Exploration of fossil fuels (oil, gas, coal) Exploration of bulk mineral deposit (mineral, sand, gravel) Exploration of underground water supplies Engineeringconstruction site investigation Cavity detection Glaciology Regional and global tectonics Geology, volcanology Shape of the Earth, isostasy Army
m1m2 !!! F =G r Gravity - Truong Quoc Thanh 8/17/2016 Introduction Gravity surveying… Investigation on the basis of relative variations in the Earth gravitational field arising from difference of density between subsurface rocks Gravity - Truong Quoc Thanh 8/17/2016 Application Exploration of fossil fuels (oil, gas, coal) Exploration of bulk mineral deposit (mineral, sand, gravel) Exploration of underground water supplies Engineering/construction site investigation Cavity detection Glaciology Regional and global tectonics Geology, volcanology Shape of the Earth, isostasy Army Gravity - Truong Quoc Thanh 8/17/2016 Structure of lecture Basic theory Density of rocks Gravity of the Earth Measurement of gravity Gravity reduction Gravity anomalies and interpretation Microgravity: a case history Conclusions Gravity - Truong Quoc Thanh 8/17/2016 Basic Theory Gravity - Truong Quoc Thanh 8/17/2016 Gravity? Rocks? Huh? We all feel and see gravity’s effects: Weight (i.e a force) & downward acceleration The gravitational force depends on the rocks below us If the rocks beneath the surface change with location, we expect that the gravitational force we experience will also change If we measure small changes in gravitational forces we can use this information to make inferences about the rocks below us This is the essence of gravity surveying Gravity - Truong Quoc Thanh 8/17/2016 Newton’s Law of Gravitation Sir Isaac Newton (1642-1727): Consider two point masses that are a distance r apart Newton’s theory of gravitation predicts that they will attract each other with a force F that is given by: F =G m1 force r m1m2 r2 force m2 The quantity G is called the gravitational constant (or “big G”) but is actually a small number Newton deduced this equation from observing the motion of planets and moons in the solar system The units are as follows: F Newton (N) r metres (m) m kg G = 6.67 x 10-11 Nm2kg-2 Gravity - Truong Quoc Thanh 8/17/2016 Newton’s Law of Gravitation Newton’s law applies to point sources of mass m1 force r force m2 Earth isn’t a point source Non-point sources are treated as the sum of the forces of many small parts of the body Because force is a vector, the vector sum must be calculated This can become computationally intense for odd shapes For some simple geometric shapes the result is simple… Gravity - Truong Quoc Thanh 8/17/2016 Newton’s Law of Gravitation For the gravitational attraction due to a hollow shell or uniform sphere: The force is the same as that of a point source of the same mass located at the center of the sphere This is true only outside the sphere At the center, the gravitational force must be zero (vectors all cancel due to symmetry) Gravity - Truong Quoc Thanh Because Earth is approximately spherically symmetrical (recall this from the seismology chapter?), we can treat the Earth as a point source of mass located at the center of the Earth! 8/17/2016 Acceleration Due to Gravity Because Earth acts like a point source of mass… We can use Newton’s universal gravitation eq to calculate gravitational force on a small mass, ms, on the surface of the Earth F =G M E ms RE To consider acceleration… Insert Newton’s second law to solve for the force on the small body… F = ms g = G M E ms RE The small body's mass cancels out, and we are left with the equation for the acceleration due to gravity, g g =G ME RE This relationship implies that all bodies on earth’s surface should experience the same falling acceleration 10 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies The inverse problem The interpretation of potential field anomalies (gravity, magnetic and electrical) is inherently ambiguous The ambiguity arises because any given anomaly could be caused by an infinite number of possible sources This ambiguity represents the inverse problem of potential field interpretation, which states that, although the anomaly of a given body may be calculated uniquely, there are an infinite number of bodies that could give rise to any specified anomaly An important task in interpretation is to decrease this ambiguity by using all available external constraints on the nature and form of the anomalous body 77 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies Regional fields and residual anomalies Usually in gravity surveying it is the local anomalies that are of prime interest and the first step in interpretation is the removal of the regional field to isolate the residual anomalies The separation of regional and residual gravity anomalies from the observed Bouguer anomaly 78 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies Regional fields and residual anomalies • Such procedures must be used critically as fictitious residual anomalies can sometimes arise when the regional field is subtracted from the observed data due to the mathematical procedures employed • It is necessary before carrying out interpretation to differentiate between two-dimensional and three-dimensional anomalies • Two-dimensional anomalies are elongated in one horizontal direction so that the anomaly length in this direction is at least twice the anomaly width • Three-dimensional anomalies may have any shape and are considerably more difficult to interpret quantitatively 79 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies Interpretation • Directly from the gravity anomalies, information on the anomalous body which is largely independent of the true shape of the body • Limiting depth refers to the maximum depth at which the top of a body could lie and still produce an observed gravity anomaly Gravity anomalies decay with the inverse square of the distance from their source so that anomalies caused by deep structures are of lower amplitude and greater extent than those caused by shallow sources This wavenumber–amplitude relationship to depth may be quantified to compute the maximum depth (or limiting depth) at which the top of the anomalous body could be situated 80 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies Interpretation Half-width method The half-width of an anomaly (x1/2) is the horizontal distance from the anomaly maximum to the point at which the anomaly has reduced to half of its maximum value (Fig (a)) If the anomaly is threedimensional, the initial assumption is made that it results from a point mass Limiting depth calculations using (a) Manipulation of the point mass formula the half-width method and (b) the allows its depth to be determined in terms of gradient–amplitude ratio the half-width Here, z represents the actual depth of the point mass or the centre of a sphere with the same mass It is an overestimate of the depth to the top of the sphere, that is, the limiting depth Consequently, the limiting depth for any three-dimensional body is given by 81 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies Interpretation Half-width method A similar approach is adopted for a two dimensional anomaly, with the initial assumption that the anomaly results from a horizontal line mass.The depth to a line mass or to the centre of a horizontal cylinder with the same mass distribution is given by Limiting depth calculations using (a) the half-width method and (b) the gradient–amplitude ratio For any two-dimensional body, the limiting depth is then given by 82 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies Interpretation Gradient–amplitude ratio method This method requires the computation of the maximum anomaly amplitude (Amax) and the maximum horizontal gravity gradient (A’max) (Fig (b)) Again the initial assumption is made that a three-dimensional anomaly is caused by a point mass and a twodimensional anomaly by a line mass By Limiting depth calculations using (a) differentiation of the relevant formulae, for the half-width method and (b) the any three-dimensional body gradient–amplitude ratio and for any two-dimensional body 83 Gravity - Truong Quoc Thanh 8/17/2016 Interpretation of gravity anomalies Example : Gravity data interpretation example Consider some gravity data collected on a profile crossing a spherical iron ore body • Where is the centre of the ore body? • What is the maximum value of ∆ gz • At what distance (x½) has ∆gz fallen to half this value? • The depth of the sphere can be derived using the 84 Gravity - Truong Quoc Thanh 8/17/2016 Anomalies of a sphere and a horizontal cylinder at different depths 85 Gravity - Truong Quoc Thanh 8/17/2016 Anomalies of narrow sheets at different depths and dips 86 Gravity - Truong Quoc Thanh 8/17/2016 Gravity data interpretation The interpretation of gravity data could be only a simple qualitative analysis in a way: “Look, there is a sharp local decrease of gravity, this could be a cave!” Or a more complex quantitative analysis, where, based on the qualitative assignment, we try to somehow model the subsurface In this respect we have to bear in mind that the interpretation (inversion) of geophysical data is non-unique In gravity prospection not only that different bodies could have similar anomalies 87 Gravity - Truong Quoc Thanh 8/17/2016 88 Gravity - Truong Quoc Thanh 8/17/2016 Two half slabs with the same anomaly 89 Gravity - Truong Quoc Thanh 8/17/2016 Depth rules for various bodies 90 Gravity - Truong Quoc Thanh 8/17/2016 Gravimetry profiles showing possible occurrence of an underground cavity 91 Gravity - Truong Quoc Thanh 8/17/2016 ... Earth, isostasy Army Gravity - Truong Quoc Thanh 8/17/2016 Structure of lecture Basic theory Density of rocks Gravity of the Earth Measurement of gravity Gravity reduction Gravity anomalies and... interpretation Microgravity: a case history Conclusions Gravity - Truong Quoc Thanh 8/17/2016 Basic Theory Gravity - Truong Quoc Thanh 8/17/2016 Gravity? Rocks? Huh? We all feel and see gravity s effects:... 13 Gravity - Truong Quoc Thanh 8/17/2016 Units of gravity • gal = 10-2 m/s2 • mgal = 10-3 gal = 10-5 m/s2 àgal = 10-6 gal = 10-8m/s2 (precision of a gravimeter for geotechnical surveys) • Gravity