Retrieval of the piecewise-constant mass density in the Bergman wave equation

This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy, isotropic, homogeneous fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, generally-lossy, flat-plane layer in which the mass density and wavespeed are different from those of the host. The focus is on the inverse problem of the retrieval of the layer mass density. The data is the transmitted pressure field, obtained by simulation (resolution of the forward problem) in exact, explicit form via the domain integral form of the Bergman wave equation. This solution is exact and more explicit in terms of the mass-density contrast (between the host and layer) than the classical solution obtained by separation of variables. A perturbation technique enables the solution (in its form obtained by the domain integral method) to be cast as a series of powers of the mass density contrast, the first three terms of which are employed as the trial models in the treatment of the inverse problem. The aptitude of these models to retrieve the mass density contrast is demonstrated both theoretically and numerically.

Lithospheric Deformation at the South Island Oblique Collision, New Zealand

<p>Lithospheric deformation is investigated within the Southern Alps oblique collision zone of the Australian and Pacific plate boundary. Seismological methods and gravity modelling are used to estimate seismic anisotropy, wave-speed anomalies and mass anomalies in the uppermost mantle. While seismic anisotropy is generally interpreted to result from Cenozoic mantle shear, wave-speed and mass anomalies can be explained solely by thermal contraction of mantle rocks that results from the downward deflection of isotherms during mantle shortening. Along the eastern Southern Alps foothills and approximately 15' clockwise from their axis, earthquake Pn waves propagate at 8.54 +/- 0.20 km/s. This high wave speed is attributed to a high average Pn speed (8.3 +/- 0.3 km/s) and Pn anisotropy (7 - 13 %) in the mantle lid beneath central South Island. Two-dimensional ray-tracing suggests that the crustal thickness is 48 +/- 4 km beneath the Southern Alps' southern extent near Wanaka (western Otago). Such a thickness represents an 18 +/- 4 km thick crustal root that is thicker than necessary to isostatically sustain the approximately 1000 m topographic load of this region. A mass excess is proposed in the mantle below the region of over-thickened crust to compensate for the crustal root mass deficit. Assuming that the crustal root represents a -300 kg/m3 density contrast with the mantle lid, this mantle mass excess requires a minimum density contrast of 35 +/- 5 kg/m3, 110 +/-20 km width and 70 +/- 20 km thickness that will impart a downward pull on the overlying crust.</p>

Lithospheric Deformation at the South Island Oblique Collision, New Zealand

<p>Lithospheric deformation is investigated within the Southern Alps oblique collision zone of the Australian and Pacific plate boundary. Seismological methods and gravity modelling are used to estimate seismic anisotropy, wave-speed anomalies and mass anomalies in the uppermost mantle. While seismic anisotropy is generally interpreted to result from Cenozoic mantle shear, wave-speed and mass anomalies can be explained solely by thermal contraction of mantle rocks that results from the downward deflection of isotherms during mantle shortening. Along the eastern Southern Alps foothills and approximately 15' clockwise from their axis, earthquake Pn waves propagate at 8.54 +/- 0.20 km/s. This high wave speed is attributed to a high average Pn speed (8.3 +/- 0.3 km/s) and Pn anisotropy (7 - 13 %) in the mantle lid beneath central South Island. Two-dimensional ray-tracing suggests that the crustal thickness is 48 +/- 4 km beneath the Southern Alps' southern extent near Wanaka (western Otago). Such a thickness represents an 18 +/- 4 km thick crustal root that is thicker than necessary to isostatically sustain the approximately 1000 m topographic load of this region. A mass excess is proposed in the mantle below the region of over-thickened crust to compensate for the crustal root mass deficit. Assuming that the crustal root represents a -300 kg/m3 density contrast with the mantle lid, this mantle mass excess requires a minimum density contrast of 35 +/- 5 kg/m3, 110 +/-20 km width and 70 +/- 20 km thickness that will impart a downward pull on the overlying crust.</p>

Multiscale nonlinear inversion of gravity data for depth-to-basement estimation via coupled stochastic-deterministic optimization

We have developed a multiscale approach for solving 2D and 3D nonlinear inverse problems of gravity data in estimating the basement topography. The inversion is carried out in two stages in which the long-wavelength features of the basement are first estimated from smoothed gravity data via a stochastic optimization algorithm. The solution of this stage is used as the starting model for a deterministic optimization algorithm to reconstruct the short-wavelength features from the full-spectrum gravity data. The forward problem is capable of handling lateral and vertical variations in the density of sediments. Two cases are considered regarding prior knowledge about the density: (1) The density contrast between sediments at the surface and the underlying basement and its vertical variations are a priori known, and (2) only the density contrast at the surface is known with its vertical gradient to be recovered in the inversion. In the former case, the unknowns of the problem are the depths, whereas in the latter case, they are the depths and density gradients defined individually for each prism. Therefore, the inverse problem is ill-posed and has many local minima. The stochastic optimization algorithm uses a random initial model and estimates a coarse model of the basement topography. By repeating the stochastic inversion, an ensemble of solutions is formed defining an equivalent domain in the model space supposed to be within the neighborhood of the global minimum of which several starting solutions are extracted for the secondary deterministic inversion. The presented methodology has been tested successfully in converging to the global minima in 2D and 3D cases with 50 and 2352 total number of prisms, respectively. Finally, the inversion algorithm is used to calculate the thickness of the sediments in the South Caspian Basin using the EIGEN-6c4 global gravity model.

Bird’s eye view of molecular clouds in the Milky Way

Context. Describing how the properties of the interstellar medium are combined across various size scales is crucial for understanding star formation scaling laws and connecting Galactic and extragalactic data of molecular clouds. Aims. We describe how the statistical structure of the clouds and its connection to star formation changes from sub-parsec to kiloparsec scales in a complete region within the Milky Way disk. Methods. We built a census of molecular clouds within 2 kpc from the Sun using data from the literature. We examined the dust-based column density probability distributions (N-PDFs) of the clouds and their relation to star formation as traced by young stellar objects (YSOs). We then examined our survey region from the outside, within apertures of varying sizes, and describe how the N-PDFs and their relation to star formation changes with the size scale. Results. We present a census of the molecular clouds within 2 kpc distance, including 72 clouds and YSO counts for 44 of them. The N-PDFs of the clouds are not well described by any single simple model; use of any single model may bias the interpretation of the N-PDFs. The top-heaviness of the N-PDFs correlates with star formation activity, and the correlation changes with Galactic environment (spiral- and inter-arm regions). We find that the density contrast of clouds may be more intimately linked to star formation than the dense gas mass fraction. The aperture-averaged N-PDFs vary with the size scale and are more top-heavy for larger apertures. The top-heaviness of the aperture N-PDFs correlates with star formation activity up to roughly 0.5 kpc, depending on the environment. Our results suggest that the relations between cloud structure and star formation are environment specific and best captured by relative quantities (e.g. the density contrast). Finally, we show that the density structures of individual clouds give rise to a kiloparsec-scale Kennicutt-Schmidt relation as a combination of sampling effects and blending of different galactic environments.

Density contrast, deep structure, rheology and metallogeny of the crust and upper mantle of the Verkhoyano-Kolymsky region

Research subject. The Verkhoyano-Kolymsky areal of ore mineralization in the Far East of Russia.Data and methods. We used the state metallogenic map of Russia, Sc. 1: 2 500 000 (2000) and the gravity map of Russia Sc. 1: 2 500 000 (2001). Modeling was conducted by studying the deep structure of the earth’s crust and upper mantle from the anomalies of the density contrast of geological media in the intervals between the centers of density inhomogeneities and the surfaces of equivalent spheres.Results. 3D-distributions of density contrast (µz-parameter) in the crust and upper mantle of the Verkhoyano-Kolymsky region related to the rheological properties of geological media were analyzed. In the gravity models designed without attraction of external information, the structures of thrust, splitting, stretching, as well as the structures of central type (CTS) of the plume nature, were identified. In the regional stretching zone, at the border of lithospheric segments, the revealed Indigiro-Kolymsky and Verkhoyansk CTSs were described in 3D space. These structures are characterized by a mushroom-like upwelling of the asthenosphere, associated with heat flow anomalies. The identified structures differ in terms of asthenosphere depth, age and ore mineralization. The location of ore clusters and regions in the zones of CTS obeys concentric ore-magmatic zoning, typical for this type of structures. The central (trunk-like) zone of Indigiro-Kolymsky CTS features mainly high-temperature gold-quarts mineralization. On the periphery, along with gold areas, there are tin-tungsten, tin and complex ore mineralization areas. The majority of gold fields with low-temperature gold-sulfide, tin and polymetallic mineralization are attributed to the flanks of Indigiro-Kolymsky CTS. In the Verkhoyanska CTS, the majority of ore regions are characterized by multi-formation ore mineralization. In the central part of this structure, areas with mainly low-temperature tin, mercury-antimony and gold-silver ore mineralization are located. On the flanks, gold mineralization is either absent or subsidiary.Conclusions. As a result of a simple procedure, implying generalization of multiple decisions of the elementary inverse problem of gravity potential, main features of the deep structure of the Verkhyano-Kolima region were defined. In the regional stretch zone, at the boundary of lithospheric segments, the Indigiro-Kolimskaya and Verkhoyanskaya CTSs of the plume nature that control the location of ore deposits were identified and described in 3D space.

A Multiphysics approach to constrain the dynamics of the Altiplano-Puna magmatic system

Continuous Interferometric Synthetic Aperture Radar (InSAR) monitoring (> 25 years) has revealed a concentric surface deformation pattern above the Altiplano-Puna magma body (APMB) in the central Andes. Here, we use a joint interpretation of seismic imaging, gravity anomalies and InSAR data to constrain location, 3D geometry and density of the magma body. By combining gravity modelling, thermomechanical modelling, scaling law analysis and Bayesian inference, we are able to create a relationship between the geometry of a mid-crustal magma body and surface observations. Furthermore, we can estimate the uncertainties associated with the geometry of the APMB and identify the most important parameters that control the dynamics of the system. We constrain the density contrast between the APMB and the surrounding host rock to 90 - 130 kg m−3 (2σ) and the associated melt fraction to 15 - 22 %. Our visco-elasto-plastic 3D thermomechanical model reproduces the observed surface deformation self-consistently by buoyancy driven magma transport without the need for additional pressure sources. The flow pattern is controlled by a central rise at the top of the APMB whose geometry can be constrained with the help of InSAR observations while Bouguer anomalies constrain the deeper parts of the APMB. Automated scaling law analysis shows that the rheology of the upper crust and the magma mush as well as the density contrast between the two are the most important parameters in the system and need to be constrained for a better understanding of the subsurface processes.