6 Discussion & Conclusion
Using the observations from 715 gravimeter recordings and applying three different types of nonlinear inversion methods, Monte Carlo and Newton’s method gave comparable results for both model parameters and Simulated Annealing had distinct estimations for the model parameters. According to the prior studies, the depth of the Covington pluton should be shallower with a range of 2 to 5km. Moreover, the density contrast should be around 500 kgm-3. Results of the Monte Carlo method and Newton’s method gave almost similar results for the source depth around 24 km and density contrast around 6,500 kgm-3 which seems to be higher considering the previous studies. However, simulated annealing results gave us reasonable values for both source depth and density contrast as 2.47 km and 227 kgm-3.
The Monte Carlo method is an undirected approach and the whole model space is randomly sampled. If we provide a certain number of trial solutions, the global minimum of the error will be calculated out of that range. Unfortunately, I think the number of trial solutions maybe not enough to find a better solution for this problem and we need to give a higher number for better estimates. Even though we had a good fit with predictions and observations gravity anomalies, the results of the estimates are not that accurate. In contrast, Newton’s method is completely a directed approach but still, it can fit a local minimum except reaching the global minimum of the error and I think that is the reason we got a largely deviated estimates for the model parameters. The simulated annealing method is equipped with a combination of both strength nesses of Newton’s method and Monte Carlo method and the estimated model parameters seem more accurate. Still, to obtain the best estimates the inversion should run for a large number of times and get a set of estimates to find a distribution of estimates and should come up with values from the distribution.
As a conclusion, the source depth of the Covington pluton should be around 2-4 km and the density contrast of the rocks in that region should be lower as 250 kgm-3. The simulated annealing method looks a better approach for this study and Newton’s method and the Monte Carlo method should be improved to get accurate estimates. With a facility of a forward model and a widespread of accurate observations of Bouguer gravity anomalies, the nonlinear inversion methods seem a better approach to find estimates for the subsurface materials like igneous intrusions. The inversions can be used along with the reflection, refraction, and resistivity methods for accurate estimates for analyzing subsurface materials without disturbing the surface. If we have a better idea about the shape, the spread of the subsurface materials, and more accurate gravity anomaly observations, I believe we can find more precise estimates for the source depths and density contrasts for studies like this.
7 Acknowledgment
I am very grateful to Dr. Christodoulos Kyriakopoulos for his continuous support throughout the ‘Inverse Methods in Geophysics’ course. It was a hard time for all of us but still, you gave enormous support to finish this project at a higher level. I also want to thank all of my CERI friends for their feedback and guidance.