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Geophysics

Geophysics responds to the physical properties of the subsurface media like rocks, structural features, sediments, water voids…etc.

It is the applying of principles of physics to the study of the earth. Physical measurements on surface are influenced by internal distribution of physical properties. The study may be of global scale to local objectives.

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Geophysics and Geology • Geophysics is considered as the third dimension of

geology…… How?

• Geophysics studies the hidden parts of the earth by collecting physical data on the surface. These data are the response of subsurface materials to physical signals. However collecting data may be also from air or on seas.

• In a broader sense, geophysics provides the tools for studying the structure and composition of the earth’s interior indirectly. This is because boreholes have limited depths of penetration.

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Engineering site investigation

Waste site contamination

Mineral prospecting

Archaeological investigations

Groundwaterinvestigations

Buried cavities, pipes ..etc

Hydrocarbon exploration

Making use of geophysics to investigate the subsurface and evaluating them economically. Usually it is concerned to the exploration of the earth crust and near surface to achieve a practical and economic aim.

Applied Geophysics

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Pure Geophysics

Deals with the regional study of the earth’s major features and its relation to the universe. Also called General Geophysics

Environmental Geophysics

Is the applied geophysics for the investigation of near-surface (meters, 10’s or few 100’s of meters) physico-chemical phenomena.

-Buried waste deposits represent one of the important and actual environmental problems.

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Depending upon source of energy

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Method Measured parameter “Operative” physicalproperty

Application

Gravity

Magnetic

Density

Magnetic susceptibilityand remanence

Spatial variations in thestrength of the gravitationalfield of the Earth

Spatial variations in thestrength of the geomagneticfield

Fossil fuelsBulk mineral depositsConstruction

Fossil fuelsMetalliferous mineraldeposits ,Construction

Seismic

Electromagnetic(SeaBedLogging)

Electrical-Resistivity-

Radar

Travel times ofreflected/refractedseismic waves

Response to electromagneticradiation

Earth resistance

Travel times of reflected radarpulses

Seismic velocity (and density)

Electric conductivity/resistivityand inductance

Electrical conductivity

Dielectric constant

Fossil fuelsBulk mineral depositsConstruction

Fossil fuelsMetalliferous mineraldeposits

Groundwater, environment Construction….

EnvironmentalConstruction

There are many geophysical methods, each depends upon a certain physical property, some of them are:

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All geophysical methods depend on physical property contrast between the

target and the surrounding materials. This contrast leads to Anomaly

Ordinate is gravity and magnetic intensity

High density contrastLow magnetic intensity contrast

Low density contrasthigh magnetic intensity contrast

no contrast

Magneticgravity

distance distance distance

anomaly anomaly No anomaly

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Geophysical Decision-Making ProcessSurvey Objectives

Budget Logistics

GeophysicalSpecifications

Survey DesignSpecification

Which Method?Electric, Magnetic, Gravity, Seismic….

Position Fixing Line orientationStation interval

Data Acquisition

Data storage

ProcessingInterpretation

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ApplicationsPrimary; hydrocarbon exploration, regional geological studies.Secondary; explorations for: mineral deposit, Site investigations, hydrogeology, karsts, geodesy, isostasy, archaeology and volcanic monitoring.

Gravity Method

Measurements of the gravitational field at a series of different locations over an area of interest. The objective in exploration work is to associate variations with differences in the distribution of densities and hence rock types.

Occasionally the whole gravitational field is measured or derivatives of the gravitational field, but usually the difference between the gravity field at two points is measured*.

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Newton's law of gravitation states that the mutual attractive force between two point masses**, m1 and m2, is proportional to one over the square of the distance between them. The constant of proportionality is usually specified as G, the gravitational constant. Thus, we usually see the law of gravitation written as shown below where F is the force of attraction, G is the gravitationalconstant, and r is the distance between the two masses, m1 and m2.

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When making measurements of the earth's gravity, we usually don't measure the gravitational force, F. Rather, we measure the gravitational acceleration, g. The gravitational acceleration is the time rate of change of a body's speed under the influence of the gravitational force. That is, if you drop a rock off a cliff, it not only falls, but its speed increases as it falls.In addition to defining the law of mutual attraction between masses, Newton also defined the relationship between a force and an acceleration. Newton's second law states that forceis proportional to acceleration. The constant of proportionality is the mass of the object.

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This formula says that ANY object near the surface of the planet will accelerate towards the center of the planet at the rate g, regardless of the mass of the object, so a feather will fall at the same rate as a steel ball. right?

Calculate the mass of the EarthResult is (5.97 x 1027 gm)

Learn these

tera- 1012

giga- 109

mega- 106

kilo- 103

centi- 10-2

milli- 10-3

micro- 10-6

nano- 10-9

F = m2g

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Look that there is a body of higher Density than surrounding, giving a positive anomaly

g

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Units of gravity (g)

Milligal (mGal) = 10-3cm/s2

Microgal (µGal) = 10-8 m/s2 = 0.01µm/s2

M/s2 = N.m/kg Modern gravimeters have a sensitivity of 0.01 mGal.

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Note that

The acceleration is simply called gravity (g) and it is measured during the gravity survey. g is proportional to two variables only; they are density and distance so gravity changes on a horizontal plane in a small district should be due to changes in density only. If the earth was perfectly sphere and having a homogeneous density, gravity value will not change any where on its surface

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Stages of a gravity survey 1-The main target should be well known (i.e. what are you

looking for? Size, depth, density…).2-Detailed plan should be constructed;A- Design of observation stations (i.e. profiles, grid, no. of

stations, inter-distances.B- Duration and cost C- Logistics such as demonstration affairs and politics3-Collecting data (gravity, coordinates of each measurement

point and elevation as precise as possible.)Note: to get accuracy of 0.1mGal, need to know elevation to

within one centimeter and latitude to within ~10m.4-Data analyses and interpretations.5- If it is desired to tie the survey to national maps, the network

must include at least one station where absolute g is known.

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Types of gravity measurements(Reynolds, 1997, page 42-43)

Absolute Measurement1-Using Pendulum;

Where T is the period of oscillation, L is the length of the pendulum and g is the gravitational acceleration.

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2-Free falling measurements

By dropping an object and measuring its time rate of change of speed (acceleration) as it falls. By tradition, this is the method we have commonly ascribed to Galileo Galilei.

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Relative Measurement

Because it is difficult to design precise portable absolute measuring instruments gravity is measured relatively (relative to a reference station called Base Station), these stations are or are not tied to primary base stations (primary base stations have absolute gravity values.

A net of International Base Stations are present in all countries. They are called International Gravity Standarization Network; IGSN71. The number 71 is due to the year 1971 at when the international formula was established (subject will be given later).

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Calibration of Gravimeters (See Dobrin, page 390-391)

A gravimeter is simply an extreme balance measuring gravity. Gravimeters read gravity by their own units called Scale Division (SD). This unit should be converted to gravity units such as milliGals by multiplying them by a factor called Calibration Constant (CC). This CC should be calculated precisely before field activities. Each gravimeter has its manufacturing constant but it could be changed with time. There are two methods to calculate CC:

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Time

Station B∆s

∆s

g (SD)

Station A

C.C. = ∆g/∆s mGal/SD

Using either two previously known absolute values at two base stations or using a high tower and the Free Air Gradient value (0.3086mGal/m).

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Factors that Affect Gravity

1- Temporal Variations - These are changes in the observed acceleration that are time dependent. In other words, these factors cause variations in acceleration that would be observed even if we didn't move our gravimeter.

Instrument Drift - Changes in the observed acceleration caused by changes in the response of the gravimeter over time. Tidal Affects - Changes in the observed acceleration caused by the gravitational attraction of the sun and moon.

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2- Spatial Variations - These are changes in the observed acceleration that are space dependent (from place to place), just like the geologic affects, but they are not related to geology.

Latitude Variations - Changes in the observed acceleration caused by the ellipsoidal shape and the rotation of the earth. Elevation Variations - Changes in the observed acceleration caused by differences in the elevations of the observation points and density of materials in-between these elevations. Topographic Effects - Changes in the observed acceleration related to topographic variations.

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Corrections are activities by which all above mentioned effects other than those related with subsurface variations in density are removed. (see Reynolds, page 52-76 or Dobrin, page 416-421)

Instrumental drift correction: Due to variations in temperature and motion, gravimeters tend to show some drift in the response over time because of the creeping of the delicate springs that make up the heart of the gravimeters.

-Precise time, date and coordinates should be taken for each measurement.

-Return back to the base station every 1-2hours. -At the end of work day the drift curve should be

constructed. This curve is the plot of the repeated gravity data of base station against time.

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Base Line

This value is subtracted from the gravity value of the equivalent station

T i m e

Gravity

Drift Curve

*

*

*

A certain station at this time

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Free Air Correction: Accounts for the height difference between the gravity

station and a certain datum level. Gravity decreases with height because the gravitational accelaration is proportional to 1/ r2. Therefore the free air effect is added to the gravity value of a certain station if it is above datum and subtracted if below

No accounts are taken for rock density

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+

Earth

Radius R

HeightR+h

g0

gh

g0 = G M/R2

gh = G M/ (R + h)2

By a certain derivation

gh- g0 = (1-2h/R)

= Free Air Gradient

And

F.A.C. = 0.3086 mGal x Height difference (∆h)∆h is the elevation difference between the station which is to be corrected and the

datum level

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∆g = (2g0/R) h = constant x h = 0.3086 mGal/m = 0.094 mGal/ft

*B

A*

∆h

∆h

Datum

topography

At station A the effect is added while at B it is subtracted…..Why?

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Bouguer Correction:Accounts for the effect of the attraction of rock materials between the station and datum levels, by approximating them into an infinite horizontal slab. This slab has a thickness equal to the elevation difference between the station and datum level with a homogeneous density, it is called Bouguer Slab.

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At station B the gravity is increased relative to datum because of the slab. The gravity effect is equal to 2πρGh, this is called the Bouguer Correction. Density used here is the average density of surface rocks while h is thickness.In the case of station B the effect is subtracted, in station C the effect is added while in station A there is no Bouguer effect ……Why?

Datum Level

hA

B

Rock materials

h is the Bouguer slab thickness having a density ρ

Ch

Ground surface

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B.C. = 0.04191ρh (h in meters) = 0.1277 ρh (h in feet)

Since the FAC and BC are both proportional to elevation above (or below) datum, it is usual to combine them into a simple Elevation Correction. EC = FAC – BC or = BC – FAC = 0.3086h – 0.041981ρh = [(03086 – 0.04191ρ)h] mGal/m = [(0.09406 – 0.01277ρ)h] mGal/ftHence the correction for the station B in the above figure will be:g = gO – (0.09406 – 0.01277ρ)h Where gO is the observed gravity value.

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Latitude Correction:Gravity Variation with Latitude:The force due to gravity at a point on the Earth’s surface is vector result of the attraction of the Earth and the center fugal force. The resultant acts at right angles to the ellipsoid of rotation. The angle Ø defines the geodetic (geographic) latitude

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The elliptical shape of the earth causes gravity to vary with latitude because the distance between the gravimeter and the earth's center varies with latitude. The magnitude of the gravity changes from the center of mass of the earth to the gravimeter squared. Thus, qualitatively, we would expect the gravity to be smaller at the equator than at the poles, because the surface of the earth is farther from the earth's center at the equator than it is at the poles.

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αØ

Acceleration due to center fugal force = dw2 where w is the angular velocity. Hence the gravity is reduced by a value of dw2 at any point on the surface. α is called geocentric latitudeØ is called geographic latitude.

The vector which its angle is Ø is the gravity

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If the earth was:1-Homogeneous2-Perfect sphere3-Not rotating

Gravity readings wherever on the earth’s surface will be the same.But this is not the case

Then

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- The difference in gravity between the pole and equator due to radius difference is about 5.3Gal (1% of this value is due to center fugal force).

R1=6378kmR2= 6356km

g(equator)= 978.03185mGalg(pole)=983.21772mGal

N

Increasing gravity

Increasing gravity Decreasuing

gravity

Decreasuing gravity

R2

R1

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The value of gravity at any point on the surface is given theoretically by the international formula of (Clauriat) which is widely accepted. The general form of this formula is:

gØ = g0(1+C1sin2Ø-C2sin2 2Ø)Where gØ is the theoretical value at a latitude Ø, g0 is the theoretical gravity value at equatorial sea level (=978.0318Gal), C1 and C2 are constants (0.0053024 and 0.0000059 respectively).

By differentiating this formula with respect to Ø we obtain:∆gØ = 1.307sin 2Ø mGal/mile

∆gØ = 0.812 sin 2Ø mGal/kmThis value is either added or subtracted according to the above figure

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This relation could be used for purposes of latitude corrections in local surveys where Ø is the latitude angle of base station.

Example: A station 100m north of base station in Erbil City (lat. ~36N), its correction value, which will be subtracted from the observed reading, is:0.1x [0.812 sin 2(36)] = 0.07 mGal …..(Check it)

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GeoidReferencespheroid

Warp

Anomalous mass(Exess mass)

Reference spheroid (ellipse of rotation): mean sea level surface with excess landmasses removed and oceans filled (i.e. homogeneous).Geoid: is the reference spheroid affected by masses.Warp: Is the gravity anomaly due to the excess mass. It could be downward when the case is deficiency in mass.

(see Reynolds, page 34)

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Terrain (Topographic) Correction:It accounts for the errors caused by assuming the materials between the station and datum as a slab in Bouguer correction since those materials are neither homogeneous nor of constant thickness.

In applying the slab correction to observation point B, we remove the effect of the mass surrounded by the rectangle. Note, however, that in applying this correction in the presence of a valley to the left of point B, we have accounted for too much mass because the valley actually contains no material. Thus, a small adjustment must be added back into our Bouguer corrected gravity to account for the mass that was removed as part of the valley and, therefore, actually didn't exist.

Bouguer slab

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Principle of (always) adding the effect of Terrain correction is illustrated below

Pendulum normal, towards earth's center

Pendulum deflected towards (excess) mass oraway from the (deficiency) in mass; in both cases it leads to reduce gravity value.

valley Hill

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Terrain correction must be calculated for every gravity station and for all significant topographic features. It is usually necessary for the heights greater or equal to 5% of the distance from the topography to the gravity station (i.e.if height is ~0.05 the distance). For the details of doing the correction please refer to Dobrin, 1976, Sharma, 1996, Reynolds, 1997, Keary and Brooks, 1991 or any other geophysical textbook. (all these texts are present in the department’s library).

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See Rynolds, page 62-64 or Keary and Brooks, page 129

Hammer Chart

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Bouguer Anomaly (see Reynolds, page 70-71)

The end product of gravity data corrections is the Bouguer Anomaly (B.A.), which should correlates only with lateral variations in density of the upper parts of the crust and which are of most interest to applied geophysicists and geologists.

The B.A. is the difference between the observed gravity value (go) adjusted by the algebraic sum of all the necessary corrections, and that at a certain base station (gbase)

∆gb = go +∑ (all corrections) - gbase = (go – gbase) + [∆ Drift C. + ∆ (FAC – BC) +/- ∆LC + ∆TC] = B.A.

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Simple Bouguer Anomaly (SBA): when no terrain correction is applied.Complete Bouguer Anomaly (CBA): when terrain correction is applied. Free Air Anomaly (FAA): Is the Bouguer Anomaly without Bouguer and Terrain Corrections (i.e. without the effect of density).FAA = (go-gbase) +/- LC +/- FACFAA's are drawn because - No assumptions are made; it is strongly influenced by topography.Generally the FAA could easily be correlated with the general topography of the surveyed area, while the observed data show a profile shape that is opposite to the surface topographic shape.

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Gravimeters:(See also Dobrin, page 386-390)

Gravimeters are devices by which relative measurements of gravity are made (i.e. measuring change in gravity from point to point).

The principal part of gravimeters is composed of delicate spring and small mass that is affected by change in place leading to change in gravity. The movement of the mass is either translation or rotational.

Transational Rotational

mg

mg

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The stable type of gravimeters principally depend upon the two forces named force of gravity (downward) and force of sprig pulling the mass upward.In practice, variation of the weight (mg) of the mass caused by the variation of gravity cause the length of the spring to vary and give a measure of change of gravity. Hook’s law can be utilized to explain:

m∆g α sm∆g=k∆s where k is the elastic spring constant∆s = m/k ∆g∆s should be measured to a precission of ~ 1/108 for the purposes of exploration.

S S + ∆S

Measure of gravity = m∆gThere is aneed to measure changes in length of the spring of 30nm (nanometer) for 30cm long spring (3nm is much less than the wavelength of the visible light. Therefore a sort of amplifier is needed.

m(g+∆g)mg

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Because of the dual function of the spring (named the support of the mass and the measuring device) the stable types of gravimeters are of restricted range of sensitivity although some forms of optical, mechanical or electrical amplifications are used.Fine adjustment screw to bring to null positionScale (photocell + galvanometer)Light beammirrormassSpring beamLight source

Example: -Askania Gravimeter:

Fine adjustment screw to bring to null position

Scale (photocell + galvanometer)

Light beam

mirror

mass

Spring beam

Light source

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The unstable gravimeters (astatic) on the other hand employs

additional force (other than the spring in static gravimeters) which is called (third force) that acts in the same sense as the extension or contraction of the spring and amplifies the movement directly.

These gravimeters are designed so that when its sensitive element is displaced due to change in gravity, other force/s tending to increase the displacement comes into play. The force necessary to return the element to its equilibrium position is a measure for the gravity change.

The measure of gravity in a certain station is carried out by the force necessary to return the element to its equilibrium state.