In this note, we present the Bursa-Wolf seven-parameter transformation from one geodetic system to another, showing how to determine the 7 parameters by the method of least squares and calculate them numerically following the number of the parameters 4,5 or 7.

To celebrate the launch of the "Tunisian Land Information System (TLIS)" project, we would like to recall some of the history of Tunisian geodesy since its inception, and describe in detail the terrestrial and spatial geodetic systems that have been used since then.

In this note, we present the Bursa-Wolf seven-parameter transformation from one geodetic system to another, showing how to determine the 7 parameters by the method of least squares and calculate them numerically.

In this note, we give a method to resolve the equation β(φ)=Y used in geodesy, where β(φ) is the length of the arc of the meridian of an ellipse or an ellipsoid from the equator to the point of geodetic latitude φ.

A Specific Magnitude Budget for the Detection of 44 Nuclear Earthquakes near Large Urban Areas subject to a Natural Seismic Hazard was crucial for finding the typical parameters of the Nuclear Earthquakes : $5.9-7.9~M_w$, from 1st January 1960 to 15th September 2023, $R_i <160~km$ with the index $i$ spanning the $1230$ largest cities and having a maximal horizontal shaking ratio $10^{M_w,i} /R_i^2$ for each specific city $i$ satisfying these typical parameters. Therefore, it allows to build a filter $mathcal{F}_Z$ and to filter out a total of $189$ earthquakes around $372$ cities with a relatively low background of Natural Earthquakes with respect to the Nuclear ones. By including the $189$ filtered earthquakes around these $372$ cities, there is a total of $393$ cities having enough seismic data, with respect to a sufficiently large background of the recent smaller earthquakes around these same cities ($M_wgeq M_{w,0} =4.0$, 1980-2022, $R_i < R_{max}=160~km$, Gutenberg-Richter law and $Delta N_i geq 10^{5.9-4.0}>79$ in the case of an absence of filtered earthquakes with the filter $mathcal{F}_Z$), in order to derive the Probability Estimation of having a such maximal horizontal shaking ratio. Finally, there is a 8.4-$sigma$ anomaly from a statistical excess of the maximal horizontal shaking ratio of the filtered earthquakes with the filter $mathcal{F}_Z$ and with a Probability Estimation Cutoff of $<0.43$ (There is an artifact close to $1$ arising from an exponential behavior inside the Probability Estimation formula of having a such maximal horizontal shaking ratio). Of course, by taking some random positions for the $1230$ largest cities, it vanishes completely that 8.4-$sigma$ anomaly.

This is the part III and the last of the correction of the collection of exams of geodesy and mathematical cartography. These exams are from the German school, namely from the Institute of Geodesy of the University of Stuttgart where the eminent professor Erik W. Grafarend (1939-2020) taught geodesy courses and in particular mathematical cartography. This is an opportunity for French-speaking students to share the German methodology.

This is the part II of the correction of the collection of exams of geodesy and mathematical cartography. These exams are from the German school, namely from the Institute of Geodesy of the University of Stuttgart where the eminent professor Erik W. Grafarend (1939-2020) taught geodesy courses and in particular mathematical cartography. This is an opportunity for French-speaking students to share the German methodology.

This is the part I of the correction of the collection of exams of geodesy and mathematical cartography. These exams are from the German school, namely from the Institute of Geodesy of the University of Stuttgart where the eminent professor Erik W. Grafarend (1939-2020) taught geodesy courses and in particular mathematical cartography. This is an opportunity for French-speaking students to share the German methodology.

This paper contains a selected collection of exams of geodesy and mathematical cartography. These exams are from the German school, namely from the Institute of Geodesy of the University of Stuttgart where the eminent professor Erik W. Grafarend (1939-2020) taught geodesy courses and in particular mathematical cartography. This is an opportunity for French-speaking students to share the German methodology.

This paper is a tribute to the memory of professor and geodesist Helmut Moritz who passed away in December 2022. We present a paper about the theory of geodetic refraction written by him and presented during the International Symposium " Figure of the Earth and Refraction ",Vienna, March 14th-l7th, 1967.

It is a tribute to the memory of my professor of geodesy Jacques Le Menestrel. We give a numerical version of the two first chapters of his booklet "Dynamical Geodesy". It is part of his complete geodesy course, taught in the 70s of the last century, at the Ecole Nationale des Sciences Géographiques (ENSG), France.

In this short note, we give some elements on the gravity field and gravimetry. In addition, we will return to applications for altitude definitions and precision leveling observations as well as distance reductions.

Multiple underground nuclear explosions may trigger the rupture of seismic faults and mimic a natural earthquake. Moreover, multiple nuclear explosions can be spatially arranged (on a vertical line for instance) and temporally synchronized in order to reduce significantly the P-waves (except inside both spherical cones along the vertical line arrangement).A Specific Magnitude Budget, with the relevant elementary approximations, is relatively enough accurate to compare unambiguously the energy of the stress drop over the fault rupture and the energy of the radiated seismic waves.Indeed, for the largest natural earthquakes precisely recorded ($6.9 leq M_wleq 7.3$), we define very conservatively their average seismic radiation efficiency to $0.25$. It follows from that definition, the natural seismic radiation efficiency ranges between $0.113$ and $0.520$ around the average $0.269$ (the natural Specific Magnitude Budget range between $Delta_{nat}^{min} M_Z=-0.630$ and $Delta_{nat}^{max} M_Z=-0.189$ around the average $Delta_{nat}^{mean} M_Z=-0.380$).On the other hand, the nuclear seismic radiation efficiency ranges between $1.185$ and $1~113$ around the average $81.9$ (the nuclear Specific Magnitude Budget range between $Delta^{min}_{nuc} M_Z=0.049$ and $Delta^{max}_{nuc} M_Z=2.031$ around the average $Delta_{nuc}^{mean} M_Z=1.275$).In practice, the natural seismic radiation efficiency is always $2.278times$ times smaller than the nuclear seismic radiation efficiency (an artificial gap of the Specific Magnitude Budget $Delta_{gap} M_Z=0.238$ is found). Indeed, to provoke a more powerful stress drop over the fault rupture with multiple underground explosions, an accurate information about the future epicenters should be known which is impossible in practice. Lowering too much the energy of the multiple underground nuclear explosions would also increase the risk of not triggering at all the rupture of a seismic fault.

This note, written after my participation in 1982 in the astronomical campaign for observations of 8 Laplace points, presents the procedure for determining the astronomical azimuth of a direction by observing the pole star, notingthe time of its observation, i.e. the so-called time method.

Recently, in an article, we reviewed some models of equipotential surfaces of the normal field of gravity relative to the Earth. In this note, we will apply the important theorems of surface theory to the surface obtained from the second model whose normal gravitational field is given by:$$ U= frac{Gm}{r}+frac{1}{2}omega^2left(x^2+y^2ight) $$

The object of this note is to present the equation of the surface which defines the equipotential field of gravity $U=U_0$ for certain models of the normal potential of gravity $U$.

In this additional note on least squares, we will come back to a few theorems of the theory of errors and that of least squares which are not well enough known even among geodesists. This is due to the absence of documentation in French on the subject. It is thanks to a work of the Russian school, of the mathematician Yori Vladimirovich LINNIK (1915-1972) on the theory of least squares, published in French in 1963 which I was inspired to write this note.

If one compares long-term recordings of the air pressure measured by neighboring barometers, one observes synchronous oscillations at certain frequencies for which there is no known cause. Are they excited by gravitational waves?

With the introduction of GPS (Global Positioning System) technology, which provides the user with his three-dimensional (X,Y,Z) position in the global geocentric system called WGS84 (World Geodetic System 1984), it is necessary to know the transformation of altitudes from the world geodetic system to the national or local geodetic system. We present below some models of transformations of passage of altitudes between geodetic systems.

In this note, we study the variation of m the distortion in length in the function of the geodetic latitude phi of the Tunisian Lambert map projection.

This paper presents some solutions on how to unify the geodetic terrestrial networks established by the geometers of the National Mauritanian Society of the Mining Industries (SNIM).

This document presents a tribute to the memory of my colleague and friend Abdelkader Sellal, a retired geodesist engineer from the Algerian Institute of Cartography and Remote Sensing. I published a report he had written in 2004where he had proposed projects concerning the modernization of Algerian Geodesy in particular :- Establishment of a Network of Permanent GPS Stations and a Basic Geodetic Network.- GPS calculations. Re-Adjustment and redefinition of the Algerian national geodetic network using adjustment software.- Definition of a System and a Reference of Altitudes in Algeria.- The Geoid: Studies on the determination of a gravimetric geoid in Algeria.

In this paper about the oblique Mercator representation, we present the calculation of the geographical coordinates $(\Phi,\Lm)$ images of the coordinates $(\fii,\lm)$ of a point on the sphere. We have added some exercises.

In this first paper, we present the plane representation of Laborde applied to Madagascar. We come back to the formulas and the mathematical details from the source document namely fascicle n°4 of the "Treaty of Projections of Geographical Maps, for the Use of Cartographers and Geodesists ", published in 1926, by L. Driencourt and J. Laborde. We have used modern language for certain old expressions cited in the source document.

Tunisian geodesy has known a multitude of geodetic systems giving different coordinates. On the occasion of the unification of these systems into a new system called "The New Tunisian Triangulation - NTT", we have written these notes for the attention of the technical assistants of the OTC to prepare them for the use of the new system and above all the question of switching from existing systems to the new NTT system.

This report is a new version of that of 2008. It is a statement of the reasons concerning the unification of the Tunisian terrestrial geodetic systems to meet the needs of the cartographic, topographic works and the installation of the geographical and cadastral information systems.

This monograph presents a course of mathematical cartography for engineers including essentially the following elements: - the definitions of characteristic terms, - the types of plane cartographic representations or "projections", - some known examples, - and a set of problems and exercises for the reader.

In this booklet, we give elements of the theory of Errors and notions of the Least Squares method for technicians working in the field of topography, geodesy and geomatics.

In this note, we will describe the history of the astronomical observations and those of the measurements of the bases of the eight triangles of the Primordial Tunisian Geodetic Network carried out in 1982 in the framework of the works of the modernization of the Tunisian Geodesy started by the Office of Topography and Cartography (OTC).

It is a chapter that concerns the geometry of the ellipse and the ellipsoid of revolution. We give the formulas of the 2D plane coordinates and the 3D Cartesian coordinates $(X,Y,Z)$ in function of the geodetic coordinates $(\varphi,\lm,he)$. A section is devoted to the geodesic lines of the ellipsoid of revolution. We give the proofs of the differential equations of the geodesic lines and their integration.

A model of freezing soils is developed that accounts for the dependence of the frost heave rate on particle trapping. At sufficiently low cooling rates the soil experiences primary frost heave with a single growing ice lens that rejects all soil particles. At higher cooling rates ice lenses start to engulf the largest soil particles and the rate of segregation heave is reduced. At the highest freezing rates all particles are engulfed by the ice and the pore water freezes in situ. A new kinetic expression for the segregation potential of the soil is obtained that accounts for particle trapping. Using this expression a simple transient frost heave model is developed and compared with experimental data.

In this note, we give the expression of the tolerance of the closure of the horizontal angles of a plane triangle and its numerical estimation for an equilateral triangle.

In this paper, we give the different definition of heights and the corrected terms to take in consideration. An example is presented on how to correct a line of the spirit levelling by introducing gravity observations.

This paper concerns the study of systematic errors in the combination of Doppler data and classical terrestrial observations in the adjustment of geodetic networks. This study is taken from the thesis presented in October 1986 for obtaining the Civil Geographic Engineer diploma from the National School of Geographic Sciences (ENSG / IGN France).

In this paper, we give the formula of the curvature of the curve image, in the case of a conformal map projection, of geodesic curves of the ellipsoid as the model of the Earth. As an example, we consider the UTM map projection and we give the expression of the formula of the curvature.

In this paper, we present the calculus of astronomic latitude and longitude determined by astronomic observations method called "equal height". We give also the standard deviation of each unknowns.

The theorem given in 'Equations of Hydro-and Thermodynamics of the Atmosphere when Inertial Forces Are Small in Comparison with Gravity' (2018) is wrong, since the passage to the limit from the system of Navier-Stokes equations to the system of equations of (quasi) hydrostatic approximation, as the vertical acceleration approaches zero, does not exist. The main consequence is that the scales given in the paper are not suitable for application of hydrostatic approximation. The correct asymptotics should be given by the traditional hydrostatic parameter H/L, where H and L are the vertical and horizontal scales of motion. Also scale analysis of the L.F. Richardson's equation for vertical velocity in hydrostatic approximation is not correct. (О гидростатическом приближении Р.И. Нигматулина и уравнении Л.Ф. Ричардсона. Теорема, сформулированная в статье `Уравнения гидро- и термодинамики атмосферы при малых силах инерции по сравнению с силой тяжести' (2018), не верна, поскольку предельного перехода от уравнений Навье-Стокса к системе уравнений гидростатического приближения при вертикальном ускорении, стремящемся к нулю, не существует. Основное последствие заключается в том, что предложенные в статье масштабы не приемлемы для применения гидростатического по вертикали приближения (квазистатического приближения). Корректная асимптотика задается традиционным параметром гидростатичности H/L, где H и L - вертикальный и горизонтальный масштабы течения. Анализ масштабов в уравнении Л.Ф. Ричардсона для вертикальной скорости в гидростатическом приближении также является некорректным. Ключевые слова: гидростатическое приближение, уравнение Ричардсона, квазистатическое приближение, синоптические масштабы, мезомасштабы, микрометеорология, уравнения сохранения, силы инерции.

A model of the growth of an ice lens in a saline porous medium is developed. At high lens growth rates the pore fluid becomes supercooled relative to its equilibrium Clapeyron temperature. Instability occurs when the supercooling increases with distance away from the ice lens. Solute diffusion in the pore fluid significantly enhances the instability. An expression for the segregation potential of the soil is obtained from the condition for marginal stability of the ice lens. The model is applied to a clayey silt and a glass powder medium, indicating parameter regimes where the ice lens stability is controlled by viscous flow or by solute diffusion. A mushy layer, composed of vertical ice veins and horizontal ice lenses, forms in the soil in response to the instability. A marginal equilibrium condition is used to estimate the segregated ice fraction in the mushy layer as a function of the freezing rate and salinity.

In this paper, we present the details of the proposal for definition and implementation of a unified geodetic referential for the countries of North Africa as : - the choice of the system of the referential, - the steps of the realization of the project, - the training of the geodesists working on the project.

Using the geodetic coordinates $(\varphi,\lambda,h)$, we give the expression of the laplacian $\Delta V=\ds \frac{\partial^2 V}{\partial x ^2}+\frac{\partial^2 V}{\partial y ^2}+\frac{\partial^2 V}{\partial z ^2}$ in these coordinates. A solution of $\Delta V=0$ of type $V=f(\lambda).g(\varphi,h)$ is given. The partial differential equation satisfied by $g(\varphi,h)$ is transformed in an ordinary differential equation of a new variable $u=u(\varphi,h)$.

Many geodetic works currently exist on the surface of the globe, which have developed through regional networks, usually each having a fundamental point, where the astronomical data (\phi= latitude,\lambda=longitude,Az=azimuth) of a reference are confused with the counterparts geodetic data. The comparison of 2 networks, and, step by step, of all the connectable networks, can be done by the analysis of the coordinates of their common points. To this end, we can use 3 types of coordinates: - Geographical coordinates = simple method, but not very convenient for different ellipsoids. - Three-dimensional cartesian coordinates, the most rigorous method in the case where the so-called geoid correction has been made. - Coordinates in conformal projection. An analysis of the main formulas that can be used is studied by the first author in this article.

I have often received students in geomatic requests asking me to provide them with exercises or problems of geodesy, topography, astronomy or the application of the theory of least squares. The paper is a collection of exercises and problems that comes to fill the need of the students in this matter.

This note gives the elements on the attraction of the sun and the moon. It was inspired by the reading of the book by Helmut Moritz and Ivan I. Muller entitled Earth Rotation: Theory and Observation which can be a tidal introductory course. \\ It includes the following chapters: - The lunar-solar tidal potential. - Zonal, sectoral and tesseral terms

Having a unified reference system, established on a universally accepted and utilitarian basis, is an important contribution to the judicious use of geographic information to promote Africa's economic development at the national level, regional and continental. To do so, it is important today to make the best use of space technologies and to assimilate them, especially through Cartographic National Institutions. This paper: - is written for small African mapping institutions, - defines the organizational prerequisites for rapidly implementing the Unified Reference System at the continental level. - serves as a framework to guide the debate on the real questions to be asked in this area.

Five days before the 2008 Sichuan M8.0 Earthquake, I observed strange electrical signals from a tomato plant in Yilan, Taiwan. That opened my door to quake forecast. Since then, I observed electrical signals of plants, tofu, soil, water or air to predict earthquakes. I successfully predicted a lot of quakes. Now I have about 30 quake forecast stations all over the world. I will publish a series of papers for my discoveries in the past 10 years. This paper is the start of the series. I am Founder and CEO of Taiwan Quake Forecast Institute.

In this paper we discuss the previously unnoticed connection of the Tunguska explosion to natural events decades or even centuries long: 1) the third geomagnetic maximum appeared not too far from the epicenter of the Tunguska explosion in the 19th century and has been moving towards the epicenter of the Tunguska explosion along a straight line since 1908; 2) the magnetic North Pole is moving along the path leading to the epicenter of the Tunguska explosion, 3) all magnitude > or = 7.6 earthquakes sufficiently far from the ocean form an arrow pointing towards the epicenter of the Tunguska explosion; 4) the Tunguska explosion occurred at the end of the twisted portion in the path of the magnetic North Pole and at the time when magnitude > or =8.2 earthquakes and VEI > or = 5 volcanic eruptions recovered correlation with syzygies.

Wave is a fundamental action of the universe. Water waves when it is disturbed by internal or external force. And, there be higher water level when waves meet the shore. This study examines the driving forces of waving gas, liquid, and solid anew when gravity is not force of attraction.

<p>Gravity is the inward force of keeping it's spherical shape. Force of tectonic motion has to fight against gravity to push the crust from the ocean floor to the top of mountain ranges. The only force that is persistently counteracting and can be stronger then gravity is the centrifugal force. It is likely the centrifugal acceleration made Earth oblate spheroid, and the main driving force of waving mantle along with crust, water and atmosphere.</p> <p>This preliminary is only an open proposal for further study from the view of mantle/crust waves. Additionally, the added mass and energy of Solar particles and momentum could impact the crust. Like kneading Earth dough, the magnitude could be larger than we think by far. Further study is also recommended. </p>

In this paper a tracer prognostic differential equation related to the marine chemistry HAMOC model is studied. Recently, the present author found that the Navier Stokes equation has no exact solution. The following question can therefore be justified. Do numerical solutions from prognostic equations provide unique information about the distribution of nutrients in the ocean.

It is my thesis to obtain the diploma of Engineer from the French National School of Geographic Sciences(ENSG, IGN France), presented in October 1981. The first part of the thesis is concerned with the determination of the equation of the observation of Laplace point in the option of 3D geodesy. The second part is about a study of a 3D model of deformation of geodetic networks that was presented by the Senior Geodesist H.M. Dufour in two dimensions.

In an article, E. Grafarend and B. Schaffrin studied the geometry of non-linear adjustment of the planar trisection problem using the Gauss Markov model and the method of the least squares. This paper develops the same method working on an example of the determination of a point by trilateration in the three-dimensional geodetic option for determining the coordinates (x, y, z) of an unknown point from measurements known distances to n points.

The goal of seismic processing is to convert input data collected in the field into a meaningful image based on signal processing and wave equation processing and other algorithms. It is normally a global approach like tomography or FWI (full waveform inversion). Seismic imaging or inversion methods fail partly due to the thin-lens effect or rough surfaces. These interfaces are non-invertible. To mitigate the problem, we propose a more stable method for seismic imaging in 4 steps as layer stripping approach of INVERSION + DATUMING + STATIC + ENHANCEMENT.

The thesis investigates the flow of non-Newtonian fluids in porous media using pore-scale network modeling. Non-Newtonian fluids show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. They are generally classified into three main categories: time-independent, time-dependent and viscoelastic. Two three-dimensional networks representing a sand pack and Berea sandstone were used. An iterative numerical technique is used to solve the pressure field and obtain the flow rate and apparent viscosity. The time-independent category is investigated using two fluid models: Ellis and Herschel-Bulkley. The analysis confirmed the reliability of the non-Newtonian network model used in this study. Good results are obtained, especially for the Ellis model, when comparing the network model results to experimental data sets found in the literature. The yield-stress phenomenon is also investigated and several numerical algorithms were developed and implemented to predict threshold yield pressure of the network. An extensive literature survey and investigation were carried out to understand the phenomenon of viscoelasticity with special attention to the flow in porous media. The extensional flow and viscosity and converging-diverging geometry were thoroughly examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model was identified as a promising candidate for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm that employs this model was implemented in the non-Newtonian code and the initial results were analyzed. The time-dependent category was examined and several problems in modeling and simulating the flow of these fluids were identified.

Inthis paper, random dynamic systems theory is applied to time series ($\Delta t=5$ minutes) of measurement of water level, $W$, temperature, $T$, and barometric pressure, $P$, in sea dikes. The time series were obtained from DDSC and are part of DMC systems dike maintenance program of the Ommelanderzeedijk in northern Netherlands. The result of numerical analysis of dike $(W,T,P)$ time series is that after the onset of a more or less monotone increase in barometric pressure, an unexpected relatively sharp increase or decrease in water level can occur. The direction of change is related to random factors shortly before the onset of the increase. From numerical study of the time series, we found that $\Delta W_{max}\approx \pm 0.5$ mNAP\footnote{NAP indicates New Amsterdam water level which is a zero determining water level well known in the Netherlands.}. The randomness in the direction of change is most likely explained by the random outcome of two competitive processes shortly before the onset of a continuous barometric pressure increase. The two processes are pore pressure compaction and expulsion of water by air molecules. An important cause of growing barometric pressure increase can be found in pressure subsidence following a decrease in atmospheric temperature. In addition, there is a diurnal atmospheric tide caused by UV radiation fluctuations. This can give an additional $\Delta P_{tide}\approx\pm 0.1$ kPa barometric fluctuation\footnote{1Pa=1Pascal=$1Nm^{-2} \approx 10kg s^{-2}m^{-1}$.} in the mid latitudes ($30^{\circ}N-60^{\circ}N$).

It is a memoir of mathematical cartography concerning the traduction of the paper '' A Conformal Mapping Projection With Minimum Scale Error” de W.I. Reilly, published in Survey Review, Volume XXII, n°168, april 1973.

This paper gives a rappel of the theory of Pizzetti-Somigliana for the determination of a geoid. It is the first part of an investigation to use the approch of A. Ardalan for the calcul of a regional géoid of high resolution to determine a tunisian geoid.

The investigation concerns the combination of Doppler data and terrestrial classical observations for the adjustment of geodetic networks and the determination of the 7 parameters (translation, rotation and scale) between terrestrial geodetic and Doppler networks. Models of adjustment are presented. They are part of two groups : 1- a combined adjustment, 2- a commun adjustment. Bursa-Wolf’s model and Molodensky formulas are used to determine the parameters. Systematic errors in orientation and scale of geodetic terrestrial networks are studied.

Cette étude permettra d'analyser les fondements d'un réseau géodésique de base ou primordial et de comparer les déformations que subit le réseau en des points séparés par de longues distances.

A course of mathematical cartography and transformations between geodetic systems, given to the students of Geomatic department of the ESAT school, the first semester of 2015.

In this paper, a review of the regional inverse referential is presented with application on geodesy for the determination of the parameters of the passage from a geodetic system to another. An numerical exemple is also given.

It is a preliminary version of a book on " Geodesy and the Theory of Least Squares". The book contains two parts. The first part is about geomtric and spatial geodesy. The second part concerns the theory of errors of least squares, we give an idea of the theory when we use non-linear models.

Ce papier représente la traduction de la communication du Professeur Helmut Moritz (1988) intitulée " Equilibrium Figures In Geodesy And Geophysics". Il étudie le problème des figures d'équilibre hydrostatique terrestre. L'auteur passe en revue les publications à ce sujet.

Après avoir défini les lignes géodésiques d'une surface, on établit les équations des géodésiques pour une surface donnée. Comme application, nous détaillons celles de l'ellipsoïde de révolution. On fera l'intégration de ces équations.

During the last decade the existence of space as a quantum-dynamical system was discovered, being first indicated by the measured anisotropy of the speed of EM radiation. The dynamical theory for space has been under development during that period, and has now been successfully tested against experiment and astronomical observations, explaining, in particular, the observed characteristics of galactic black holes. The dynamics involves G and alpha- the fine structure constant. Applied to the earth this theory gives two observed predictions (i) the bore hole g anomaly, and the space-inflow effect.The bore hole anomaly is caused by a black hole (a dynamical space in-flow effect) at the centre of the earth. This black hole will be associated with space-flow turbulence,which, it is suggested, may lead to the generation of new matter, just as such turbulence created matter in the earliest moments of the universe.This process may offer a dynamical mechanism for the observed expanding earth.

The article discusses the global aspects of the (almost) antipodal symmetry on Earth which should have been widely known by now but somehow managed to stay unnoticed.

The present study is an investigation of the thermal history of the earth using heat transfer modeling. Assuming that the earth was a hot ball at a homogeneous temperature upon its formation, the model makes the following two predictions about conditions 4.5 Ga later (the earth's approximate present age): (i) there will be a geothermal gradient within a range of 1.5-5.0C per 100 meters in the rst km of the earth crust; and (ii) the earth's crust will be about 45 km thick, which is in agreement with average continental crust thickness. The fact that oceanic crust is much thinner (around 5-10 km thick) is explained by convective heat transfer and plate tectonics. The strong agreement between he predicted thickness of earth's crust with the average actual continental crust thickness, helps confirm the accuracy of the current inner core model of the earth indicating a solid inner core made of iron based on seismological studies.

Storage of water within a drainage basin is often estimated indirectly by analyzing the recession flow curves as it cannot be directly estimated with the aid of available technologies. However, two major problems with recession analysis are: i) late recession flows, particularly for large basins, are usually not observed ii) and early recession flows indicate that initial storage is infinite, which is not realistic. We address this issue by using the recently proposed geomorphological recession flow model (GRFM), which suggests that storage-discharge relationship for a recession event is exponential for the early recession phase and power-law for the late recession phase, being distinguished from one another by a sharp transition. Then we obtain a simple expression for the 'drainable' storage within a basin in terms of early recession curve characteristics and basin geomorphology. The predicted storage matches well with the observed storage (R^2=0.96), indicating the possibility of reliably estimating storage in river basins for various practical purposes.

Exactly 100 years ago, German scientist -- Alfred Lothar Wegener, sailed against the prevailing wisdom of his day when he posited that not only have the Earth's continental plates receded from each other over the course of the Earth's history, but that they are currently in a state of motion relative to one another. To explain this, Wegener setforth the hypothesis that the Earth must be expanding as a whole. Wegener's inability to provide an adequate explanation of the forces and energy source responsible for continental drift and the prevailing belief that the Earth was a rigid solid body resulted in the acrimonious dismissal of his theories. Today, that the continents are receding from each other is no longer a point of debate but a sacrosanct pillar of modern geology and geophysics. What is debatable is the energy source driving this phenomenon. An expanding Earth hypothesis is currently an idea that is not accepted on a general consensus level. Anti-proponent of the expanding Earth mercilessly dismiss it as a pseudo or fringe science. Be that it may, we show herein that from the well accepted law of conversation of spin angular momentum, Stephenson9 and Morrison (1995)'s result that over the last 2700 years or so, the length of the Earth's day has undergone a change of about +17.00 microsecond/yr, this result invariably leads to the fact the Earth must be expanding radially at a paltry rate of about +0.60mm/yr. This simple fact, automatically move the expanding Earth hypothesis from the realm of pseudo or fringe science, to that of real and ponderable science.

Conductive core of Earth is as hot as causing freedom of the valence electrons after which these released electrons distribute themselves toward the core surface and move along with the rotation of Earth causing that magnetic field which forms the big magnet inside Earth. This is a simple account for the geomagnetic field. By accepting this theory we also be leaded to a conclusion justifying the magnetic inversions of Earth based on the existence of several changes in axial rotation of Earth which most probably has had direct influence on expansion of polar ice on one hemisphere and a permanent day on the other hemisphere both causing extinction of species (including dinosaurs). Based on the presented discussions a practical way for direct determination of ionization energies of different elements is proposed.