1. A fast finite-element software for gravity anomaly calculation in complex geologic regions Yongen Cai Department of Geophysics Peking University, Beijing, 100871 Chi-yuen Wang Department of Earth and Planetary Science University of California, Berkeley, CA 94720

2. Introduction For geologically complex regions, forward computation of the gravity anomaly of a density model may be computationally demanding and the bottle-neck in gravity inversion. We present a fast finite-element software for solving this problem.

3. P(x,y,z) dv

4. GBOX （ R.J.Blakely,1995) x y z P(0,0,0) R

5. Boundary value problem g (x, y, z) = －

6. Boundary condition （ Jeffreys, 1962 ）

7. FEM formulation

8. Accuracy verification Density model for verifying (c= 0.001 kg/m4 ）

9. GBOX （ average density ） FFEM （ distributed density ）

11. Application to Taiwan Figure 7(b) (GBOX) Source elements: 76,500 Source nodes: 83,448 Calculated gravity points GBOX:4636 points only at ground surface FEM: 285488 at all nodal points Computer: PC with 2.3 GHz CPUs

12. Comparison between FFEM and GBOX mGal Figure 7(b) (GBOX) FFEM: used cpu time : 280 s GBOX: used cpu time : 6780 s

13. Application to Sirrea Nevada (Cai, Zhang and Wang, 2006) Calculated Bouguer anomalies by FFEM Calculated Bouguer anomalies by classical method

14. Conclusion A software FFEM is provided which is more accurate and much faster than the classical integration method, if density in the material body is highly heterogeneous. The computational efficiency for the FFEM method is more pronounced in regions with greater heterogeneities.

15. Density model The density distribution can be obtained from the velocity from seismic tomograph.