Kristofer Davis

Research Associate

ESB 4055-2
(604) 827-1426
researcher

Originally from Pittsburgh, Pennsylvania, I am a fan of the Steelers, Pirates, and Penguins. I have also been converted to the fanbase of the Colorado Rockies and have been known to have been pursuaded to pull for the Canucks (when not playing my Pens). Other than following my favourite sports teams, I like to curl, bike, hike, and backpack. My wife, Jess, and dog, Kepler, typically follow me to the mountains and shores of BC for adventure.

My research interests include adaptive mesh algorithms for large-scale inversion, application of inversion in potential fields, and mining geophysics. The title of my dissertation was: Improving potential-field processing and inversion through the use of gradient measurements and data adaptive models.

Current Projects:
3D magnetic inversion in highly magnetic environments using an octree mesh discretization: Standard techniques for inverting magnetic field data are marginalized when the susceptibility is high and when the magnetized bodies have considerable structure. A common example is a Banded Iron Formation where the causative body is highly elongated, folded, and has susceptibility greater than unity. In such cases the effects of self-demagnetization must be included in the inversion and this can be done by working with the full Maxwell's equations for magnetostatic fields. This problem has previously been addressed in the literature, but there are still challenges with respect to obtaining a numerically robust and efficient inversion algorithm. We use a finite volume discretization of the equations and an adaptive octree mesh. The octree mesh greatly reduces the number of active cells compared to a regular mesh, which leads to a decrease of the storage requirement as well as a substantial speed up of the inversion.

Large-scale magnetic inversion using differential equations and ocTrees:The inversion of large-scale magnetic data sets has historically been achieved through integral transforms of the large, dense sensitivity matrix. Two well-known types, the discrete Fourier and multi-dimensional wavelet transform, reduce the size of storage and ultimately speed of the inversion by storing only the necessary coefficients without losing accuracy. The main drawback to this type of approach is the required calculation of the dense sensitivity matrix prior to the transform leading to the inversion costing a fraction of the total computation time. We solve the magnetostatic Maxwell's equation on an ocTree-based mesh to reduce the amount of time required for the entire inversion process. The non-linear inversion requires only forward modelling, which decreases the storage requirement of the problem. The principal mesh is broken up into sub-domain ocTree grids for the parallelization of the forward problem causing a general speed decrease. These grids extend the entire domain of the principal mesh to include regional features that may influence the data.

Model objective function: Magnetic field inversions are non-unique but a realistic goal is to find a causative earth structure that is compatible with the geophysical data, the petrophysical constraints, and with geology. Invariably the inversion results are improved as the number and diversity of constraints is increased. In this paper we concentrate upon the inclusion of geologic structural information. Geologic structural modelling programs can import faults, boundaries, and strike and dips of geologic units and interpolate this sparse information in space. When provided with a 3D voxel mesh, they can compute a strike, dip, and plunge for each cell. Following previous work, structural geologic information is incorporated into the inversion as a weak constraint by encapsulating it into the model objective function. The model objective function is formed such that each prism has its own set of rotated vectors to enforce smoothness along the direction of the geology. User-controlled parameters specify the degree of smoothness throughout the 3D volume and thus allow additional geologic insight to be directly incorporated. In addition to structural geology, the inversion algorithm utilizes reference models and bound constraints that help us realize our goal of incorporating all available information.

Past Projects:

  • Joint three-dimensional inversion of gravity and muon tomography data to recover density contrast.
  • Large-scale processing and inversion of magnetic data via an adaptive mesh discretization, space-filling curves, and wavelet compression
  • Joint processing and inversion of magnetic total-field and gradient data
  • Practical resolution analysis and survey design for time-lapse (4D) gravity surveys
  • Rapid gravity gradiometry terrain correction
  • Time-lapse (4D) gravity of an aquifer storage and recovery (ASR) system
  • Unexploded Ordnance (UXO)
  • Archeology

Education:
PhD, Geophysics, Colorado School of Mines, 2010
BSc, Geophysical Engineering, Colorado School of Mines, 2005

Professional Societies:
Austrailian Society of Exploration Geophysicists (ASEG)
Society of Exploration Geophysicists (SEG)