simpegEM: An open-source resource for simulation and parameter estimation problems in electromagnetic geophysics

A large suite of problems in applied geophysics can be tackled by simulating and inverting electromagnetic (EM) data. Problems can be treated in the time- or frequency-domain, sources can be magnetic or electric and either natural or controlled, techniques such as primary-secondary may be employed and different problem dimensionalities, including 1D, 2D and 3D, may be considered. To address the inverse problem, derivatives of each of these element must be readily accessible so they may be composed to form the sensitivity for the approach taken. For many applications, efficient algorithms have been designed and implemented. However, inconsistencies between implementations of different problem-types and modeling techniques often limits extensibility and interoperability, particularly when addressing the inverse problem. Building on top of the open-source simulation and gradient based parameter estimation framework, SimPEG (http://simpeg.xyz), we have developed simpegEM to be a modular framework for geophysical problems in electromagnetics.

The SimPEG implementation in Python provides finite-volume discretizations for both structured and semi-structured meshes, along with machinery for the inversion, including optimization and regularization routines. The elements of the EM simulation, including the formulation of Maxwell’s equations and definitions of the sources and receivers as well as their derivatives are implemented in a modular, object-oriented manner. This structure and organization of the code allow elements to be readily interchanged and extensions made.

In this presentation, we discuss an example with steel-cased wells. Steel is highly conductive, has a significant magnetic permeability and is very thin compared to its length, making it a challenging structure to model. Using the open-source frameworks of SimPEG and simpegEM, we solve this using a primary-secondary approach that employs multiple formulations of Maxwell’s equations and both a 2D cylindrically symmetric mesh and a 3D tensor mesh. We explore results from these numerical experiments and discuss our goals for the ongoing construction of a platform to support a community of researchers using EM geophysical simulations and inversions.

presented at the 2015 AGU Fall Meeting

Transcript

1. simpegEM An open-source resource for simulation and parameter estimation problems in electromagnetic geophysics Lindsey Heagy, Rowan Cockett, Seogi Kang, Guðni Rosenkjær & Doug Oldenburg Geophysical Inversion Facility University of British Columbia
2. Why Electromagnetics? Calistemon, 2010 Gretar Ivarsson, 2006 MagentaGreen, 2014 Electrical conductivity is a diagnostic physical property in many settings Johnson, 2007
3. • Fields Math! magnetic flux density current density • Physical Properties • Fluxes Constitutive Relations Maxwell’s Equations (quasi-static) electric field magnetic field electrical conductivity magnetic permeability Time Frequency
4. Steel casing in EM This is a problem. Physical Properties • highly conductive • significant (variable) magnetic permeability Significant impact on signals Geometry • cylindrical • thin compared to length Numerically challenging Want to characterize this (SEG Abstract: Heagy et al, 2015)
5. primary magnetic flux density Interpolate secondary source current density Casing 3D Geology Data Simulate
6. Inverse Problem
7. (How?)
8. What do we need? grounded electric Physics: Maxwell’s Equations Time Frequency Physical Properties electrical conductivity magnetic permeability anisotropy... Meshes 2D Cylindrical & 3D Sources inductive loop primary-secondary Data & Sensitivities …
9. What do we need? grounded electric Physics: Maxwell’s Equations Time Frequency Physical Properties electrical conductivity magnetic permeability anisotropy... Meshes 2D Cylindrical & 3D Sources inductive loop primary-secondary Data & Sensitivities … Also want: • optimize • regularize • invert
10. What do we need? grounded electric Physics: Maxwell’s Equations Time Frequency Physical Properties electrical conductivity magnetic permeability anisotropy... Meshes 2D Cylindrical & 3D Sources inductive loop primary-secondary Data & Sensitivities … and also: • modular • extensible sensitivity test
11. Implemented in Python! Open Source! http://simpeg.xyz
12. Forward Inverse
14. ?
15. Model & Physical Properties: What should we invert for? (SEG Abstract: Kang et al, 2015) Derivatives using chain rule: or : • Active reservoir layer • Parametric representation • ... inversion model physical properties
16. ?
17. grounded electric inductive loop point dipole (electric or magnetic) fields from a primary problem natural source Sources: How do we excite the Earth?
18. ?
19. Solve 2nd order system Solve E-B, H-J ? or and compute derivative Physics: How do we solve Maxwell’s equations
20. ?
21. compute fields everywhere: what we solved for from source derivative Fields: How do we calculate the EM fields and fluxes? from source from physics
22. ?
23. ... Data: Receivers: What, and where, do we measure?
24. Plug in the pieces
25. Sensitivities
26. Sensitivities Framework • modular • extensible sensitivity test
27. Sensitivities Framework • modular • extensible
28. Built in the open Documentation The team: http://simpeg.xyz Part of an Ecosystem
29. - Rowan Cockett - Seogi Kang - Lindsey Heagy • Wed 4:15 - SimPEG • Wed 4:20 - Time Domain IP • Fri 8-12 - Simulations & Education Thank You! Except where noted, this work is licensed under a Creative Commons Attribution 4.0 International License Questions? simpeg.xyz github.com/simpeg @ lindsey@simpeg.xyz Other Presentations!
30. SCRAPS
31. Forward Simulation
32. simpeg.xyz github.com/simpeg @ lindsey@simpeg.xyz Want more?
33. Testing Practices
34. Steel casing in EM Estimate: Solve for: Interpolate to compute source Invert for 3D conductivity : Model dependence on RHS Primary Secondary
35. • Fields • Fluxes • Physical Properties Finite Volume Forward Modelling electric field magnetic field magnetic flux density current density electrical conductivity magnetic permeability
36. Steel casing in EM Motivation: How do we characterize 3D conductivity distributions in settings with steel cased wells? Modelling 3D geology Modelling Maxwell’s equations Modelling the Casing Approaching the inverse problem
37. Modelling with 3D geology: Primary Secondary Primary: Secondary: Casing & Source, Layered Earth Fields from casing, 3D Earth Interpolate
38. magnetic flux density secondary source current density Casing 3D Geology Data Simulate
39. Forward Inverse
40. primary magnetic flux density Interpolate secondary source current density