a b s t r a c tInverse modeling is a powerful tool for extracting information about the subsurface from geophysical data. Geophysical inverse problems are inherently multidisciplinary, requiring elements from the relevant physics, numerical simulation, and optimization, as well as knowledge of the geologic setting, and a comprehension of the interplay between all of these elements. The development and advancement of inversion methodologies can be enabled by a framework that supports experimentation, is flexible and extensible, and allows the knowledge generated to be captured and shared. The goal of this paper is to propose a framework that supports many different types of geophysical forward simulations and deterministic inverse problems. Additionally, we provide an open source implementation of this framework in Python called SIMPEG (Simulation and Parameter Estimation in Geophysics, http://simpeg.xyz). Included in SIMPEG are staggered grid, mimetic finite volume discretizations on a number of structured and semi-structured meshes, convex optimization programs, inversion routines, model parameterizations, useful utility codes, and interfaces to standard numerical solver packages. The framework and implementation are modular, allowing the user to explore, experiment with, and iterate over a variety of approaches to the inverse problem. SIMPEG provides an extensible, documented, and well-tested framework for inverting many types of geophysical data and thereby helping to answer questions in geoscience applications. Throughout the paper we use a generic direct current resistivity problem to illustrate the framework and functionality of SIMPEG.

We have developed an open source 3D, MATLAB based, resistivity inversion package. The forward solution to the governing partial differential equation is efficiently computed using a second-order finite volume discretization coupled with a preconditioned, biconjugate, stabilized gradient algorithm. Using the analytical solution to a potential field in a homogeneous half space, we evaluate the accuracy of our numerical forward solution and, subsequently, develop a source correction factor that reduces forward modeling errors associated with boundary effects and source electrode singularities. For the inversion algorithm we have implemented an inexact Gauss-Newton solver, with the model update being calculated using a preconditioned conjugate gradient algorithm. The inversion uses a combination of zero and first order Tikhonov regularization. Two synthetic examples demonstrate the usefulness of this code. The first example considers a surface resistivity survey with 3813 measurements. The discretized model space contains 19,040 cells. For this example, the inversion package converges in approximately [Formula: see text] on a [Formula: see text] Pentium 4, with [Formula: see text] of RAM. The second example considers the case of borehole based data acquisition. For this example there were 4704 measurements and 13,200 model cells. The inversion for this example requires [Formula: see text] of computational time.

Abstract:Understanding groundwater processes in alpine watersheds is critical to understand the timing of water release and late-season stream flow for both headwater and downstream environments. Moraines and talus features can play an important role in groundwater flow and storage processes in alpine watersheds, but neither process is well understood for these features. We examined the complex hydrogeological environment of a partially ice-cored moraine in the Lake O'Hara watershed in the Canadian Rockies. Electrical resistivity imaging (ERI) and seismic refraction tomography delineated regions of buried ice and frozen and unfrozen moraine material. Seismic refraction data also clearly indicated the depth to bedrock, which varied primarily due to the thickness of the overlying moraine material. Water levels in a lake and several tarns on the moraine responded differently to inputs of rain, snowmelt, and glacier melt, indicating the different degree of hydrological connectivity of these features to the groundwater flow system in the moraine. Such differences reflect the effects of bedrock topography and the location and geometry of buried ice. Ground-penetrating radar images and ERI indicated regions of perched groundwater and focused infiltration. The location of these regions appears to be controlled by buried ice. All geophysical and hydrological data suggest that a relatively thin (<5 m) layer of saturated sediments and/or fractured bedrock likely provides a major flow system within the moraine.

Variations in temperature during time-lapse electrical resistivity imaging (ERI) surveys introduce changes in electrical conductivity (EC). When the goal of the time-lapse ERI survey is to image changes in EC due to changes in saturation or pore water salinity, compensation must be made for the effect of temperature variations. A temperature-compensation method can approximate time-lapse ERI data with the effect of temperature variations removed. First uncompensated ERI data are inverted. The inversion model then is adjusted to a standard temperature image. Forward simulations are performed using the uncompensated inversion and the standard temperature equivalent model. The temperature-compensated simulated resistance data are subtracted from the uncompensated simulated resistance data, forming data correction terms. The data correction terms then are subtracted from the measured data to yield temperature-compensated data. Using the temperature-compensated data, inversions have been carried out on two synthetic data sets and a field example. Differencing two temperature-compensated data inversions is found to be superior to differencing two postinversion standard temperature equivalent images. Temperature compensation on the data allows temperature corrections to be applied to time-lapse difference inversion schemes and hydrogeophysical inversion where postinversion temperature-correction methods are not easily applied.