# User:ValentinaOS/Sandbox

• CodeCogs for Math
• Example: ${\displaystyle G(f)=\left\vert A(f)\right\vert e^{j\gamma (f)}}$

# Bulk Modulus

The bulk modulus (K) of a fluid, gas or solid denotes the resistance to change of the material when a uniform pressure is applied. It is given by

${\displaystyle K={\frac {\Delta P}{\frac {\Delta V}{V}}}}$

with ΔP being pressure change required to change a volume, V is the initial volume and ΔV is volume variation. The dimensional analysis of the term shows that it has unit of ${\displaystyle FL^{-1}}$, ${\displaystyle {\frac {N}{m^{2}}}}$

Bulk modulus

## Notes

Wave phenomena

Material properties

# Potential Field (Methods)

Potential Field methods are surface passive geophysical techniques that depend on the location of observation within the field, in order to estimate the strength and direction of the field. These methods include Gravimetric and Magnetometry methods. They provide information on the composition of materials within the Earth.

## Gravimetry

### Derivation of Gravitational Potential

Taking a small infinitesimal mass m:

${\displaystyle dm=dm(\epsilon ,\xi ,\psi )}$

${\displaystyle dm=\rho dV}$

${\displaystyle dm=d\epsilon d\xi d\psi }$

${\displaystyle dg={\frac {Gdm}{r^{2}}}}$

r is the displacement vector denoted as:

${\displaystyle r=[(\epsilon -x)^{2}+(\xi -y)^{2}+(\psi -z)^{2}]^{\frac {1}{2}}}$

${\displaystyle \cos \alpha ={\frac {\epsilon -x}{r}},\cos \beta ={\frac {\xi -y}{r}},\cos \gamma ={\frac {\psi -z}{r}}}$

${\displaystyle dg_{x}={\frac {Gdm\cos \alpha }{r^{2}}}}$

${\displaystyle dg_{y}={\frac {Gdm\cos \beta }{r^{2}}}}$

${\displaystyle dg_{z}={\frac {Gdm\cos \gamma }{r^{2}}}}$

Integrating over volumes ${\textstyle V,V_{x},V_{y},V_{z}}$

${\displaystyle V_{x}=G\int _{V}{\frac {\rho dV\cos \alpha }{r^{2}}}=G\int _{V}{\frac {(\epsilon -x)\rho dV}{r^{3}}}}$

${\displaystyle V_{y}=G\int _{V}{\frac {\rho dV\cos \beta }{r^{2}}}=G\int _{V}{\frac {(\xi -y)\rho dV}{r^{3}}}}$

${\displaystyle V_{z}=G\int _{V}{\frac {\rho dV\cos \gamma }{r^{2}}}=G\int _{V}{\frac {(\psi -x)\rho dV}{r^{3}}}}$

We can express each term as

${\displaystyle V_{x}={\frac {\partial V}{\partial x}}}$

${\displaystyle V_{y}={\frac {\partial V}{\partial y}}}$

${\displaystyle V_{z}={\frac {\partial V}{\partial z}}}$

Therefore, the gravitational potential can be expressed as

${\displaystyle V=G\int _{V}{\frac {\rho dV}{r}}}$

## Gravity Anomalies

### Theoretical Gravity

${\displaystyle g_{t}=g_{e}(1+0.005278895\sin ^{2}\phi +0.000023462\sin ^{4}\phi )}$

### Free Air correction

The free air correction (${\displaystyle \delta g_{F}}$) accounts for the inverse squared radius decrease in gravity with distance from the center of the Earth.

### Free air Gravity anomaly

${\displaystyle g_{F}=g_{obs}-g(\lambda )+\delta g_{F}}$

${\displaystyle =g_{obs}-g(\lambda )+{\frac {2h}{R_{E}}}g(\lambda )}$

${\displaystyle =g_{obs}-g(\lambda )+(1-{\frac {2h}{R_{E}}})g(\lambda )}$

# Geophysicist

Is the scientist that applies the principles of physics to study the Earth and its processes. Traditionally speaking, earth scientists whose work is oriented to the study of the Earth using gravity, magnetic, electrical, and seismic methods are considered geophysicists. However, the term geophysicist can be extended to other scientists whose focus belong to fields such as atmospheric, oceanographic and ionospheric.

Geophysicists usually carry out surveys and have an active role in the acquisition, processing and modelling of the data from the field.

# Gravity

Gravity is the force exerted on a mass due to a combination of

1. the gravitational attraction of the Earth of mass M
2. the rotation of the Earth.

Ref: Lille's Whole Earth Geophysics

# Water Table

It is fundamental concept in hydrogeology, it denotes the depth in the subsurface where the pores of soil are saturated with water.

Water Table

# Magnetotellurics

Magnetotellurics comes from the composition of two Greek words Magneto (magnet) and tellurics (earth). It involves the use of artificial or natural electromagnetic field to image the layers of the Earth. This method is aimed towards mainly for mineral exploration, hydrocarbon exploration, deep crustal studies, geothermal studies, groundwater and earthquake monitoring.

## History

The magnetotelluric method was first developed in the early 1950's by Cagniard and Tikhonov

## Magnetotelluric Surveys

Typical MT survey array.