I'm a Ph.D. student (Prime Minister's Research Fellow) working in Joint Inversion, under the supervision of
Prof. Anand Singh, in the Department of Earth Sciences, IIT Bombay. I have completed my M.Sc. in Applied Geophysics from IIT Bombay and B.Sc. (Physics Honours) from the University of Delhi.
My CV can be accessed here.
As a part of the present research, I'm investigating various subsurface discretization scheme to model any irregular topography and complex shaped body. In literature, various forward formulations are already available which can model an n-sided polyhedron. I'm employing those forward formulations which are compatible with the unit cell geometry of my subsurface discretization approach. Using this approach, forward modeling, and in turn, synthetic data for various geophysical methods (viz Gravity, Magnetic, DC, IP, etc.) can be calculated for any anomalous body buried in subsurface. Since this approach can provide multi-domain synthetic geophysical data over a given geological scenario, these multi-domain geophysical data in turn, can be inverted simultaneously to recover the subsurface structure more accurately. As we know, there are inherent non-uniqueness is associated with the inversion of a single domain geophysical data. Performing a joint inversion can suppress this inherent ambiguity and provide a more reliable subsurface model.
Brief description about research
Model Parameterization
In the present study, an unstructured grid-based mesh is made by discretizing the subsurface using Delaunay triangulations. Given N (< = 3) non-linear and noncyclic discrete points in a plane, Delaunay triangles are drawn such that no point in set N is inside the circumcircle of any Delaunay triangle. This property ensures that Delaunay triangulation maximizes every triangle’s minimum angle among all conceivable triangulation of the given point set. This characteristic will avoid the generation of silver triangles. For a given set of points in a plane, there is a unique associated Delaunay-triangulation. This property provides a unique subsurface discretization for multiple code runs, making our forward and inverse modelling results reproducible.
Voronoi diagrams are the dual graph of Delaunay triangles. We can draw a Voronoi diagram by connecting the circumcenter of Delaunay triangles. The Voronoi diagram’s vertices are circumcenters of Delaunay triangles, and the edges of the Voronoi diagram are along the perpendicular bisector of sides of Delaunay triangles.
Modelling the subsurface by regular gridding is widespread for the forward and inverse problems. In turn, Unstructured grid-based modelling provides the following benefits:
- In the unstructured grid-based discretization, topographical variation is generated using the triangles' sides; hence it will include a more accurate topographical model than regular grid-based methods.
- It can model any complex shaped anomalous body.
- The use of triangular grid will reduce the number of model parameters, this will reduce the computation time and make the solution more stable.
Forward and Inverse modelling
We have designed the framework of forward modelling for Gravity, Magnetic, DC resistivity and IP Methods in such a way that it can support the resulted anomaly due to a three-sided polygon which in our case is a Delaunay triangular cell. Since, Gravity, Magnetic, DC resistivity and IP Methods are potential field based methods, hence they follow the principle of superposition and allows us to calculate the net response of the anomalous subsurface structure by summing the effect due to all individual triangular cells.
For inversion, we have used the optimization scheme of the Conjugate Gradient method (CGM) and Gauss-Newton algorithm. CGM guarantees the convergence within n-steps for n-dimensional model space. We have provided preconditioning to our CGM to improve the kernel matrix's condition number and to achieve a faster convergence to the solution. Preconditioning is also compensating for depth decay of potential field anomalies. Non linear inversion equation of DC resisitivity and IP methods is handled by employing Gauss-Newton algorithm.
Joint Inversion Framework
By making a relationship between two different set of geophysical model parameters, individual inversion results can be improved to provide trustworthy subsurface structures. We have implemented a cooperative style of inversion methodology. Same subsurafce discretization is applied for the forward modeling of different geophysical methods. First, we have tried to invert in one model domain (say density), and then use this inverted density model inside our resistivity inversion algorithm as an additional set of model parameters and invert this density-resistivity combined model parameters simultaneously, constrained by introducing Fuzzy C-Means clustering (FCM) algorithm. For application of FCM, we are required to provide number of geological unit as apriori information, this information can be collected from the geological field scenarios under consideration.
Results and Discussion
The developed approach is tested on a real field data set for large scale Gravity-ERT profile of Cheb basin (Nickschick et. al., 2019). This data when incorporated in individual inversion is producing the different subsurface structures. There is lack of structural similarity between subsurface models produced by individual density and resistivity inversion. The power of Joint inversion is discernible in these results, It is capable of producing the similar gravity-resistivity subsurface structures. This research is also ready with the joint inversion framework of Gravity and Magnetic, and this framework is successful in recovering the inverted model of a synthetic cuboid shape body buried in subsurface, We look forward to apply it on a real field data set. A further intention of this research is to employ different methodology for joining the different geophysical methods in the joint inversion framework, Design methodology to couple different geophysical model parameters and test the designed algorithm on more field data sets.
Vornoi diagram
Subsurface Discretization
Forward Formulation
PCG algorithm
Gauss Newton algorithm
Joint Inversion Framework