Gravity Modeling

1. Ali Oncel [email_address] Department of Earth Sciences KFUPM Gravity Modeling Introduction to Geophysics Introduction to Geophysics-KFUPM Highest peaks on the planet

4. The type of isostatic compensation depends on the flexural rigidity of the supporting material . The models (Pratt/Airy) are based on the local isostasy where no rigidity , compensation is directly below the load. Local Isostasy & flexure Introduction to Geophysics-KFUPM

5. Regional Isostasy & flexure Material with rigidity are flexed , distributing the load over a broader region. Introduction to Geophysics-KFUPM

6. Introduction to Geophysics-KFUPM

7. Flexural Rigidity (D) A thin diving board (small elastic thickness) has low flexural rigidity. A thin, weak board ( small D ) bends greatly, especially near the diver. D is the resistance to bending ., thus depends on the elastic thickness of each board. Introduction to Geophysics-KFUPM

8. Flexural Rigidity (D) A thick board (large elastic thickness) of the same material behaves more rigidly (D high); the diver causes a smaller deflection . Introduction to Geophysics-KFUPM

9. Introduction to Geophysics-KFUPM

10. Flexural Modeling X =horizontal distance from the load to a point on the surface of the plate Ρ a = density of the material above the plate Ρ b = density of the material below the plate q(x)= load applied to the top of the plate at x. Parameters for 2 dimensional model of a plate flexed by a linear load. Both plate and load extend infinitely in and out of the page. Introduction to Geophysics-KFUPM D =the (flexural) rigidity W = vertical deflection of plate at x Turcotte and Schubert (1982)

12. Positions of depressions and bulges formed on the surface of a flexed plate. A strong plate has shallow but wide depression. Introduction to Geophysics-KFUPM Large D (Strong Plate) ~ Small Amplitude Deflection

13. The depressions and peripheral bulges have larger amplitudes on a weak plate, but are closer to the load. Small D (Weaker Plate) ~ High Amplitude Deflection Introduction to Geophysics-KFUPM

14. A very weak plate collapses into local isostatic equilibrium. D=0 ~ Collapse for Local Isostasy Introduction to Geophysics-KFUPM

16. Examples of Lithospheric Flexure A flexural bulge and depression (trench) develop as the downgoing plate is flexed at a subduction zone. The weight of a mountain range causes adjacent depressions that fill with sediment (foreland basins). Introduction to Geophysics-KFUPM

17. Introduction to Geophysics-KFUPM Example: Application of Flexure Modelling