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# ÖNCEL AKADEMİ: INTRODUCTION TO GEOPHYSICS

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### ÖNCEL AKADEMİ: INTRODUCTION TO GEOPHYSICS

1. 1. Ali Oncel [email_address] Department of Earth Sciences KFUPM Gravity Methods 2 Introduction to Geophysics Introduction to Geophysics-KFUPM
2. 2. Previous Lecture <ul><li>Gravity Methods </li></ul><ul><li>Earth's Gravity Potential Field </li></ul><ul><li>Earth's Magnetic Potential Field </li></ul><ul><li>Differences in Earth's Potential Fields </li></ul><ul><li>Earth's Gravity Field </li></ul><ul><li>Earth's Gravitational Acceleration </li></ul><ul><li>Theoretical Gravity </li></ul><ul><li>Free Air Gravity Correction </li></ul><ul><li>Gravity Anomaly </li></ul><ul><li>Free Air Gravity Anomaly </li></ul><ul><li>Bouguer Correction </li></ul>Introduction to Geophysics-KFUPM
3. 3. Recall: Theoretical Gravity The average value of gravity for a given latitude is approximated by the International Association of Geodesy in 1967. g n = Normal Gravity: Gravitational acceleration expected for a rotating ellipsoidal earth without any geologic complications and no surface features . Ф =latitude Gravitation increase from the equator ( Ф =0) =978,03185 mGal to the pole ( Ф =90)=983,217.72 mGal Introduction to Geophysics-KFUPM
4. 4. Recall: Gravity Anomaly <ul><li>What is an anomaly? </li></ul><ul><li>Difference between observed gravity and International Gravity Formula (IGF) for same location or relative to local base station, termed the gravity anomaly , D g </li></ul><ul><li>Dg = g obs - g n </li></ul><ul><li>difference is the result of density contrasts in the subsurface below the measurement point </li></ul>Introduction to Geophysics-KFUPM
5. 5. Δ g fa = g – g t + FAC g = gravitational acceleration observed at station g t = theoretical gravity Introduction to Geophysics-KFUPM Δ g fa = free gravity anomaly
6. 6. Recall: Free Air Gravity Correction <ul><li>The free air correction (FAC) accounts for the extended radius to an observation point, elevated h meters above a sea level datum. </li></ul><ul><li>The above equation illustrates that, for every 3 m (about 10 feet) upward from the surface of the Earth , the acceleration due to gravity decreases by about 1 mGal. </li></ul><ul><li>The basis of this correction is that it makes allowance for the reduction in magnitude of gravity with height above the geoid (pp.55, Reynolds, 2005). </li></ul>Introduction to Geophysics-KFUPM
7. 7. Bouguer Correction <ul><li>The extra mass of mountains results in higher gravity relative to areas near sea level. </li></ul><ul><li>The Bouguer Correction (BC) accounts for the gravitational attraction of the mass above the sea-level datum. </li></ul>Introduction to Geophysics-KFUPM
8. 8. Bouguer Correction <ul><li>Thus, to account for the excess mass above a sea level datum, the Bouguer correction assumes an infinite slab of density ( ρ ), with thickness ( h ) equal to the station’s elevation. </li></ul><ul><li>BC= 2 π ρ G h </li></ul><ul><li>G=Universal Gravitational Constant (6,367,000 m) </li></ul><ul><li>H= thickness of the slab (station elevation) </li></ul><ul><li>Substituting the values of G and 2 π yields: </li></ul><ul><li>BC= 0.419 ρ h </li></ul>Introduction to Geophysics-KFUPM b
9. 9. Introduction to Geophysics-KFUPM The extra mass of mountains results in higher gravity relative to the near sea level. To account for the excess mass above a sea level datum , The BC assumes an infinite slab of density ( ρ ), with thickness (h) equal to the station’s elevation. Bouguer Correction BC= 0.419 ρ h
10. 10. To determine the Bouguer correction, the density of the infinite slab ( ρ ) is needed to assumed as a reduction density of 2.67 g/cm , which is equal to typical density of granite. Bouguer Gravity Anomaly on Land Δ g B = Δ g fa -BC The simple Bouguer gravity anomaly results from subtracting the effect of the infinite slab (BC) from the free air gravity anomaly: BC= 0.419 ρ h =0.419 (2.67g/cm 3 ) h =(0.112 mGal/m)*h (m) Δ g B = Δ g fa -(0.112 mGal/m) h Introduction to Geophysics-KFUPM
11. 11. Bouguer Gravity Anomaly on Sea Δ g B = Δ g fa - 0.419 ρ h Station elevations (h) are zero, Then, Δ g B = Δ g fa Thus, if a type of Bouguer correction is applied, then equation (see page 233 of Lillie) is: Δ g B = Δ g fa + (0.0687 mGal/m)h w Introduction to Geophysics-KFUPM
12. 12. Bouguer Gravity Anomaly on Sea Introduction to Geophysics-KFUPM Δ g fa = g – g t + FAC Δ g B = Δ g fa - BC BC = 0.419 ρ h FAC = h x (0.308 mGal/m)