# Diff of /trunk/doc/inversion/CookGravity.tex

revision 4150 by caltinay, Thu Jan 10 03:38:17 2013 UTC revision 4151 by azadeh, Tue Jan 22 00:23:39 2013 UTC
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3  This instrument is designed to prepare practical and obvious information to apply gravity and magnetic inversion packages which have joint application in magnetic and gravity inversion. This codes were written in 2012 at the department of Earth science , University of Queensland.\\  This instrument is designed to prepare practical and obvious information to apply gravity and magnetic inversion packages which have joint application in magnetic and gravity inversion. This codes were written in 2012 at the department of Earth science , University of Queensland.\\
4  It enables geologists and geophysicists, but who is not necessarily versed in the details of inverse theory, to process, visualize and interpret multi-volume geophysical data using attributes and modern visualization techniques.This is not only a functional interpretation system, it is also a research and development environment for geophysics analysis.\\  It enables geologists and geophysicists, but who is not necessarily versed in the details of inverse theory, to process, visualize and interpret multi-volume geophysical data using attributes and modern visualization techniques.This is not only a functional interpretation system, it is also a research and development environment for geophysics analysis.\\
5  We present a package for inverting ground or airborn surveys gravity and magnetic data to generate a 2-D or 3-D distribution of density and susceptibility contrast. In this approach, the earth is clearly modeled by using a large number of rectangular cells of constant value such as density or susceptibility, and the final distribution is obtained by minimizing a model objective function subject to fitting the observed data.\\  We present a package for inverting ground or airborn surveys gravity and magnetic data to generate a 2-D or 3-D distribution of density and susceptibility contrast. In this approach, the earth is clearly modeled by using a large number of rectangular cells of constant value such as density or susceptibility, and the final distribution is obtained by minimizing a model objective function subject to fitting the observed data.\\
6
7  This package could be used to provide a model which introduce density and susceptibility together to fit a given set of magnetic and gravity anomalies. The given data might contain negative and positive in value for both onshore and offshore region. However the model is a 3-dimentional that any cross or depth sections are extracted from. Being the result of big region as well as small area is one of the advantages of this package.\\  This package could be used to provide a model which introduce density and susceptibility together to fit a given set of magnetic and gravity anomalies. The given data might contain negative and positive in value for both onshore and offshore region. However the model is a 3-dimentional that any cross or depth sections are extracted from. Being the result of big region as well as small area is one of the advantages of this package.\\
8  Data type should be prepared attentively to have all corrections and processing. Model is described as a big volume which has changed in density and susceptibility smoothly in all directions. The apparent characteristics of the topography are very sophisticated.\\  Data type should be prepared attentively to have all corrections and processing. Model is described as a big volume which has changed in density and susceptibility smoothly in all directions. The apparent characteristics of the topography are very sophisticated.\\
9  \newpage  \newpage
# Line 22  This inversion method is contained itera Line 23  This inversion method is contained itera
23  \textbf{Gravity Data} \\  \textbf{Gravity Data} \\
24
25  Theoretically weighs depends on the force of gravity at that position and the force of gravity varies with elevation, rock densities, latitude and topography. Mass, however, does not depend on gravity but is a constitutive quantity throughout the earth. So the spring stretch in mass suspension is related to the gravity force. In addition with a constant mass, difference in spring stretch illustrate the changes in acceleration of gravity. The principal of gravity exploration is based on the topography of the basement, thickness of the sedimentary section with various density and porosity of the layer and elevation.\\  Theoretically weighs depends on the force of gravity at that position and the force of gravity varies with elevation, rock densities, latitude and topography. Mass, however, does not depend on gravity but is a constitutive quantity throughout the earth. So the spring stretch in mass suspension is related to the gravity force. In addition with a constant mass, difference in spring stretch illustrate the changes in acceleration of gravity. The principal of gravity exploration is based on the topography of the basement, thickness of the sedimentary section with various density and porosity of the layer and elevation.\\
26
27  The amount of $g$ at sea level is about 980 $kg/s^2$ or 980,000 $mgal$. Gravity acceleration is measured in two types. The first correspondes to specify the absolute magnitude of gravity at any place and the second refers to the alteration in garavity from one place to another. In gravity stuty variation of this value which is caused by underground structure, is plotted as a residual gravity. Closed variation in residual gravity indicates subsurface geological structure.\\  The amount of $g$ at sea level is about 980 $kg/s^2$ or 980,000 $mgal$. Gravity acceleration is measured in two types. The first correspondes to specify the absolute magnitude of gravity at any place and the second refers to the alteration in garavity from one place to another. In gravity stuty variation of this value which is caused by underground structure, is plotted as a residual gravity. Closed variation in residual gravity indicates subsurface geological structure.\\
28  The Gravity data are taken from onshore and offshore observation recorded at many gravity stations with high precision of determination in elevation and position (latitude and longitude). All Raw reading gravity observations require to process with many corrections.\\  The Gravity data are taken from onshore and offshore observation recorded at many gravity stations with high precision of determination in elevation and position (latitude and longitude). All Raw reading gravity observations require to process with many corrections.\\
29
30  The sun and moon gravitational forces make curvature in Earth's shape. These tide effects change figure of oceans, atmosphere and even solid body of the Earth, which impress gravity measurement and it is necessary to compensate it, which vary with location, date and time of the day.\\  The sun and moon gravitational forces make curvature in Earth's shape. These tide effects change figure of oceans, atmosphere and even solid body of the Earth, which impress gravity measurement and it is necessary to compensate it, which vary with location, date and time of the day.\\
31  The surface of the Earth is lumpy on land and water. However for Geophysical and Geological study, a smooth closed surface is assumed. The main one is a spheroid flattened at the poles which is called ellipsoid. The new data are used to defined a best-fitting obtained ellipsoid. The second suggestion is geoid which is really mathematical convenience. There is a uniform mass between gravity stations and ellipsoid, that's effect must be removed with corrections.\\  The surface of the Earth is lumpy on land and water. However for Geophysical and Geological study, a smooth closed surface is assumed. The main one is a spheroid flattened at the poles which is called ellipsoid. The new data are used to defined a best-fitting obtained ellipsoid. The second suggestion is geoid which is really mathematical convenience. There is a uniform mass between gravity stations and ellipsoid, that's effect must be removed with corrections.\\
32  Also the level of topography for hilly and valley measurements is important. The gravity amount which is made up by that equal the mass of hill or valley must be added as a terrian correction to have a measurement on a level surface.\\  Also the level of topography for hilly and valley measurements is important. The gravity amount which is made up by that equal the mass of hill or valley must be added as a terrian correction to have a measurement on a level surface.\\
33  Because gravity descend towards the poles the latitude correction must be added to the observed gravity.\\  Because gravity descend towards the poles the latitude correction must be added to the observed gravity.\\
34  Free-air correction that must be added to observation, ignores the effects of material between the measurement and refrence level which is positive for above sea-level station and is negetive for station below sea-leve.\\  Free-air correction that must be added to observation, ignores the effects of material between the measurement and refrence level which is positive for above sea-level station and is negetive for station below sea-leve.\\
35  The gravitational accelaration or Bouguer correction is calculated for known thickness (between measurements station and ellipsoid) and density (depends on local rock) which must be subtracted from the measurements garavity if station is above sea-level. and the station is below sea-level this must be added.\\  The gravitational accelaration or Bouguer correction is calculated for known thickness (between measurements station and ellipsoid) and density (depends on local rock) which must be subtracted from the measurements garavity if station is above sea-level. and the station is below sea-level this must be added.\\
36
37  For this adjustment first of all Tidal correction apply based on tidal table or calculated tidal effect for given time and location of gravity data. The second one is Terrian correction. Then Latitude, Free air and Bouguer correction have applied. The standard Bouguer density is 2670 $kg/m^3$.\\  For this adjustment first of all Tidal correction apply based on tidal table or calculated tidal effect for given time and location of gravity data. The second one is Terrian correction. Then Latitude, Free air and Bouguer correction have applied. The standard Bouguer density is 2670 $kg/m^3$.\\
38
39  (in the input file, bouguer anomaly is used as residual gravity  which have to be gridded )\\  (in the input file, bouguer anomaly is used as residual gravity  which have to be gridded )\\
# Line 63  Specifying maximum iteration depends on Line 67  Specifying maximum iteration depends on
67
68  \item[THICKNESS] Depth of the model should be assigned to have dipper or shallower inversion also it is assigned to the layer where shows inversion in.The parameter values must be real numbers, and they represent depths in km.  \item[THICKNESS] Depth of the model should be assigned to have dipper or shallower inversion also it is assigned to the layer where shows inversion in.The parameter values must be real numbers, and they represent depths in km.
69
70  \item[l_air] length of air is hight of the model above the sea level.  \item[l_air] Length of air is hight of the model above the sea level.
71
72  \item[n_cells_in_data] The last important part of the inversion property is the number of elements in data of the model which shows the finer or coarser cells in the model so its delimitation have affected on resolution.  \item[n_cells_in_data] The last important part of the inversion property is the number of elements in data of the model which shows the finer or coarser cells in the model so its delimitation have affected on resolution.
73
74  \item[mu]it is defined in accordance with the noise of data and it has a wide range to select from 1 to 100.  \item[mu]It is defined in accordance with the noise of data and it has a wide range to select from 0.0001 to 100.
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76  \end{description}  \end{description}
77
# Line 79  After final iteration the silo file is v Line 83  After final iteration the silo file is v
83
84  \textbf{Reference}\\  \textbf{Reference}\\
85
86  There are some example files for 2D and 3D gravity inversions with artificial input data.  There are three examples for 2D and 3D gravity inversions with artificial input data.\\
87  In first step, an area with synthetic density section is suggested  In first step, an area with synthetic density section is suggested. Then based on forward modeling it's gravitational data is collected. Afterwards with generated gravity data, escripts simulate a volume of inverted density. Whilst new density mass could be compared with the synthetic density section to verify the inversion.\\
88
89    Some of the presumptions are the same for all of the examples to simplify the situation to make a logical comparison between synthetic input and output. which is as followed:\\
90    \begin{verbatim}
91    n_cells_in_data=100
92    depth_offset=0.*U.km
93    l_data = 100 * U.km
95    THICKNESS=20.*U.km
96    l_air=6*U.km
97    \end{verbatim}
98    The others assumptions comes with each examples.\\
99
100    1.  A 2D density section with a maximum in centre was assumed. The refrence density and inverted will be shown. The padding area is excluded. \\
101    \begin{verbatim}
102    n_cells_in_data=100
103    n_humbs_h= 1
104    n_humbs_v=1
105    mu=100
106    \end{verbatim}
107
108    \begin{figure}
109    \centering
110    \includegraphics[width=\textwidth]{grav2D1.png}
111    \caption{2D density model up) reference  down) result}
112
113    \end{figure}
114
115    2. A 2D density properties with two maximun in corners and one minimum in the centre was inverted. The result have eliminated the effects in padding area. \\
116    \begin{verbatim}
117    n_cells_in_data=100
118    n_humbs_h= 3
119    n_humbs_v=1
120    mu=100
121    \end{verbatim}
122
123    \begin{figure}
124    \centering
125    \includegraphics[width=\textwidth]{grav2D3.png}
126    \caption{2D density model up) reference  down) result}
127
128    \end{figure}
129
130    3. A 3D model with a maximum in the center was used as input data and the result after simulation in shown in the next image which determined a good distribution of density through the model in the main area.\\
131    \begin{verbatim}
132    n_cells_in_data=50
133    n_humbs_h= 1
134    n_humbs_v=1
135    mu=10
136    \end{verbatim}
137
138    \begin{figure}
139    \centering
140    \includegraphics[width=\textwidth]{density3D-ref.png}
141    \caption{3D density model of reference as synthetic data}
142
143    \end{figure}
144
145    \begin{figure}
146    \centering
147    \includegraphics[width=\textwidth]{gravity3D.png}
148    \caption{3D density model of result}
149
150    \end{figure}

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