Using Sequential Self-Calibration Method to Identify Conductivity Distribution: Conditioning on Tracer Test data

An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases.     

The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application

Many decision-making processes in the Earth sciences require the combination of multiple data originating from diverse sources. These data are often indirect and uncertain, and their combination would call for a probabilistic approach. These data are also partially redundant with each other or with all others taken jointly. This overlap in information arises due to a variety of reasons—because the data arises from the same geology, because they originate from the same location or the same measurement device, etc. The proposed tau model combines partially redundant data, each taking the form of a prior probability for the event being assessed to occur given that single datum. The parameters of that tau model measure the additional contribution brought by any single datum over that of all previously considered data; they are data sequence-dependent and also data value-dependent. Data redundancy depends on the sequence in which the data is considered and also on the data values themselves. However, for a given sequence, averaging the tau model parameters over all possible data values leads to exact analytical expressions and corresponding approximations and inference avenues. Information on multiple-point connectivity of permeability arrives from core data, well-test data and seismic data which are defined over varying supports with complex redundancy between these information sources. In order to compute these tau weights for determining connectivity, one needs a model of data redundancy, here expressed as a vectorial training image (Ti) constructed using a prior conceptual knowledge of geology and the physics of data measurement. From such a vectorial Ti, the tau weights can be computed exactly. Neglecting data redundancy leads to an over-compounding of individual data information and the possible risk of making extreme decisions.     

Group Time Delay in the Reflection of P-Polarized Electromagnetic Plane Waves at a Stratigraphic Interface

The group time delay (GTD) formulae of quasi-total reflection of inhomogeneous P-polarized electromagnetic waves (P-PEW, whose electric field parallels to the plane of incidence), caused by the Goos–Hänchen effect, is derived by the phase shift of the wave. A numerical example where the frequency equals to 1 GHz is given. The curves of calculating results show that there are three discontinuous points at the critical angle of phase shift vector, the critical angle of attenuation vector and 90^○. When the angle of incidence is equal to one of these three angles, the GTD will become infinite, and the electromagnetic wave will propagate along the interface. The GTD will be very large, when the angle of incidence is close to one of these three angles. The results indicate that there is an important relationship between the two critical angles and the conductivity and permittivity of the two strata, and that the GTD has an important relationship with the angle of incidence. These results can be used to determine the lithology of the strata and to delimit the interfaces of strata more effectively. It is suggested that this research may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.     

Stability Analysis and Numerical Simulation of Differential Frost Heave

Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analysis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution occurs at shallow freezing depths and near-zero surface loads when positive perturbations in the ice content at the freezing front lead to a concomitant increase in thermomolecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface patterns will evolve with a length scale in the order of 2–4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Attenuation relations for strong seismic ground motion in the Himalayan region

Strong motion data from various regions of India have been used to study attenuation characteristics of horizontal peak acceleration and velocity. The strong ground motion data base considered in the present work consists of various earthquakes recorded in the northern part of India since 1986 with magnitudes 5.7 to 7.2. Using these data, relations for horizontal peak acceleration and velocity, which are $$\begin{gathered} log_{10} a = 1.14 + 0.31M + 0.65log_{10} R \hfill \\ log_{10} v = 0.571 + 0.41M + 0.768log_{10} R \hfill \\ \end{gathered} $$ have been proposed wherea is the peak horizontal acceleration in cm/sec²,v is the peak horizontal velocity in mm/sec,M is body wave magnitude, andR is the hypocentral distance in km. The proposed relations are in reasonable agreement with the small amount of strong ground motion data available for the northern part of India. The present results will be useful in estimating strong ground motion parameters and in the earthquake resistant design in the Himalayan region.     

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.     

Petrogenesis of the late-Delamerian gabbroic complex at Black Hill,South Australia: Implications for convective thinning of the lithospheric mantle

Summary A group of funnel-shaped gabbroic plutons at Black Hill, South Australia, consist of a lower series of layered peridotite, troctolite and olivine gabbro cumulates overlain by gabbronorites and potassic gabbronorites, the latter yielding a Sm-Nd isochron of 489 ± 39 Ma. Mineral assemblages in the gabbros record an olivine compositional hiatus (Fo_75-55) and a high temperature (1200-1000°C), low pressure (1 kbar), continental tholeiitic fractionation trend under moderate f_{O 2} (QFM) conditions. The liquid line of descent involved complex open system processes including recharge and crustal assimilation. In one pluton, fine-grained norites may reflect assimilation which resulted in an increaseda _SiO2 ^liquid causing orthopyroxene to crystallize prior to plagioclase.All the gabbros, including the most primitive peridotites, are LREE and incompatible element enriched. Moreover, the calculated parental magma composition in equilibrium with the most primitive troctolite has high La/Yb, La/Nb, Ti/Y and low Rb/Ba, similar to that of basaltic dykes which cut the gabbroic complex. Such compositions are untypical of melts derived from the asthenosphere suggesting that the incompatible element enrichment is not simply due to small degrees of melting. Given the isotopic constraints (Nd_i 3.4 to –4.6,⁸⁷Sr/⁸⁶Sr_i 0.7038-0.7065), this enrichment is not easily reconciled by crustal contamination either, and instead it is inferred to reflect an enriched lithospheric mantle source. Published data on mantle xenoliths from local Tertiary volcanoes overlap the isotopic and geochemical array of the gabbros and dykes, supporting this hypothesis.In conjunction with A-type granites and minor volcanic rocks, the gabbroic plutons form part of a high temperature, bimodal magmatic suite which intruded the Adelaide fold belt just after the cessation of convergent deformation during the Cambro-Ordovician Delamerian Orogeny. The appearance of such magmas is problematic since thick orogenic lithosphere severely restricts the likelihood of decompression melting in the asthenosphere. One solution to this dilemma is that convective thinning of the lithospheric mantle beneath the orogen promoted melting of hydrated, enriched regions within the lithospheric mantle. Such a model can reconcile the strong lithospheric mantle signature in the gabbros with the observation that their intrusion was coincident with uplift and the cessation of deformation.

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Die Petrogenese eines spätdelamerischen Gabbrokomplexes von Black Hill, Südaustralien: Schlußfolgerungen zur konvektiven Ausdünnung des lithospharischen Mantels

Zusammenfassung Eine Gruppe von trichterförmigen, gabbroiden Plutonen von Black Hill, Südaustralien, setzt sich aus einer unteren Serie von geschichteten Peridotiten, Troktoliten and Olivin-Gabbro-Kumulaten, die von Gabbro-Noriten und potassischen Gabbros überlagert werden, zusammen; letzgenannte Gesteine ergaben ein Sm-Nd Isochronenalter von 489 ± 39 Ma. Die Mineralzusammensetzungen der Gabbros belegen eine Mischungslücke bei Olivin (Fo_75-55). Die Gesteine folgen einem kontinentalen, tholeiitischen Fraktionierungstrend und kristallisierten bei hohen Temperaturen (1200-1000°C), unter niedrigem Druck ( 1 kbar) and moderatem fo₂ ( QFM). Wiederholte Magmenzufuhr und Krustenassimilation sind weitere zu beriicksichtigende, komplexe Prozesse, die sich in einem offenen System abspielten. Feinkörnige Norite von einem der Plutone könnten durch Assimilationsprozesse - she äußern sich in einer Erhöhung desa _SiO₂ ^liquid liquid - entstanden sein. In diesen Gesteinen kristallisierte Orthopyroxen vor Plagioklas.Alle Gabbros, einschließich der primitivsten Peridotite, sind an LREE und inkompatiblen Elementen angereichert. Die berechnete Zusammensetzung des Ausgangsmagmas, das im Gleichgewicht mit dem primitivsten Troktolit steht, weist hohe La/Yb, La/Nb, Ti/Y and niedrige Rb/Ba auf. Basaltische Dykes, die die Gabbros durchsetzen zeigen ähnliche Elementverhältnisse. Derartige Zusammensetzungen sind untypisch für astenosphärische Schmelzen und belegen, daß die Anreicherung an inkompatiblen Elementen nicht einfach nur mit geringen Aufschmelzungsraten zu erklären ist. Auf Grund der Isotopendaten (Nd_i 3.4 to -4.6,⁸⁷Sr/⁸⁶ Sr_i 0.7038–0.7065) kann these Anreicherung auch nicht leicht mit Krustenkontamination erklärt werden. Vielmehr wird eine angereicherte, lithosphärische Mantelquelle vermutet. Publizierte Daten an Mantelxenolithen von tertiären Vulkanen zeigen sehr ähnliche isotopische und geochemische Zusammensetzungen and belegen these Hypothese.Gemeinsam mit A-Typ Graniten und untergeordnet, vorkommenden, vulkanischen Gesteinen sind die Gabbros Teil einer hochtemperierten bimodalen, magmatischen Serie, die den Adelaide Fold Belt postdeformativ, während der kambro-ordovizischen delamerischen Orogenese, intrudierten. Das Vorkommen solcher Magmen ist problematisch, da die Präsenz dicker, orogen gebildeter Lithosphäre die Möglichkeit der Dekompressions-Aufschmelzung der Astenosphäre stark vermindert. Eine mögliche Lösung dieses Dilemmas ist, daß konvektives Ausdünnen des lithosphärischen Mantels unterhalb der Orogenzone das Aufschmelzen von hydratisierten, angereicherten Regionen innerhalb der Lithosphäre förderte. Dieses Modell bringt die Beobachtungen, daß die Gabbros einerseits eine lithosphärische Signatur zeigen, andererseits aber während der Hebungsphase und am Ende des Deformationsgeschehens intrudierten, in Einklang.

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With 15 Figures