Gravity And Magnetics

Front 1

LaPlace‘s equation

Back 1

The potential field satisfies this equation for
source free region

Front 2

Poisson‘s equation

Back 2

If there is a source (mass),
then, potential satisfies Poisson‘s
equation

Front 3

Gauss‘s theorem

Back 3

volume integral over a region of space

Front 4

Stokes‘s theorem

Back 4

surface integral over surface to the line integral

Front 5

Different models have been used to define the normal gravity field of the Earth

Back 5

Sphere
•Level Ellipsoid (currently, World Geodetic System 84 – WGS48 is used)
•Geoid (quasi geoid)

Front 6

WGS84 is used for the definition of

Back 6

the Normal gravity field of the Earth

Front 7

Geoid

Back 7

(surface of constant potential)

Front 8

The potential due to a spheroid can be obtained from the first three terms of
the expansion:
This accounts for both _________________ of the model Earth

Back 8

gravitation and rotation

Front 9

Geoid (Spheroid):

Back 9

Solution of the LaPlace’s
equation in spherical
coordinate system.

Front 10

The potential U

Back 10

- decreases with R
- is a sinusoidal function of λ

Front 11

International Gravity Formula:
Currently, the standard formula is that of

Back 11

Somigliana

Front 12

The gradient of the ________ is gravity. gn = gradU
•The coefficients are obtained from the best fit of the theoretical model to _______________.
•Gravity data from satellite missions, land and marine surveys are used to ______________________

Back 12

potential

gravity observations

constrain the model

Front 13

Combined solution:

Anomalies =

Back 13

GRACE, land & marine data

observed – Normal (theoretical) value

Front 14

Geoid undulation N =

Back 14

distance between equipotential surface and the surface of conventional ellipsoid of revolution

Front 15

Absolute measurements

Relative measurements

Back 15

•Swinging pendulum
•Free fall technique

•Portable pendulum
•Mass on a spring system

Front 16

Absolute gravity can be determined by measuring

•Relative measurement

Back 16

length and/or time

gives the differences in g between two observation points.

Front 17

Why do we need to correct the observed gravity field (gobs)?

Back 17

Gravitational acceleration

Front 18

Why do we need to correct the observed gravity field (gobs)?

Back 18

Bouguer anomaly (gB)

Front 19

Why do we need to correct the observed gravity field (gobs)?

Back 19

1) There are variations in:
•Topography
•Elevation
•Latitude
•Tide
2) Instrumental drift

Front 20

Gravity data reduction:

Back 20

•Drift correction
•Tidal correction
•Latitude correction
•Free air correction
•Bouguer correction
•Terrain/Topographic correction
•Bouguer, Free air anomalies

Front 21

gB =

Back 21

gobs – gtheoretical

Front 22

Apply _____ and _____ corrections on the observed gravity field

Back 22

tidal drift

Front 23

Latitude correction:

Back 23

-Angular velocity decreases from equator to poles
-Centrifugal acceleration acts in opposite sense to the direction of gravitational acceleration at the equator
-Equatorial bulge

Front 24

Large scale survey

Back 24

Use the Normal gravity formula γn

Front 25

Normal gravity
field is calculated
on the surface of
the

Back 25

ellipsoid

Front 26

Free-air correction
Consider a ________ Earth:
Newton's
Correction is added: for station above datum
- Correction is subtracted: for station below datum

Back 26

spherical
Law of Universal Gravitation
for station above datum
for station below datum

Front 27

Three parts: bouguer correction

Back 27

slab
curvature
terrain

Front 28

gB =

Back 28

g – γn + 0.3086 h – 0.0419 hρ – B + T

Front 29

Isostatic anomaly or IC

Back 29

is the gravity effect of crustal root.

Front 30

Airy

Pratt

Back 30

Compensation by low density
crustal root in the mantle

Compensation by lateral density variation

Front 31

Isostatic anomaly:

Back 31

can be estimated by computing the gravity effect of the crustal root using an infinite slab

Front 32

Isostatic residual anomaly

Back 32

Bouguer anomaly – Isostatic regional field

Front 33

Correction is added:
- Correction is subtracted:

Back 33

when the ship is moving to the east
when the ship is moving to the west

Front 34

Geoid height anomaly (ΔN) is directly
related to the anomaly in

Back 34

gravitational
potential (ΔU) on the spheroiD

Front 35

Nettleton method

Back 35

Collect closely spaced gravity values
Calculate Free-air anomaly
Apply Bouguer correction using various densities
The density value at which the BA is least correlated with the topography is considered to be correct

Front 36

Borehole Gravity reading

Back 36

The remaining gravity
difference is attributed to the
attraction of an infinite slab.

Front 37

Density from seismic wave velocity

Back 37

5 KINDS

Front 38

Sobolev

Back 38

Convert the in situ velocity to velocity at normal P-T conditions
Calculate densities at normal P-T conditions
Convert the densities at normal P-T conditions to in situ densities

Front 39

Density from PREM

Back 39

radial variations in longitudinal and shear wave velocities as well as density

Front 40

Qualitative interpretation

Back 40

Interpretation of gravity anomalies in context with known geological features in the study area (e.g. geological unit, volcano, fault etc.)

Front 41

Quantitative interpretation

________ problem

Back 41

Determination of model parameters (E.g. depth to the source, shape and density of the anomalous structures)

forward

Front 42

Forward problem
The model parameters of the source are _____ (model vector 𝐦).
- The gravity filed (data vector 𝐝 ) is calculated from the known ____________ (𝐦).

Back 42

known.

model parameters

Front 43

Inverse problem
The gravity field is ________
The ____________ (model vector 𝐦) are calculated from the known gravity field

Back 43

known

model parmaters

Front 44

Inverse The solution is ________.

Back 44

non unique

Front 45

Forward problem (mathematical formulation) The gravitational acceleration is the gradient of the

Back 45

potential

Front 46

Characteristics of well-posed problems:

Back 46

1) The solution to the inverse problem must exist
2) The solution must be unique
3) The solution must be stable

Front 47

Depth estimate from Half-width of anomaly
Depths to the _________ bodies are estimated from the gravity formulae of
___________

Back 47

causative
simple shapes

Front 48

Gravitational effect of a 2D cross-section (irregular body):

Back 48

Line integral method
Polygon method
graphical method

Front 49

Representation of the cross-sectional shapes of a 3D structure with

Back 49

n-sided polygonal lamina

Front 50

Anomaly resolution Two identical

Back 50

sphere At the same depth

Front 51

Processed gravity data

Back 51

Fourier transformation
Inverse Fourier transformation

Front 52

Fourier transform F(k) is complex function with

Back 52

real and imaginary parts

Front 53

Convolution integral

Back 53

This is a mathematical expression of linear relationship between input and output

Front 54

The BA anomalies at wavelength < ___ km are mostly caused by density heterogeneity in the crust
The BA anomalies at wavelength >___ km are caused by deep structures

Back 54

100
200

Front 55

_____ wavelength anomalies of shallow origin
____ wavelength gravity anomalies of deep origin

Back 55

short
long

Front 56

Short wavelength anomalies are ________
Long wavelength anomalies are _________

Back 56

attenuated
enhanced

Front 57

It is a processes by which potential field data are mathematically projected downward from one datum (usually surface) to a level surface below the datum surface

Back 57

Downward continuation

Front 58

It is a processes by which potential field data are mathematically projected upward from one datum (usually surface) to a level surface above the datum surface

Back 58

Upward continuation

Front 59

Enhances or sharpen local anomalies masked by broader regional trends

Back 59

vertical derivative filter

Front 60

location of an abrupt lateral changes in density

Back 60

Maximum Horizontal Gradient

Front 61

removes the regional components (long wavelength) in the Bouguer anomalies

Back 61

Regional - residual separation

Front 62

Each gravimeter has its own

Back 62

calibration constant

Front 63

IGSN 71

Back 63

reference for international gravity measurements

Front 64

A mathematical model of the Earth used to define the coordinates of a point on a map

Back 64

Reference ellipsoid

Front 65

work done on a mass by the gravitational force of attraction to bring the mass from infinity to any position in the field

Back 65

Gravitational potential energy