Joint inversion of aquifer test, MRS, and TEM data

Abstract

This paper presents two methods for joint inversion of aquifer test data, magnetic resonance sounding (MRS) data, and transient electromagnetic data acquired from a multilayer hydrogeological system. The link between the MRS model and the groundwater model is created by tying hydraulic conductivities (k) derived from MRS parameters to those of the groundwater model. Method 1 applies k estimated from MRS directly in the groundwater model, during the inversion. Method 2 on the other hand uses the petrophysical relation as a regularization constraint that only enforces k estimated for the groundwater model to be equal to MRS derived k to the extent that data can be fitted. Both methodologies can jointly calibrate parameters pertaining to the individual models as well as a parameter pertaining to the petrophysical relation. This allows the petrophysical relation to adapt to the local conditions during the inversion. The methods are tested using a synthetic data set as well as a field data set. In combination, the two case studies show that the joint methods can constrain the inversion to achieve estimates of k, decay times, and water contents for a leaky confined aquifer system. We show that the geophysical data can assist in determining otherwise insensitive k, and vice versa. Based on our experiments and results, we mainly advocate the future application of method 2 since this seems to produce the most reliable results, has a faster inversion runtime, and is applicable also for linking k of 3-D groundwater flow models to multiple MRS soundings.

Testing alternative uses of electromagnetic data to reduce the prediction error of groundwater models

“…Applications of sequential and joint versions of hydrologic and geophysical data using a petrophysical relationship in groundwater modeling have been demonstrated by Herckenrath et al (2013a) and Vilhelmsen et al (2014). Herckenrath et al (2013a) were comparing a SHI with JHI for a largescale groundwater model using ground-based EM data.…”

“…Herckenrath et al (2013a) were comparing a SHI with JHI for a largescale groundwater model using ground-based EM data. Vilhelmsen et al (2014) were demonstrating a method for joint inversion of aquifer test data, magnetic resonance sounding data, and ground-based electromagnetic data. For synthetic benchmarking, both of these studies were using a simple model with a few layers with constant parameter values, and they were evaluating the model performance by the means of improved model parameter values and reduction of parameter uncertainty.…”

“…The step may also include estimation of geophysical model parameters on the basis of the data sets produced in step 3. The simultaneous estimation of the hydrologic and geophysical parameters can be done by using either the coupled (CHI) or joint (JHI) hydro-geophysical inversion approaches (Hinnell et al, 2010;Vilhelmsen et al, 2014). When the number of parameters is large compared to the number of data, the minimization can be aided by using a regularization technique (for example singular value decomposition or Tikhonov regularization); see Oliver et al (2008) for an overview.…”

On determining uncertainties of magnetic resonance sounding estimated transmissivities for groundwater modeling

“…References suggesting how uncertainty of transmissivity (or hydraulic conductivity) can be estimated from MRS are numerous (e.g., Legchenko et al, 2004;Chalikakis et al, 2008;Plata and Rubio, 2008;Boucher et al, 2009;Günther and Müller-Petke, 2012;Vilhelmsen et al, 2014) but the methods or their documentation are often incomplete. In some references, it is just stated that the uncertainty given for the MRS-estimated transmissivities takes into account the uncertainty of the MRS data, MRS parameters, and transmissivity estimates (Legchenko et al, 2004;Boucher et al, 2009), but the method is not documented or explained.…”

“…Chalikakis et al (2008) estimate the uncertainty of the MRS-based transmissivity estimates, but they only seem to take equivalent solutions into account. Uncertainties of effective hydraulic conductivity can be estimated using joint inversion between TEM, MRS, and aquifer test models (Vilhelmsen et al, 2014), but the methodology is tedious and remains to be documented for sites with multiple MRS and aquifer tests. Plata and Rubio (2008) provide a detailed analysis of the importance of the uncertainty of transmissivities estimated using hydrological methods, but they do not give a detailed description on how to take this uncertainty into account.…”