Gravity & Magnetic

2. Gravity & Magnetic By BAKHTIAR QADER AZIZ Assistance professor 2010-2011

3. The Second Semester Gravity Method Magnetic Method

4. Syllabus of the Gravity Method: • Introduction • Theoretical background • Data Reduction • Survey procedure • applications • Instruments for measuring gravity • Interpretation • Separation of Anomaly • Regional and Residual gravity • Methods of separation • Ambiguities in gravity • modeling

5. References: • Applied Geophysics,1996, Telford, W.,M. • An introduction to applied and environmental geophysics, 1997, Reynolds, J. M. • Introduction to geophysical prospecting, 1988, Durbin, M. B. • Applied and environmental geophysics, 1999, Sharma,V.,P. • www.Geophysics.Com • www.Geophysics.net

6. The gravitation law of attraction was discovered by Isaac Newton in 1685 Gravity: It is an attractive force between all pairs of massive objects in the universe. Newton is referred to “Universal Mutual Gravitation” Universal: Gravity works every where in the universe, not just on the earth. Mutual: Gravity works between pairs of objects. The force of gravity depend on: 1- Mass 2- Distance Mass and weight: In popular language mass and the weight refer to the same thing. Weight= Mass x Gravity Mass is a measure of how much materials are in an object, while weight is a measure of the gravitational force exerted on that material. Mass= Density x Volume Note: Mass is constant for an object.

7. r m1 m2 Gravity in Physics: It is a rate of increase of velocity measured by cm/Sec2 It is constant : 1- The earth is perfect sphere 2- The earth is uniform or homogenous Newton’s Law of Gravitation states that the force of attraction F between two masses m1 and m2 is directly proportional to the product of the masses and inversely to the square of distance between them. G: is a gravitational constant equal to the force between two unit mass (1 Gram) separate by a distance of 1 cm. = 6.67x10-8 Dyne. Cm2/gm2 The relation between force and distance is known as “Inverse Square law”

8. m2 r Earth m1 Acceleration of Gravity: It is a force acting on a unit mass 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 infuence of the gravitational force. Units Associated With Gravitational Acceleration Units Associated with Gravitational Acceleration As described earlier, acceleration is de¯ned as the time rate of change of the speed of a body. Speed, sometimes incorrectly referred to as velocity, is the distance an object travels divided by the time it took to travel that distance (i.e., meters per second (m/s)). Thus, we can measure the speed of an object by observing the time it takes to travel a known distance, If the speed of the object changes as it travels, then this change in speed with respect to time is referred to as acceleration. Positive acceleration means the object is moving faster with time, and negative acceleration means the object is slowing down with time. Acceleration can be measured by determining the speed of an object at two different times and dividing the speed by the time difference

9. between the two observations ,Therefore, the units associated with acceleration is speed (distance per time) divided by time; or distance per time per time, or distance per time squared. If an object such as a ball is dropped, it falls under the influence of gravity in such a way that its speed increases constantly with time. That is, the object accelerates as it falls with constant acceleration. At sea level, the rate of acceleration is about 9.8 meters per second squared. In gravity surveying, we will measure variations in the acceleration due to the earth's gravity. As will be described next, variations in this acceleration can be caused by variations in subsurface geology. Acceleration variations due to geology, however, tend to be much smaller than 9.8 meters per second squared. Thus, a meter per second squared is an inconvenient system of units to use when discussing gravity surveys. The units typically used in describing the graviational acceleration variations observed in exploration gravity surveys are speci¯ed in milliGals. A Gal is de¯ned as a centimeter per second squared. Thus, the Earth's gravitational acceleration is approximately 980 Gals. The Gal is named after Galileo Galilei. The milliGal (mgal) is one thousandth of a Gal. In milli- Gals, the Earth's gravitational acceleration is approximately 980,000. 1 gal = 10-2m/s2 = 10-2newton/m2 1 mgal = 10-5m/s2 = 10-3gal 1ugal = 10-8m/s2 = 10-3mgal

10. Figure 1: The concept of velocity. Figure 2: The concept of acceleration.

11. Gravity High Gravity Distance 2.1 2.6 3 2.4 2.1 High density The fundamental physical property of gravity is density Density = Mass / Volume Observe the following cases: Gravity Gravity Low Gravity Constant Gravity Distance Distance 3.1 2.7 2.3 2.6 3.2 2.1 2.1 2.1 2.1 2.1 Low density Constant density

12. Gravity and Geology How is the Gravitational Acceleration, g, Related to Geology? Density is defend as mass per unit volume. For example, if we were to calculate the density of a room filled with people, the density would be given by the average number of people per unit space (e.g., per cubic foot) and would have the units of people per cubic foot. The higher the number, the more closely spaced are the people. Thus, we would say the room is more densely packed with people. The units typically used to describe density of substances are grams per centimeter cubed (gm/cm3); mass per unit volume. In relating our room analogy to substances, we can use the point mass described earlier as we did the number of people. Consider a simple geologic example of an ore body buried in soil, Figure 3. We would expect the density of the ore body, d2, to be greater than the density of the surrounding soil, d1. The density of the material can be thought of as a number that quantifies the number of point masses needed to represent the material per unit volume of the material just like the number of people per cubic foot in the example given above described how crowded a particular room was. Thus, to represent a high-density ore body, we need more point masses per unit volume than we would for the lower density soil3, Figure 4. Now, let's qualitatively describe the gravitational acceleration experienced by a ball as it is dropped from a ladder, Figure 5. This acceleration can be calculated by measuring the time rate of change of the speed of the ball as it falls.

13. Figure 3: Earth density model of an ore body. Figure 4: Point mass representation of the ore body density model. Figure 6: Building a gravity profile. Figure 5: More point masses mean more acceleration.