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| {{Use dmy dates|date=February 2013}}
| | Have you been thinking "how do I accelerate my computer" lately? Well chances are should you are reading this article; then you may be experiencing one of numerous computer issues which thousands of individuals discover which they face regularly.<br><br>Document files allow the consumer to input data, images, tables plus other ingredients to improve the presentation. The just problem with this format compared to other file types including .pdf for illustration is its ability to be readily editable. This signifies which anyone viewing the file may change it by accident. Also, this file formatting is opened by additional programs but it does not guarantee that what we see inside the Microsoft Word application can nonetheless be the same whenever you view it utilizing another system. However, it is still preferred by many computer users for its ease of use plus qualities.<br><br>So, this advanced dual scan is not only one of the greater, nevertheless it is equally freeware. And as of all of this which several regard CCleaner 1 of the greater registry products inside the marketplace now. I would add that I personally choose Regcure for the easy reason that it has a greater interface plus I learn for a fact it is ad-ware without charge.<br><br>Chrome enables customizing itself by applying range of themes available found on the internet. If you had newly applied a theme which no longer works properly, it results in Chrome crash on Windows 7. It is recommended to set the authentic theme.<br><br>To fix the problem that is caused by registry error, you want to utilize a [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities]. That is the safest and easiest technique for average PC consumers. However there are thousands of registry products accessible available. You have to discover a superior 1 that could really resolve the problem. If you use a terrible 1, you might expect more difficulties.<br><br>The initial thing you need to do is to reinstall any program which shows the error. It's typical for various computers to have specific programs that require this DLL to show the error whenever we try and load it up. If you see a particular system show the error, you need to initially uninstall which program, restart your PC and then resinstall the program again. This must replace the damaged ac1st16.dll file plus cure the error.<br><br>It is important which we remove obsolete registry entries from a system regularly, if you need your program to run faster, that is. If you don't keep a registry clean, a time comes when a program usually stop functioning completely. Then, your just choice is to reformat the hard drive and begin over!<br><br>There is a lot a good registry cleaner may do for your computer. It will check for plus download updates for Windows, Java plus Adobe. Keeping updates current is an significant piece of advantageous computer wellness. It could furthermore protect the individual and company confidentiality in addition to the online protection. |
| {{Geodesy}}
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| The '''geoid''' is the shape that the surface of the oceans would take under the influence of Earth's [[gravitation]] and rotation alone, in the absence of other influences such as winds and tides. All points on that surface have the same [[scalar potential]]—there is no difference in [[potential energy]] between any two.
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| Specifically, the geoid is the [[equipotential surface]] that would coincide with the mean ocean surface of the Earth if the oceans and atmosphere were in equilibrium, at rest relative to the rotating Earth,<ref name=conrad>http://www.soest.hawaii.edu/GG/FACULTY/conrad/classes/GG612_S11/Lecture_03.pdf</ref> and extended through the continents (such as with very narrow canals). According to [[Carl Friedrich Gauss|Gauss]], who first described it, it is the "mathematical figure of the Earth", a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive [[gravity|gravitational]] measurements and calculations. Despite being an important concept for almost two hundred years in the history of [[geodesy]] and [[geophysics]], it has only been defined to high precision in recent decades, for instance by works of [[Petr Vaníček]], and others. It is often described as the true physical [[figure of the Earth]],<ref name=conrad/> in contrast to the idealized geometrical figure of a [[reference ellipsoid]].
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| The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly (mass deficit).<ref>{{cite book|last=Fowler|first=C.M.R.|title=The Solid Earth; An Introduction to Global Geophysics|year=2005|publisher=Cambridge University Press|location=United Kingdom|isbn=9780521584098|page=214}}</ref> The differences in gravity, and hence the scalar potential field, arise from the uneven distribution of mass in the Earth.
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| ==Description==
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| [[File:Geoid height red blue averagebw.png|thumb|350px|Map of the [[undulation of the geoid]], in meters (based on the [[EGM96]] gravity model and the [[WGS84]] reference ellipsoid).<ref>data from http://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html</ref>]]
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| [[File:Geoida.svg|thumb|right|350px|1. Ocean<br>
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| 2. [[Reference ellipsoid]]<br>
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| 3. Local [[Plumb-bob|plumb line]]<br>
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| 4. Continent<br>
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| 5. Geoid]]
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| The geoid surface is irregular, unlike the [[reference ellipsoid]] which is a mathematical idealized representation of the physical Earth, but considerably smoother than Earth's physical surface. Although the physical Earth has excursions of +8,000 m ([[Mount Everest]]) and −418 m ([[Dead Sea]]), the geoid's variation ranges from −106 to +85 m, less than 200 m total<ref>http://www.csr.utexas.edu/grace/gravity/gravity_definition.html visited 2007-10-11</ref> compared to a perfect mathematical ellipsoid.
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| If the ocean surface were [[isopycnic]] (of constant density) and undisturbed by tides, currents, or weather, it would closely approximate the geoid. If the continental land masses were criss-crossed by a series of tunnels or canals, the sea level in these canals would also very nearly coincide with the geoid. In reality the geoid does not have a physical meaning under the continents, but [[geodesist]]s are able to derive the heights of continental points above this imaginary, yet physically defined, surface by a technique called [[spirit leveling]].
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| Being an [[equipotential surface]], the geoid is by definition a surface to which the force of gravity is everywhere perpendicular. This means that when travelling by ship, one does not notice the undulations of the geoid; the local vertical ([[Plumb-bob|plumb line]]) is always perpendicular to the geoid and the local horizon [[tangential component|tangential]] to it. Likewise, spirit levels will always be parallel to the geoid.
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| Note that a [[GPS]] receiver on a ship may, during the course of a long voyage, indicate height variations, even though the ship will always be at sea level (tides not considered). This is because GPS [[satellite]]s, orbiting about the center of gravity of the Earth, can only measure heights relative to a geocentric reference ellipsoid. To obtain one's geoidal height, a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a tidal measurement station, as in traditional land surveying, will always be geoidal height.
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| Modern GPS receivers have a grid implemented inside where they obtain the geoid (e.g. EGM-96) height over the [[World Geodetic System]] (WGS) ellipsoid from the current position. Then they are able to correct the height above WGS ellipsoid to the height above [[WGS84]] geoid. In that case when the height is not zero on a ship it is due to various other factors such as ocean tides, atmospheric pressure (meteorological effects) and local sea surface topography.
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| ==Simplified example==
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| The gravitational field of the earth is neither perfect nor uniform. A flattened ellipsoid is typically used as the idealized earth, but even if the earth were perfectly spherical, the strength of gravity would not be the same everywhere, because density (and therefore mass) varies throughout the planet. This is due to magma distributions, mountain ranges, deep sea trenches, and so on.
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| If that perfect sphere were then covered in water, the water would not be the same height everywhere. Instead, the water level would be higher or lower depending on the particular strength of gravity in that location.
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| ==Spherical harmonics representation==
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| [[Spherical harmonic]]s are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is [[EGM96]] (Earth Gravity Model 1996),<ref>NIMA Technical Report TR8350.2, ''Department of Defense World Geodetic System 1984, Its Definition and Relationships With Local Geodetic Systems'', Third Edition, 4 July 1997. [Note that confusingly, despite the title, versions after 1991 actually define EGM96, rather than the older WGS84 standard, and also that, despite the date on the cover page, this report was actually updated last on 23 June 2004. Available electronically at: http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html]</ref> determined in an international collaborative project led by [[National Geospatial-Intelligence Agency|NIMA]]. The mathematical description of the non-rotating part of the potential function in this model is
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| :<math>
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| V=\frac{GM}{r}\left(1+{\sum_{n=2}^{n_\text{max}}}\left(\frac{a}{r}\right)^n{\sum_{m=0}^n}
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| \overline{P}_{nm}(\sin\phi)\left[\overline{C}_{nm}\cos m\lambda+\overline{S}_{nm}\sin m\lambda\right]\right),
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| </math>
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| [[File:Geoids sm.jpg|thumb|350px|right|Three-dimensional visualization of geoid undulations, using [[Gal (unit)|units of gravity]].]]
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| where <math>\phi\ </math> and <math>\lambda\ </math> are ''geocentric'' (spherical) latitude and longitude respectively, <math>\overline{P}_{nm}</math> are the fully normalized [[associated Legendre polynomials]] of degree <math>n\ </math> and order <math>m\ </math>, and <math>\overline{C}_{nm}</math> and <math>\overline{S}_{nm}</math> are the numerical coefficients of the model based on measured data. Note that the above equation describes the Earth's gravitational [[potential]] <math>V\ </math>, not the geoid itself, at location <math>\phi,\;\lambda,\;r,\ </math> the co-ordinate <math>r\ </math> being the ''geocentric radius'', i.e., distance from the Earth's centre. The geoid is a particular<ref>[http://www.ngs.noaa.gov/PUBS_LIB/EGM96_GEOID_PAPER/egm96_geoid_paper.html There is no such thing as "The" EGM96 geoid]</ref> [[equipotential]] surface, and is somewhat involved to compute. The gradient of this potential also provides a model of the gravitational acceleration. EGM96 contains a full set of coefficients to degree and order 360 (i.e. <math>n_\text{max} = 360</math>), describing details in the global geoid as small as 55 km (or 110 km, depending on your definition of resolution). The number of coefficients, <math>\overline{C}_{nm}</math> and <math>\overline{S}_{nm}</math>, can be determined by first observing in the equation for V that for a specific value of n there are two coefficients for every value of m except for m = 0. There is only one coefficient when m=0 since <math> \sin (0\lambda) = 0</math>. There are thus (2n+1) coefficients for every value of n. Using these facts and the formula, <math>\sum_{I=1}^{L}I = L(L+1)/2</math>, it follows that the total number of coefficients is given by
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| :<math>
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| \sum_{n=2}^{n_\text{max}}(2n+1) = n_\text{max}(n_\text{max}+1) + n_\text{max} - 3 = 130317</math> using the EGM96 value of <math>n_\text{max} = 360
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| </math> .
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| For many applications the complete series is unnecessarily complex and is truncated after a few (perhaps several dozen) terms.
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| New even higher resolution models are currently under development. For example, many of the authors of EGM96 are working on an updated model<ref>Pavlis, N.K., S.A. Holmes. S. Kenyon, D. Schmit, R. Trimmer, "Gravitational potential expansion to degree 2160", ''IAG International Symposium, gravity, geoid and Space Mission GGSM2004'', Porto, Portugal, 2004.</ref> that should incorporate much of the new satellite gravity data (see, e.g., [[Gravity Recovery and Climate Experiment|GRACE]]), and should support up to degree and order 2160 (1/6 of a degree, requiring over 4 million coefficients).
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| <span style="vertical-align:-25%;"> </span> [[National Geospatial-Intelligence Agency|NGA]] has announced the availability of EGM2008, complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159.<ref>http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html, page accessed 5 November 2008</ref> Software and data is on the [http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html Earth Gravitational Model 2008 (EGM2008) - WGS 84 Version] page. | |
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| ==Precise geoid==
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| The 1990s saw important discoveries in the theory of geoid computation. The '''Precise Geoid Solution''' by [[Petr Vaníček|Vaníček]] and co-workers improved on the [[George Gabriel Stokes|Stokesian]] approach to geoid computation.<ref>{{cite web |url=http://gge.unb.ca/Research/GRL/GeodesyGroup/software/UNB%20precise%20GEOID%20package/geoid_index.htm |title=UNB Precise Geoid Determination Package |accessdate=2 October 2007 |work= |publisher= |date= |archiveurl = http://web.archive.org/web/20071120045344/http://gge.unb.ca/Research/GRL/GeodesyGroup/software/UNB+precise+GEOID+package/geoid_index.htm <!-- Bot retrieved archive --> |archivedate = 20 November 2007}}</ref> Their solution enables millimetre-to-centimetre [[accuracy]] in geoid [[computation]], an [[order of magnitude|order-of-magnitude]] improvement from previous classical solutions.<ref>{{cite journal |last=Vaníček |first=P. |authorlink= |coauthors=Kleusberg, A. |year=1987 |month= |title=The Canadian geoid-Stokesian approach |journal=Manuscripta Geodaetica |volume=12 |issue=2 |pages=86–98 |id= |url= |accessdate= |quote= }}</ref><ref>{{cite journal |last=Vaníček |first=P. |authorlink= |coauthors=Martinec, Z. |year=1994 |month= |title=Compilation of a precise regional geoid |journal=Manuscripta Geodaetica |volume=19 |issue= |pages=119–128 |id= |url=http://gge.unb.ca/Personnel/Vanicek/StokesHelmert.pdf |accessdate= |quote= }}</ref><ref>[http://gge.unb.ca/Personnel/Vanicek/GeoidReport950327.pdf Vaníček et al. Compilation of a precise regional geoid] (pdf), pp.45, Report for Geodetic Survey Division - DSS Contract: #23244-1-4405/01-SS, Ottawa (1995)</ref>
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| ==Causes for geoid anomalies==
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| [[File:Gravity, geoid anomaly synthetic cases with local isostasy 2.gif|thumb|350px|[[Gravity anomaly|Gravity]] and Geoid anomalies caused by various crustal and lithospheric thickness changes relative to a reference configuration. All settings are under local [[isostasy|isostatic]] compensation.]]
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| Variations in the height of the geoidal surface are related to density anomalous distributions within the Earth. Geoid measures help thus to understand the internal structure of the planet. Synthetic calculations show that the geoidal signature of a thickened crust (for example, in [[orogen|orogenic belts]] produced by [[continental collision]]) is positive, opposite to what should be expected if the thickening affects the entire [[lithosphere]].
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| ==Time-variability==
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| Recent satellite missions, such as [[Gravity Field and Steady-State Ocean Circulation Explorer|GOCE]] and
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| [[Gravity Recovery and Climate Experiment|GRACE]], have enabled the study of time-variable geoid signals. The first products based on GOCE satellite data became available online in June 2010, through the European Space Agency (ESA)’s Earth observation user services tools.<ref>http://www.esa.int/SPECIALS/GOCE/SEMB1EPK2AG_1.html</ref><ref>http://www.esa.int/SPECIALS/GOCE/SEMY0FOZVAG_0.html</ref> ESA launched the satellite in March 2009 on a mission to map Earth's gravity with unprecedented accuracy and spatial resolution. On 31 March 2011, the new geoid model was unveiled at the Fourth International GOCE User Workshop hosted at the Technische Universität München in Munich, Germany.<ref>[http://www.esa.int/esaCP/SEM1AK6UPLG_index_0.html Earth's gravity revealed in unprecedented detail]</ref> Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles,<ref>{{cite journal|last1=Schmidt|first1=R|last2=Schwintzer|first2=P|last3=Flechtner|first3=F|last4=Reigber|first4=C|last5=Guntner|first5=A|last6=Doll|first6=P|last7=Ramillien|first7=G|last8=Cazenave|first8=A|last9=Petrovic|first9=S| displayauthors = 8|title=GRACE observations of changes in continental water storage|journal=Global and Planetary Change|volume=50|pages=112|year=2006|doi=10.1016/j.gloplacha.2004.11.018|bibcode = 2006GPC....50..112S }}</ref> mass balances of [[ice sheet]]s,<ref>{{cite journal|last1=Ramillien|first1=G|last2=Lombard|first2=A|last3=Cazenave|first3=A|last4=Ivins|first4=E|last5=Llubes|first5=M|last6=Remy|first6=F|last7=Biancale|first7=R|title=Interannual variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE|journal=Global and Planetary Change|volume=53|pages=198|year=2006|doi=10.1016/j.gloplacha.2006.06.003|bibcode = 2006GPC....53..198R|issue=3 }}</ref> and [[postglacial rebound]].<ref>{{cite journal|last1=Vanderwal|first1=W|last2=Wu|first2=P|last3=Sideris|first3=M|last4=Shum|first4=C|title=Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America|journal=Journal of Geodynamics|volume=46|pages=144|year=2008|doi=10.1016/j.jog.2008.03.007|bibcode = 2008JGeo...46..144V|issue=3–5 }}</ref> From postglacial rebound measurements, time-variable GRACE data can be used to deduce the [[viscosity]] of [[Earth's mantle]].<ref>{{cite journal|last1=Paulson|first1=Archie|last2=Zhong|first2=Shijie|last3=Wahr|first3=John|title=Inference of mantle viscosity from GRACE and relative sea level data|journal=Geophysical Journal International|volume=171|pages=497|year=2007|doi=10.1111/j.1365-246X.2007.03556.x|bibcode = 2007GeoJI.171..497P|issue=2 }}</ref>
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| ==See also==
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| *[[Physical geodesy]]
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| *[[Geodesy]]
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| *[[International Terrestrial Reference Frame]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| *[http://earth-info.nga.mil/GandG/wgs84/index.html Main NGA (was NIMA) page on Earth gravity models]
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| *[http://www.iges.polimi.it International Geoid Service (IGeS)]
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| *[http://cddis.gsfc.nasa.gov/926/egm96/egm96.html EGM96 NASA GSFC Earth gravity model]
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| *[http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html Earth Gravitational Model 2008 (EGM2008, Released in July 2008)]
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| *[http://www.ngs.noaa.gov/GEOID/ NOAA Geoid webpage]
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| *[http://geographiclib.sourceforge.net GeographicLib] provides a utility GeoidEval (with source code) to evaluate the geoid height for the EGM84, [[EGM96]], and EGM2008 earth gravity models. Here is an [http://geographiclib.sourceforge.net/cgi-bin/GeoidEval online version of GeoidEval].
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| *[http://www.kiamehr.ir/geoid.htm Kiamehr's Geoid Home Page]
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| *[https://sites.google.com/site/maltapplication/home A free windows calculator which yields, among other calculation, the height difference between EGM96 geoid and mean sea level at every point on earth]
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| *[http://www.fugro-gravmag.com/resources/Technical%20Papers/Li_Goetze_Geophysics_2001.pdf Geoid tutorial from Li and Gotze] (964KB pdf file)
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| *[http://www.csr.utexas.edu/grace/gravity/gravity_definition.html Geoid tutorial at GRACE website]
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| *[http://www.infra.kth.se/geo/geollab.htm Precise Geoid Determination Based on the Least-Squares Modification of Stokes’ Formula](PhD Thesis PDF)
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| *[http://www.surveying.org/home.htm View EGM2008, EGM96 and EGM84 on Google Maps]
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| *{{Cite journal |author=H. Moritz |year=2011 |title=A contemporary perspective of geoid structure |journal=Journal of Geodetic Science |volume=1 |issue=March |pages=82–87 |publisher=Versita |doi=10.2478/v10156-010-0010-7 |bibcode = 2011JGeoS...1...82M }}
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| [[Category:Gravimetry]]
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| [[Category:Geodesy]]
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Have you been thinking "how do I accelerate my computer" lately? Well chances are should you are reading this article; then you may be experiencing one of numerous computer issues which thousands of individuals discover which they face regularly.
Document files allow the consumer to input data, images, tables plus other ingredients to improve the presentation. The just problem with this format compared to other file types including .pdf for illustration is its ability to be readily editable. This signifies which anyone viewing the file may change it by accident. Also, this file formatting is opened by additional programs but it does not guarantee that what we see inside the Microsoft Word application can nonetheless be the same whenever you view it utilizing another system. However, it is still preferred by many computer users for its ease of use plus qualities.
So, this advanced dual scan is not only one of the greater, nevertheless it is equally freeware. And as of all of this which several regard CCleaner 1 of the greater registry products inside the marketplace now. I would add that I personally choose Regcure for the easy reason that it has a greater interface plus I learn for a fact it is ad-ware without charge.
Chrome enables customizing itself by applying range of themes available found on the internet. If you had newly applied a theme which no longer works properly, it results in Chrome crash on Windows 7. It is recommended to set the authentic theme.
To fix the problem that is caused by registry error, you want to utilize a tuneup utilities. That is the safest and easiest technique for average PC consumers. However there are thousands of registry products accessible available. You have to discover a superior 1 that could really resolve the problem. If you use a terrible 1, you might expect more difficulties.
The initial thing you need to do is to reinstall any program which shows the error. It's typical for various computers to have specific programs that require this DLL to show the error whenever we try and load it up. If you see a particular system show the error, you need to initially uninstall which program, restart your PC and then resinstall the program again. This must replace the damaged ac1st16.dll file plus cure the error.
It is important which we remove obsolete registry entries from a system regularly, if you need your program to run faster, that is. If you don't keep a registry clean, a time comes when a program usually stop functioning completely. Then, your just choice is to reformat the hard drive and begin over!
There is a lot a good registry cleaner may do for your computer. It will check for plus download updates for Windows, Java plus Adobe. Keeping updates current is an significant piece of advantageous computer wellness. It could furthermore protect the individual and company confidentiality in addition to the online protection.