. There were many instances during the IQSY when lowenergy detectors on satellites and space probes registered small intensity increases. However, few of these events were associated with protons of energies exceeding 10 MeV. Moreover, the maximum intensities (E _p > 500 keV) were typically 1–8/cm²sec ster. Most of these events were below the threshold of riometer detection.The largest solar cosmic ray event observed in 1964 by polar-based riometers was that of March 16. This event was observed by 30 and 50 Mc/s riometers at McMurdo Sound, Antarctica, and Shepherd Bay, N.W.T., Canada.The largest event in 1965 occurred on February 5 and was the largest during the IQSY. It was associated with a class 2 flare at about 1750 UT, February 5. The propagation time between the sun and Earth was about one hour. This event was well observed by satellites, space probes, and riometers.This paper discusses primarily the 5 February 1965 event. Some discussion is also given to the 16 March 1964 event, other small events during the IQSY, and the recent event in March 1966.