Vening Meinesz Research Articles

MOHO DEPTHS VERSUS GRAVITY ANOMALIES

Isostatic gravity anomalies are the best suited anomalies for different geodetic applications, such as the interpolation and the geoid determination. Different isostatic hypothesis are discussed and used to compute the depths of the Mohorovic˘ié discontinuity (Moho depths). Isostatic anomalies are then computed using different isostatic hypothesis. Comparison among the different kinds of the gravity anomalies and their empirical covariance functions are made. Vening Meinesz isostatic model gives, more or less, realistic Moho depths. Both Airy-Heiskanen and Vening Meinesz isostatic models give nearly the same isostatic anomalies. Computing the Vening Meinesz Moho depths, and hence the Vening Meinesz isostatic anomalies, is a time-consuming task. Therefore, if the isostatic anomalies are the main goal of the computation, one may easily use the better known Airy-Heiskanen isostatic model.

Geology, petrology, and petrogenesis of Little Barrier Island, Hauraki Gulf, New Zealand

Little Barrier Island is the emergent part of a large, isolated, dacite‐rhyodacite volcano in the active Hauraki Rift, 80 km northeast of Auckland. Two volcanic episodes are recognised: Waimaomao Formation was emplaced as a rhyodacite dome at 3 Ma, whereas the more extensive dacitic lavas of Haowhenua Formation were erupted between 1.2 and 1.6 Ma. All Little Barrier lavas are strongly porphyritic and contain phenocrysts of plagioclase, orthopyroxene, and hornblende. Geochemically, they are subduction related and distinct from the older lavas of the Coromandel Volcanic Group, being Zr rich but Rb and Ba poor. Their Sr and Nd isotope ratios are similar to those of the Tonga‐Kermadec arc volcanoes. Modelling of the dacite supports petrographic evidence that recharge and mixing were important in the magmatic system. Little Barrier and two dacite domes of similar age and composition near Whangarei form a northwest‐trending lineament subparallel to the Alexandra Volcanics and the Vening Meinesz Fracture Zone.

Simplification of the Southwest Pacific Neogene arcs: inherited complexity and control by a retreating pole of rotation

Abstract Neogene arc activity in the Southwest Pacific began simultaneously at 25 Ma on three differently oriented sectors. Two sectors (Norfolk-Three Kings and Colville Ridges), aligned north and north-northeast, were near-orthogonal to subduction, while the intervening Northland-Reinga sector (northwest aligned) was strongly sinistral-oblique and produced twin parallel arcs of differing compositions. This complexity was inherited from a complex late Eocene-Oligocene margin that was convergent but amagmatic, and was due primarily to its proximity to the Pacific-Australia pole of rotation. The inception of arc magmatism at 25 Ma was triggered by a 20° increase in convergence angle between the north moving Australia Plate and the northwest moving Pacific plate (from 44° to 65°), and an increase in convergence rate from c. 20 to 30–40 mm yr −1 . Between 25 and 15 Ma three subduction zones were required. The Pacific Plate was subducted at the Colville Arc, and a South Fiji Basin Plate was subducted at the Norfolk-Three Kings Arc in a manner analogous to the present-day Philippine Sea Plate located between the Mariana Arc and the Japan Trench. During this interval the Norfolk Basin opened as a back-arc basin, while the Three Kings Arc moved eastwards between two fracture zones. Eastward movement of the Three Kings Arc ( c. 350 km) was sufficient to drive a magma-producing subduction rate of c. 35 mm yr −1 independently of Pacific Plate convergence which was therefore taken up at the Colville Subduction Zone. Sinistral-oblique subduction beneath the Northland-Reinga sector was also driven by Pacific Plate convergence of c. 30 mm yr −1 . At 15 Ma the Colville Ridge extended 400 km southwestwards across North Island, New Zealand, to become a Colville-Coromandel-Taranaki Arc, and the two other arc segments died; this was the main simplification event, and it was probably a response to the progressive southeasterly retreat of the pole of Pacific-Australia rotation located to the south of New Zealand and the consequent increase in convergence rate. Between 15 and 5 Ma there was stability and no back-arc basin formed. A big change at 5Ma was probably driven by further movement of the pole, this time to the southwest, and an increase in convergence rate across New Zealand. In response, the arc split to form the still-active Lau-Havre Back-arc Basin and the active Tonga-Kermadec-Taupo Arc, and the New Zealand mountains formed. Factors remaining to be resolved are the time of collision of the oceanic Hikurangi Plateau, which has entered the New Zealand Subduction Zone, and the timing of dextral displacement(s) of the forearc to its present location along the eastern margin of the North Island. Arc simplification was accompanied by further fragmentation and dispersal of New Zealand continental crust which had already been fragmented by late Cretaceous extension. The Vening Meinesz Fracture Zone, 900 km long, originated as an Eocene near-transform sinistral boundary, and had a complex Cenozoic record of strike-slip and transpressional activation and reactivation, with both sinistral and dextral sense.

Global derivation of marine gravity anomalies from Seasat, Geosat, ERS-1 and TOPEX/POSEIDON altimeter data

SUMMARY Marine gravity anomalies over the area 82s to 82N and 0E to 360E on a 2' x 2' grid have been derived from Seasat, Geosat, ERS-1 and TOPEX/POSEIDON altimeter data. The inverse Vening Meinesz formula with a 1-D FFT method was used to compute gravity anomalies from gridded north-south and west-east geoid gradients, in a remove-restore procedure with the EGM96 gravity model as the reference field. This paper presents a new gridding technique and an altimeter data management system that help to extract data efficiently. In the 12 areas where ship-measured gravity and satellite-derived gravity were compared, rms agreements of 5-14 mgal were obtained. Special discussions of the gravity anomalies over selected inland seas, the Arctic, Antarctica and coastal waters are presented. The derived gravity anomalies show detailed tectonic structures of the world ocean. The global data set will be continuously updated with more altimeter data included in the derivation.

Basement geology from Three Kings Ridge to West Norfolk Ridge, southwest Pacific Ocean: evidence from petrology, geochemistry and isotopic dating of dredge samples

We present new petrographie, X-ray fluorescence, electron microprobe, Ar-Ar radiometric, fission track, and Sr, Nd and Pb isotopic data for igneous and metamorphic rocks from 18 dredges from a number of basins and ridges in the southwest Pacific Ocean. The dredge samples can be divided into four groups: (1) Permian to Cretaceous gabbroids, granitoids and hornfelses from the West Norfolk and Wanganella Ridges; (2) mainly Cretaceous mafic igneous rocks from the Reinga Ridge and Vening Meinesz escarpment; (3) subduction-related Late Oligocene and Early Miocene basalts and shoshonites from the Three Kings and southern Norfolk Ridges; and (4) back-arc basin and intraplate basalts of Early Miocene age in the South and North Norfolk Basins, respectively, and intraplate basalts of Pliocene age in the Reinga Basin. Our dredge data, combined with regional magnetic and gravity data, provide much-needed tests of earlier tectonic interpretations of the region. Correlatives of the Permian Brook Street Terrane and Mesozoic Median Tectonic Zone of onshore New Zealand clearly extend along the West Norfolk and Wanganella Ridges. The Three Kings Ridge was active at least in the 19- to 20-Ma period, and was probably generated above a west-dipping subduction zone. The Norfolk Basin was a back-arc basin to this arc, and had opened by 18–20 Ma. The oldest Cenozoic volcanic rocks in the region are 26-Ma subduction-related volcanic breccias on the southern Norfolk Ridge; they probably predate opening of the Norfolk Basin and associated eastward migration of the Three Kings Ridge.

Inverse Vening Meinesz formula and deflection-geoid formula: applications to the predictions of gravity and geoid over the South China Sea

Using the spherical harmonic representations of the earth's disturbing potential and its functionals, we derive the inverse Vening Meinesz formula, which converts deflection of the vertical to gravity anomaly using the gradient of the H function. The deflection-geoid formula is also derived that converts deflection to geoidal undulation using the gradient of the C function. The two formulae are implemented by the 1D FFT and the 2D FFT methods. The innermost zone effect is derived. The inverse Vening Meinesz formula is employed to compute gravity anomalies and geoidal undulations over the South China Sea using deflections from Seasat, Geosat, ERS-1 and TOPEX//POSEIDON satellite altimetry. The 1D FFT yields the best result of 9.9-mgal rms difference with the shipborne gravity anomalies. Using the simulated deflections from EGM96, the deflection-geoid formula yields a 4-cm rms difference with the EGM96-generated geoid. The predicted gravity anomalies and geoidal undulations can be used to study the tectonic structure and the ocean circulations of the South China Sea.

Improvements in the computation of deflections of the vertical by FFT

Deflections of the vertical are computed by the effective FFT method using the Vening Meinesz integral formula in spherical convolution form. The gravimetric deflection components are compared with those derived by the planar FFT techniques as well as with observed astrogeodetic components in order to assess the improvements, in terms of accuracy, obtained by the spherical approximation. The use of the spherical two-dimensional (2D) FFT improves considerably the computational efficiency with little sacrifice of accuracy in comparison with the one-dimensional (1D) FFT results. Moreover, various tests are performed with respect to the different kernel functions used, while 100% zero-padding is used in combination with discrete and analytical spectra in order to avoid the effect of circular convolution. Also discussed is the development of the software used in numerical tests, and ways of its further improvement by applying alternative formulations.

Anatomy of a continent-backarc transform ? The Vening Meinesz Fracture Zone northwest of New Zealand

The northwestern continental margin of New Zealand offers one of the finest examples of a continent-backarc transform. This transform, part of the Vening Meinesz Fracture Zone (VMFZ), accommodated about 170 km of sea-floor spreading in the Norfolk backare basin together with eastward migration of a volcanic arc, the Three Kings Ridge, in the Mid- to Late Miocene. Before the onset of spreading, strain along the VMFZ may have been linked to a major Early Miocene obduction event — the emplacement of the Northland Allochthon. The transform is manifested by a belt up to 50 km wide of left-stepping, linear fault scarps up to 2000 m high within an approximately 100 km-wide deformed zone. A marginal ridge, the Reinga Ridge, which includes a faulted, folded and uplifted Miocene sedimentary basin, occurs within the high-standing continental side of the deformed zone, whereas a narrow strip of linear detached blocks occupies the deep backarc oceanic side. Prespreading uplift and erosion of crust in the proto-backarc region, are volcanism, and obduction of the allochthon, supplied clastic sediments to the basin on the continental side. This basin was complexly deformed as the transform evolved. The transform was initiated as a dextral strike-slip fault zone, which developed right-branching splays and left-steps along its length, uplifting and cutting the continental margin into left-hand, en echelon blocks and relays. Folds formed locally within relay blocks and at the distal ends of the splays. Only the high continental side of this zone (the Reinga Ridge) remains, the formerly adjacent crust (the Three Kings Ridge) having been displaced towards the southeast. As the Three Kings block moved and the Norfolk Basin opened, opposing rift margins of the backarc basin foundered to form terraces. The oceanic side of the transform also subsided to produce the belt of detached blocks (some laterally displaced by strike slip) and linear troughs along the main escarpment system.

Oblique rifting in the Havre Trough and its propagation into the continental margin of New Zealand: Comparison with analogue experiments

The Havre Trough is opening by oblique back-arc rifting which is propagating into the continental margin of New Zealand at the Taupo Volcanic Zone. Variations of deformational style along the rift axis have been investigated by comparison with analogue experiments which incorporate brittle and ductile rheologies and are scaled for gravity. Based on the results of the analogue experiments, we present a tectonic model for oblique rifting in the Havre Trough, which involves the rheological contrast between oceanic and continental lithosphere and the oblique geometry of the continental margin of New Zealand with respect to the regional rift trend. The model shows that the continental margin, which is weaker than both oceanic and continental lithosphere, cannot support large shear stresses. The two lithospheres can be decoupled during extensional events along the marginal shear and, depending on the continental margin orientation, this shear can modify the regional stress field. A heterogeneous stress field will rotate normal stresses to be perpendicular or parallel to the margin. As the two lithospheres decouple during extension, the rift grabens and internal faults of the oblique rift system propagate normal to the marginal shear. This model explains the oblique trend of the Havre Trough's tectonic fabric and its relationships to the Vening Meinesz Fracture Zone which represents the oceanic/continental lithospheric boundary.

Thin-plate spline quadrature of geodetic integrals

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Statistical behaviour of the free-air, Bouguer and isostatic anomalies in Austria

Some selected test areas in the Austrian territory are presented. Free-air and Bouguer anomalies as well as isostatic anomalies (based on Vening Meinesz' isostatic model) are computed. Statistics of these anomalies are given. Also, an extensive comparison between their empirical covariance functions is made and will be discussed. The results show that the isostatic anomalies for our test areas still contain, in general, a trend part.

Satellite radar altimetry aids seafloor mapping

The connection between gravity and oceanic water depth was realized more than a century ago. In 1859, J. H. Pratt derived a formula relating anomalous vertical deflection and sea level height on the coast of India to the depth of the adjacent Indian Ocean. Because the predicted deflections (5′–20′ for a mean depth of 4.8 km) were not measurable, Pratt later (in 1871) inferred an excess of mass below the ocean basins, thus prefiguring the concept of isostasy in marine geology. With the accurate measurement of marine gravity on submarines by F. A. Vening Meinesz in the 1920s and 1930s, isostasy was verified and later [e.g., Watts and Ribe, 1984] related to the thickness and flexural rigidity of mechanical lithosphere.

Gravity field of the southeast central Pacific from Geosat Exact Repeat Mission Data

Efficient techniques for mapping the marine gravity field with Geosat Exact Repeat Mission (ERM) data are demonstrated. Geosat has completed more than fifty‐two 17‐day, global ERM repeat cycles and has collected roughly 50 million observations of geoid undulations or, more precisely, sea surface topography. Because the global ground track repeats every 17 days, the ERM observations are highly redundant. By averaging the repeat cycles, very precise profiles of alongtrack geoid undulations are obtained for a region of the southeast central Pacific. Without any crossing‐arc, orbit adjustments, these profiles are shown to be repeatable to within 10 cm over their entire 3000km length (i.e., to three parts in 108). This southeast central Pacific region contains a portion of the East Pacific Rise as well as some cross‐grain gravity field lineations and is therefore of considerable geophysical interest. In addition to profiles of alongtrack deflections of the vertical, regularly gridded gravity anomalies are derived for this region and portrayed in color. The procedure used for recovering gravity has two stages: in stage 1, alongtrack deflections of vertical are derived by fitting cubic splines to alongtrack heights, computing alongtrack slopes at standardized latitudes, and then averaging slopes for coincident passes; in stage 2, gridded, band‐limited gravity anomalies are recovered from deflections by using fast Fourier transform techniques to accomplish the necessary inverse Vening Meinesz transformation. High‐precision GEM‐T1 orbits are used and crossover adjustments are not performed. The operational Navy Astronautics Group orbits are shown to have systematic errors which may be as large as 10 m.

The use of FFT techniques in physical geodesy

The fast Fourier transform (FFT) technique is a very powerful tool for the efficient evaluation of gravity field convolution integrals. It can handle heterogeneous and noisy data, and thus presents a very attractive alternative to the classical, time consuming approaches, provided gridded data are available. This paper reviews the mathematics of the FFT methods as well as their practical problems, and presents examples from physical geodesy where the application of these methods is especially advantageous. The spectral evaluation of Stokes', Vening Meinesz' and Molodensky's integrals, least-squares collocation in the frequency domain, integrals for terrain reductions and for airborne gravity gradiometry, and the computation of covariance and power spectral density functions are treated in detail. Numerical examples illustrate the efficiency and accuracy of the FFT methods.

Flexural uplift of the Transantarctic Mountains

The Transantarctic Mountains have formed at the continent‐continent boundary between East and West Antarctica. High heat flow, thin crust, normal faulting, and past and present volcanism indicate that this approximately 3000‐km‐long boundary is divergent in character. Three principal structures have developed at and adjacent to the boundary: the Transantarctic Mountains, the Wilkes Basin, and the Victoria Land Basin. The Transantarctic Mountains form the east edge of East Antarctica and consist of a block‐tilted mountain range up to 4500 m high. Running parallel but 400–500 km behind, or to the west of, the Transantarctic Mountains is the Wilkes Basin. This is a broad subglacial basin where the bedrock surface is now as much as 1 km below sea level. East of and immediately adjacent to the Transantarctic Mountain front is an area of extension called the Victoria Land Basin where at least 4–5 km of Cenozoic sediments have been interpreted from seismic reflection data. The wavelengths and amplitudes of these three structures can be accounted for by the elastic flexure of two cantilevered lithospheric plates if the boundary between East and West Antarctica is taken as a stress‐free edge. Specifically, the Wilkes Basin is modeled as a flexural “outer low” coupled to uplift of the Transantarctic Mountains. Similarly, subsidence within the Victoria Land Basin is also linked to uplift of the Transantarctic Mountains via the Vening Meinesz uplift‐subsidence mechanism and sediment loading. The maximum flexural rigidity for East Antarctica is estimated to be about 1025 N m (or effective elastic thickness, Te, of 115±10 km), one of the highest values for continental rigidity from long‐term loads. Flexural rigidity for the Ross Embayment in West Antarctica is, on the other hand, found to be more than 2 orders of magnitude less at 4×1022 N m (Te = 19 ± 5 km). This rigidity variation suggests a marked contrast in effective thermal age, and hence geotherms, between East Antarctica and the western Ross Embayment. Accordingly, one of the principal uplift mechanisms for the Transantarctic Mountains is considered to be a thermal uplift associated with lateral heat conduction from the extended and thinned West Antarctic lithosphere into the thicker lithosphere of East Antarctica. Augmenting thermal uplift of the Transantarctic Mountains are the effects of erosion and the Vening Meinesz uplift effect.

Effects of Isostasy On Large-Scale Geoid Signal-I. Geoid Anomaly Over an Earth-Like Planet

The geoid anomaly due to lithospheric changes, such as cooling, is a second-order quantity which is highly sensitive to the definition of isostasy. Many different terms must be summed over a range of depths, so a simplified test planet is required to make sure the algorithm is working correctly. Our model planet consists of an ocean underlain by lithosphere and asthenosphere; there are two ocean ridges along 0° and 180° longitudes, and two trenches along 90° and 270° longitudes. the oceanic plates are moving away from the ridge with a velocity of 5 cm yr−1 at the equator. Pressure is assumed constant at the compensation depth, which is itself an equipotential surface. We use the method of rings, in which a set of 18 rings about an arbitrary pole (observation point) cover the whole earth. This method allows the anomaly source depth to be taken into account. Changes in the equipotential surface height both above and below any ring induce mass changes due to infilling with sea-water and mantle material, respectively. These mass changes cause further changes in the geoidal height over and below all the other rings, and the problem renders itself into a set of linear simultaneous equations. the final geoid is a product of seven second-order effects. the direct dipole effect due to the density differences in the cooling lithosphere (Lister 1982) produces a geoidal elevation of ⩽11 m and ⩾−11 m over the ridge and the trench, respectively. the direct mass effect (Vening Meinesz 1946), due to the fact that a column on a sphere is pie-shaped (and not straight sided as on a flat earth model), produces a geoidal elevation of ≤12 m and ≥−11 m over the ridge and the trench, respectively. the final geoidal elevation, due to the direct and indirect effects, is ⩽26 m and ⩾−26 m over the ridge and the trench, respectively.

Working at cross‐purposes: Holmes and Vening Meinesz on convection

Beginning about 1930, Arthur Holmes and Felix Andries Vening Meinesz both argued that subcrustal convection currents were inevitable because of differential radioactive heating and that these currents exerted a viscous drag on the base of the crust. Holmes and Vening Meinesz, however, were in distinct disagreement on the mechanism by which convection currents caused crustal “downbuckling” at island arcs, and more generally, the global pattern of ascending and descending convection currents. Hence it is somewhat misleading to portray them as scientific allies, as is commonly done.

Tectonic tests of proposed polar wander paths for Mars and the Moon

We have tested the polar wander paths recently proposed for Mars by Schultz and Lutz-Garihan and for the Moon by Runcorn through a comparison of the lithospheric stress field predicted for rapid global reorientations against observed tectonic features. We have employed the theory of Vening Meinesz and of Melosh to calculate the reorientation stresses, and we argue that the formation of normal faults or graben in broad regions surrounding the former rotation poles should be the minimum tectonic signature of a reorientation that generates lithospheric stresses in excess of the extensional strength of near-surface material. Such regions of normal faults are not present in the vicinity of the most recent proposed paleopoles for Mars, despite the large magnitude of the predicted shear stress (1–2 kbar). The minimum tectonic criterion would not be relaxed by invoking gradual polar wander or by considering the superposition of stresses associated with the global lithospheric response to the Tharsis rise. We conclude that polar wander of the magnitude and timing proposed by Schultz and Kutz-Garihan did not occur. It follows either that Tharsis has always been located near the Martian equator or that Tharsis began to dominate the nonhydrostatic figure prior to the end of heavy bombardment so that any tectonic signature of reorientation has since been obliterated by cratering. The predicted directions of stresses that would result from the most recent episode of proposed polar wander on the Moon, including stresses produced by reorientation of both the rotational and tidal figures, show little or no correspondence to observed tectonic features in the vicinity of the postulated nearside paleopole. The magnitude of the predicted reorientation stress is at most a few tens of bars, however, so that the tectonic test of polar wander on the Moon is inconclusive.

Least Squares Modification of Stokes’ and Vening Meinesz’ Formulas by Accounting for Truncation and Potential Coefficient Errors

Least Squares Modification of Stokes’ and Vening Meinesz’ Formulas by Accounting for Truncation and Potential Coefficient Errors

Direct integration of Stokes' Undulation and Vening Meinesz's Deflection Equations for geographically defined gravity anomaly blocks

We give here a direct solution of this problem by converting, in an indirect way, the relevant integral equations over each block to their equivalent line integrals taken along and around the boundary curves of the block. Results of sample computations given clearly demonstrate the convergence and stability of these line integrals. We also computed geoidal parameters due to a 30°×30° inner zone alone at 71 grid locations in Cameroon, using 1°×1° anomalies and integration steps of 30″ for the four innermost blocks and 180″ for the rest of the blocks and compared these with equivalent values from the midpoint method. This comparison yielded significant differences—rms ΔN = 2.2 m, ΔNmax = 4 m; rms Δξ = 2.9″, Δξmax = 10.5″; rms Δη = 2.0″, Δηmax = 6.7″—that reflect the poor accuracy of the center point method, especially for 1°×1° blocks near the computation point.