![The gravity anomaly of this slab ∆𝑔 is given by
∆𝑔 = 2𝐺∆𝜌[− 𝑥1𝑠𝑖𝑛𝜃 + 𝑧1𝑐𝑜𝑠𝜃 × 𝑠𝑖𝑛𝜃𝑙𝑜𝑔𝑒
𝑟2
𝑟1
+ 𝑐𝑜𝑠𝜃 𝜑2 − 𝜑2 + 𝑧2𝜑2 − 𝑧1𝜑1]
INDIRECT INTERPRETATION
Parameters used in defining the gravity anomaly of a
semi-infinite slab with a sloping edge.
The computation of gravity anomalies of two
dimensional bodies of irregular cross-section.
An Introduction to Geophysical Exploration. page(143)](https://image.slidesharecdn.com/group-i-221015053558-d6c06885/85/Geophysics-Gravity-Method-11-320.jpg)
Geophysics-Gravity Method
- 1. GRAVITY DATA INTERPRETATION Group – I Shimul Al-razi Muhid Hossain Peal Sadia Islam Lovely Khatun Khalid Hasan Mahmood Mosaddeque Sajib Mahmud
- 2. INDEX The inverse problem Regional fields and residual anomalies Direct interpretation Indirect interpretation Summary
- 3. 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. For example, concentric spheres of constant mass but differing density and radius would all produce the same anomaly, since their mass acts as though located at the center of the sphere. 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. Such constraints include geological information derived from surface outcrops, boreholes and mines, and from other, complementary, geophysical techniques. An Introduction to Geophysical Exploration. page(139)
- 4. Bouguer anomaly fields are often characterized by a broad, gently varying, regional anomaly on which may be superimposed shorter wavelength local 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. REGIONAL FIELDS AND RESIDUAL ANOMALIES An Introduction to Geophysical Exploration. page(139, 140) The separation of regional and residual gravity anomalies from the observed Bouguer anomaly.
- 5. DIRECT INTERPRETATION Direct interpretation provides, directly from the gravity anomalies, information on the anomalous body which is largely independent of the true shape of the body. Limiting depth a. Half-width method b. Gradient–amplitude ratio method c. Second derivative methods Excess mass a. Inflection point b. Approximate thickness An Introduction to Geophysical Exploration. page(140, 141, 142)
- 6. a. Half-width method The depth to a line mass or to the center of a horizontal cylinder with the same mass distribution is given by 𝑧 = 𝑥1/2 3 4 − 1 For any three-dimensional body, the limiting depth is then given by 𝑧 < 𝑥1/2 3 4 − 1 .The depth to a line mass or to the center of a horizontal cylinder with the same mass distribution is given by 𝑧 = 𝑥1/2 For any two-dimensional body, the limiting depth is then given by 𝑧 < 𝑥1/2 LIMITING DEPTH Limiting depth calculations using (a) the half-width method and (b) the gradient–amplitude ratio An Introduction to Geophysical Exploration. page(140, 141)
- 7. (b) Gradient–amplitude ratio method By differentiation of the relevant formulae, for any three-dimensional body 𝑧 < 0.86 𝐴𝑚𝑎𝑥 𝐴𝑚𝑎𝑥 ′ and for any two-dimensional body 𝑧 < 0.65 𝐴𝑚𝑎𝑥 𝐴𝑚𝑎𝑥 ′ (c) Second derivative methods. LIMITING DEPTH Limiting depth calculations using (a) the half-width method and (b) the gradient–amplitude ratio An Introduction to Geophysical Exploration. page(140, 141)
- 8. EXCESS MASS The survey area is divided into 𝑛 grid squares of area ∆𝑎 and the mean residual anomaly ∆𝑔 found for each square. The excess mass 𝑀𝑒 is then given by 𝑀𝑒 = 1 2𝜋𝐺 𝑖=1 𝑛 ∆𝑔𝑖∆𝑎𝑖 To compute the actual mass 𝑀 of the body, the densities of both anomalous body 𝜌1 and country rock 𝜌2 must be known: 𝑀 = 𝜌1𝑀𝑒 𝜌1 − 𝜌2 An Introduction to Geophysical Exploration. page(141, 142)
- 9. (a) Inflection point The locations of inflection points on gravity profiles, i.e. positions where the horizontal gravity gradient changes most rapidly, can provide useful information on the nature of the edge of an anomalous body. (b) Approximate thickness If the density contrast ∆𝜌 of an anomalous body is known, its thickness 𝑡 may be crudely estimated from its maximum gravity anomaly ∆𝑔 by making use of the Bouguer slab formula 𝑡 ≈ ∆𝑔 2𝜋𝐺∆𝜌 EXCESS MASS Bouguer anomaly profiles across (a) a granite body, and (b) a sedimentary basin. An Introduction to Geophysical Exploration. page(141, 142)
- 10. INDIRECT INTERPRETATION (a) The circular gravity anomaly at Darnley Bay, NWT, Canada. Contour interval 250 gu. (b) Two possible interpretations of the anomaly in terms of a model constructed from a suite of coaxial vertical cylinders. (After Stacey 1971.) An Introduction to Geophysical Exploration. page(142, 143)
- 11. The gravity anomaly of this slab ∆𝑔 is given by ∆𝑔 = 2𝐺∆𝜌[− 𝑥1𝑠𝑖𝑛𝜃 + 𝑧1𝑐𝑜𝑠𝜃 × 𝑠𝑖𝑛𝜃𝑙𝑜𝑔𝑒 𝑟2 𝑟1 + 𝑐𝑜𝑠𝜃 𝜑2 − 𝜑2 + 𝑧2𝜑2 − 𝑧1𝜑1] INDIRECT INTERPRETATION Parameters used in defining the gravity anomaly of a semi-infinite slab with a sloping edge. The computation of gravity anomalies of two dimensional bodies of irregular cross-section. An Introduction to Geophysical Exploration. page(143)
- 12. However a model calculation is performed, indirect interpretation involves four steps: 1. Construction of a reasonable model. 2. Computation of its gravity anomaly. 3. Comparison of computed with observed anomaly. 4. Alteration of model to improve correspondence of observed and calculated anomalies and return to step 2. The most flexible of such methods is non-linear optimization (Al Chalabi 1972). All variables (body points, density contrasts, regional field) may be allowed to vary within defined limits. The method then attempts to minimize some function F which defines the goodness of fit, for example 𝐹 = 𝑖=1 𝑛 ∆𝑔𝑜𝑏𝑠𝑖 − ∆𝑔𝑐𝑎𝑙𝑐𝑖 2 INDIRECT INTERPRETATION A two-dimensional interpretation of the gravity anomaly of the Bodmin Moor granite, southwest England. (After Bott & Scott 1964.) An Introduction to Geophysical Exploration. page(143, 144)
- 13. SUMMARY Gravity data interpretation is useful in exploring regions that have different geological structures, which contain minerals, ores and oil deposits. There are different numerical methods for the model parameters (depth (z), origin location (xo), shape parameter (q) and amplitude coefficient (A)) evaluation of a covered structure such as gradient method, particle swarm optimization technique and Werner deconvolution method. In this study, application of these methods is utilized to appraise the model parametric quantity of the covered structures.