The Earth's Crust and Atmosphere

TIDAL PHENOMENA

Tidal deformation is a phenomena caused by variations in the force of gravity. The moon and to a much lesser extend the sun are the two main sources of tidal deformation.

Following Newton's first law of motion, "To every action, there is an equal but opposite reaction." The pull of the moon causes tidal deformation on both sides of the earth. Since this deformation is caused by the gravitational attraction of the moon on the earth, the tidal deformation is actually caused by a decrease in the force of gravity. This causes a deformation in the equipotential surfaces. Since water closely follows the equipotential surfaces, tides are easily recognized in water. However since the earth is elastic and not rigid, the surface of earth also rises in response to changes in the potential surfaces (only to a much less extent). The gravitational attraction of the moon is approximately 3.3 mGal, and thus represents approximately 0.00034% of the force of gravity.

CRUSTAL SURFACES

Current theory states that our crust is composed of plates containing lighter less dense material (s about 2.67 g/cm³). floating on a more dense material called the mantle (s about 3.27 g/cm³) that is weakened by continuous melting. The upper part of the crust (above 10 to 30 km) is called the lithosphere. The upper part of the mantle (above 300 to 400 km) is called the asthenosphere. These plates are subject various loads that take place on the surface of the earth. The most conspicuous load is that caused by the accumulation of snow and the formation of ice. To give an impression of the enormity of the ice load, it is currently estimated that about 2.7 × 10¹⁹ kg currently cover Antarctica. Furthermore during the last ice age, it is estimated that the ice load caused a vertical depression of the crust in North America of approximately 500 m. We are still experiencing post-glacial lift!

An equally significant load is caused by "ice-melt" (i.e., water). The only difference between water and ice is that water tends to spread out over a much larger surface area. Additionally sediment deposits at the mouths of large rivers cause another source of load. New Orleans is literally sinking into the Gulf of Mexico. Another source of loading is tidal water, and artificial water reservoir constructed to provide large cities with water. In a negative sense, removal of groundwater causes a reverse in the loading.

THE ATMOSPHERE

The atmosphere is the air mass that exist above the earth. This section will describe the atmosphere and some of its properties that affect surveying.

PHYSICAL PROPERTIES

Composed of

78% nitrogen
21% oxygen
1 % argon
traces of carbon dioxide, ozone, etc.

The density of these gases decreases with altitude. These gases are generally electrically inert, except in the uppermost layers of the atmosphere where they are ionized through exposure to various kinds of radiations.

LAYERS IN THE ATMOSPHERE

The atmosphere is generally broken down into layers. However as a caution it must be realized that the altitude of each layer can vary depending on the source. Approximately 99% of the atmosphere is between the surface of the earth and 30 km. From the lowest to the highest, the layers are:

Troposphere (lowest layer being 8 to 17 km thick)
The boundary layer above the troposphere is known as the tropopause The troposphere and tropopause contain most of the meteorological events, and can vary in altitude by season and latitude
From the tropopause to about 50 km is the stratosphere. The air in the stratosphere is very stable and dry.
The stratosphere is bounded on the top by the stratopause.
The mesosphere is a turbulent region of the atmosphere above the stratopause extending approximately 30 km, or approximately 80 km above the surface.
Above the mesosphere is the mesopause.
The ionosphere is above the mesopause. It contains a high concentration of ionized gas, and is the primary source for refraction of GPS signals.

Causes ranges to satellites to appear to be longer than they really are.

The region from an altitude of about 400 km to the extent of the earth's magnetic field is known as the magnetosphere

CHANGES WITH ALTITUDE

In general as one goes higher into the atmosphere, the

Temperature becomes lower. Globally, the temperature decreases by about 0.0065° C/m.
Density decreases. The weight of the air column on a unit area is known as (barometric) air pressure. It can be determined in the lower 40 km of atmosphere to an accuracy of 99.7 percent by

Dw = mean(s_a g)Dh
where s_a is the density of air; and the mean is taken along the column Dh.
Thus the pressure at height h is

Since changes in pressure are regular at any particular time (1 in Hg/1000 ft), barometric pressure can be used to obtain rough elevations.
Barometric pressure usually measured in bars, where 1 bar = 10^-5 N/cm² = 100 kPa = 0.75006 m of Hg
Isobaric surfaces are surfaces of equal pressure

WAVE PROPAGATION

Dependent on frequency, electromagnetic waves exhibit three distinct properties

Direct propagation
Ground mode where waves of sufficiently low frequency travel along the ground. This was the rationale behind the Navy's ELF project (never funded). This can be advantageous, or a nuisance depending on circumstance

EDM observations taken too close to ground will bend to produce a distance that is too long. You must keep sight lines about 0.5 m above the ground to avoid the lower microclimate.
Reduces need for intervisibility between transmitter and receiver.

Reflected by the ionosphere, or ground. Reflected waves are almost always a bad situation in surveying. Can cause GPS receivers to lose lock. This is known as multipathing.

Properties of Wave Transmission

Velocity of wave is inversely related to the index of refraction by the formula

v = c/n where n = 1 in a vacuum and c = 299,792,458 m/s
n is always larger than 1, and is dependent on the density of the air, and on the wavelength of transmission. The relationship between the the index of refraction and density of air is given by

where r is called the specific refractivity of the medium.
n is usually between 1.0000 and 1.0003 in the troposphere
From simple physics, it is known that v is a function of the change in distance S over the change in time t. Thus by substituting c/n for v, and integrating along the entire path of transmission, we find that

where the integration is performed along the path of the wave. A common simplification made with this formula is to integrate along a straight line between the two points. This simplification is used in GPS.