Definition of Physical Height Systems for Telluric Planets and Moons

In planetary sciences, the geodetic (geometric) heights defined with respect to the reference surface (the sphere or the ellipsoid) or with respect to the center of the planet/moon are typically used for mapping topographic surface, compilation of global topographic models, detailed mapping of potential landing sites, and other space science and engineering purposes. Nevertheless, certain applications, such as studies of gravity-driven mass movements, require the physical heights to be defined with respect to the equipotential surface. Taking the analogy with terrestrial height systems, the realization of height systems for telluric planets and moons could be done by means of defining the orthometric and geoidal heights. In this case, however, the definition of the orthometric heights in principle differs. Whereas the terrestrial geoid is described as an equipotential surface that best approximates the mean sea level, such a definition for planets/moons is irrelevant in the absence of (liquid) global oceans. A more natural choice for planets and moons is to adopt the geoidal equipotential surface that closely approximates the geometric reference surface (the sphere or the ellipsoid). In this study, we address these aspects by proposing a more accurate approach for defining the orthometric heights for telluric planets and moons from available topographic and gravity models, while adopting the average crustal density in the absence of reliable crustal density models. In particular, we discuss a proper treatment of topographic masses in the context of gravimetric geoid determination. In numerical studies, we investigate differences between the geodetic and orthometric heights, represented by the geoidal heights, on Mercury, Venus, Mars, and Moon. Our results reveal that these differences are significant. The geoidal heights on Mercury vary from ? 132 to 166 m. On Venus, the geoidal heights are between ? 51 and 137 m with maxima on this planet at Atla Regio and Beta Regio. The largest geoid undulations between ? 747 and 1685 m were found on Mars, with the extreme positive geoidal heights under Olympus Mons in Tharsis region. Large variations in the geoidal geometry are also confirmed on the Moon, with the geoidal heights ranging from ? 298 to 461 m. For comparison, the terrestrial geoid undulations are mostly within ± 100 m. We also demonstrate that a commonly used method for computing the geoidal heights that disregards the differences between the gravity field outside and inside topographic masses yields relatively large errors. According to our estimates, these errors are ? 0.3/+ 3.4 m for Mercury, 0.0/+ 13.3 m for Venus, ? 1.4/+ 125.6 m for Mars, and ? 5.6/+ 45.2 m for the Moon.     

Testing Stokes-Helmert geoid model computation on a synthetic gravity field: experiences and shortcomings

We report on testing the UNB (University of New Brunswick) software suite for accurate regional geoid model determination by use of Stokes-Helmert’s method against an Australian Synthetic Field (ASF) as “ground truth”. This testing has taken several years and has led to discoveries of several significant errors (larger than 5mm in the resulting geoid models) both in the UNB software as well as the ASF. It was our hope that, after correcting the errors in UNB software, we would be able to come up with some definite numbers as far as the achievable accuracy for a geoid model computed by the UNB software. Unfortunately, it turned out that the ASF contained errors, some of as yet unknown origin, that will have to be removed before that ultimate goal can be reached. Regardless, the testing has taught us some valuable lessons, which we describe in this paper. As matters stand now, it seems that given errorless gravity data on 1′ by 1′ grid, a digital elevation model of a reasonable accuracy and no topographical density variations, the Stokes-Helmert approach as realised in the UNB software suite is capable of delivering an accuracy of the geoid model of no constant bias, standard deviation of about 25 mm and a maximum range of about 200 mm. We note that the UNB software suite does not use any corrective measures, such as biases and tilts or surface fitting, so the resulting errors reflect only the errors in modelling the geoid.     

Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data

At the beginning of the twenty-first century, a technological change took place in geodetic astronomy by the development of Digital Zenith Camera Systems (DZCS). Such instruments provide vertical deflection data at an angular accuracy level of 0.̋1 and better. Recently, DZCS have been employed for the collection of dense sets of astrogeodetic vertical deflection data in several test areas in Germany with high-resolution digital terrain model (DTM) data (10–50 m resolution) available. These considerable advancements motivate a new analysis of the method of astronomical-topographic levelling, which uses DTM data for the interpolation between the astrogeodetic stations. We present and analyse a least-squares collocation technique that uses DTM data for the accurate interpolation of vertical deflection data. The combination of both data sets allows a precise determination of the gravity field along profiles, even in regions with a rugged topography. The accuracy of the method is studied with particular attention on the density of astrogeodetic stations. The error propagation rule of astronomical levelling is empirically derived. It accounts for the signal omission that increases with the station spacing. In a test area located in the German Alps, the method was successfully applied to the determination of a quasigeoid profile of 23 km length. For a station spacing from a few 100 m to about 2 km, the accuracy of the quasigeoid was found to be about 1–2 mm, which corresponds to a relative accuracy of about 0.05−0.1 ppm. Application examples are given, such as the local and regional validation of gravity field models computed from gravimetric data and the economic gravity field determination in geodetically less covered regions.     

Unraveling magnetic fabrics

The anisotropy of magnetic susceptibility has been proven to be an excellent indicator for mineral fabrics and therefore deformation in a rock or sediment. Low-field anisotropy is relatively rapid to measure so that a sufficient number of samples can be measured to obtain a good statistical representation of the magnetic fabric. The physical properties of individual minerals that contribute to the observed magnetic fabric include bulk susceptibility and intrinsic anisotropy of the mineral phase, its volume concentration, and its degree of alignment. Several techniques have been developed to separate magnetic subfabrics arising from magnetization types, i.e., ferrimagnetism, antiferromagnetism, paramagnetism, and diamagnetism. Susceptibility anisotropy can be measured in low or high fields and at different temperatures in order to isolate a particular subfabric. Measuring the anisotropy of a remanent magnetization can also isolate ferrimagnetic fabrics. A series of case studies are presented that exemplify the value of isolating magnetic subfabrics in a geological context. It is particularly useful in rocks that carry a paramagnetic and diamagnetic subfabric of similar magnitude, such that they negate one another. Further examples are provided for purely paramagnetic subfabrics and cases where a ferrimagnetic subfabric is also identified.     

Indirect evaluation of Mars Gravity Model 2011 using a replication experiment on Earth

Curtin University??s Mars Gravity Model 2011 (MGM2011) is a high-resolution composite set of gravity field functionals that uses topography-implied gravity effects at medium- and short-scales (??125 km to ??3 km) to augment the space-collected MRO110B2 gravity model. Ground-truth gravity observations that could be used for direct validation of MGM2011 are not available on Mars??s surface. To indirectly evaluate MGM2011 and its modelling principles, an as-close-as-possible replication of the MGM2011 modelling approach was performed on Earth as the planetary body with most detailed gravity field knowledge available. Comparisons among six ground-truth data sets (gravity disturbances, quasigeoid undulations and vertical deflections) and the MGM2011-replication over Europe and North America show unanimously that topography-implied gravity information improves upon space-collected gravity models over areas with rugged terrain. The improvements are ??55% and ??67% for gravity disturbances, ??12% and ??47% for quasigeoid undulations, and ??30% to ??50% for vertical deflections. Given that the correlation between space-collected gravity and topography is higher for Mars than Earth at spatial scales of a few 100 km, topography-implied gravity effects are more dominant on Mars. It is therefore reasonable to infer that the MGM2011 modelling approach is suitable, offering an improvement over space-collected Martian gravity field models.     

Magnetic fabric variations in Mesozoic black shales, Northern Siberia, Russia: Possible paleomagnetic implications

A 28-m-long section situated on the coast of the Arctic Ocean, Russia (74°N, 113°E) was extensively sampled primarily for the purpose of magnetostratigraphic investigations across the Jurassic/Cretaceous boundary. The section consists predominantly of marine black shales with abundant siderite concretions and several distinct siderite cemented layers. Low-field magnetic susceptibility (k) ranges from 8 × 10^− 5 to 2 × 10^− 3 SI and is predominantly controlled by the paramagnetic minerals, i.e. iron-bearing chlorites, micas, and siderite. The siderite-bearing samples possess the highest magnetic susceptibility, usually one order of magnitude higher than the neighboring rock. The intensity of the natural remanent magnetization (M₀) varies between 1 × 10^− 5 and 6 × 10^− 3 A/m. Several samples possessing extremely high values of M₀ were found. There is no apparent correlation between the high k and high M₀ values; on the contrary, the samples with relatively high M₀ values possess average magnetic susceptibility and vice versa. According to the low-field anisotropy of magnetic susceptibility (AMS), three different groups of samples can be distinguished. In the siderite-bearing samples (i), an inverse magnetic fabric is observed, i.e., the maximum and minimum principal susceptibility directions are interchanged and the magnetic fabric has a distinctly prolate shape. Triaxial-fabric samples (ii), showing an intermediate magnetic fabric, are always characterized by high M₀ values. It seems probable that the magnetic fabric is controlled by the preferred orientation of paramagnetic phyllosilicates, e.g., chlorite and mica, and by some ferromagnetic mineral with anomalous orientation in relation to the bedding plane. Oblate-fabric samples (iii) are characterized by a bedding-controlled magnetic fabric, and by moderate magnetic susceptibility and M₀ values. The magnetic fabric is controlled by the preferred orientation of phyllosilicate minerals and, to a minor extent, by a ferrimagnetic fraction, most probably detrital magnetite. Considering the magnetic fabric together with paleomagnetic component analyses, the siderite-bearing, and the high-NRM samples (about 15% of samples) were excluded from further magnetostratigraphic research.