Multivariate analysis of cross‐hole georadar velocity and attenuation tomograms for aquifer zonation

Tronicke, Jens; Holliger, Klaus; Barrash, Warren; Knoll, Michael D.

doi:10.1029/2003wr002031

Cited by 124 publications

(97 citation statements)

References 59 publications

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“…Another promising idea is to derive multivariate characteristics of subsurface parameters, for example, the correlation length of lateral structures by analysing the "raw" radar data. This approach avoids the usual smoothing effect of regularisation during inversion (Tronicke et al, 2004). Combining distributed geophysical methods with artificial and natural tracer observations seems even more promising (Kemna et al, 2002;Cassiani et al, 2006) to understand how structures/topology translate "forward" into signatures of integrated tracer responses, which is the first step towards understanding how we may backwardinfer subsurface topological properties from tracer and geophysical observations at multiple scales.…”

Section: Need For Better "Observables"mentioning

confidence: 99%

Threshold behaviour in hydrological systems as (human) geo-ecosystems: manifestations, controls, implications

Zehe¹,

Sivapalan

2009

Hydrol. Earth Syst. Sci.

196

139

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Abstract. In this paper we review threshold behaviour in environmental systems, which are often associated with the onset of floods, contamination and erosion events, and other degenerative processes. Key objectives of this review are to a) suggest indicators for detecting threshold behavior, b) discuss their implications for predictability, c) distinguish different forms of threshold behavior and their underlying controls, and d) hypothesise on possible reasons for why threshold behaviour might occur. Threshold behaviour involves a fast qualitative change of either a single process or the response of a system. For elementary phenomena this switch occurs when boundary conditions (e.g., energy inputs) or system states as expressed by dimensionless quantities (e.g. the Reynolds number) exceed threshold values. Mixing, water movement or depletion of thermodynamic gradients becomes much more efficient as a result. Intermittency is a very good indicator for detecting event scale threshold behavior in hydrological systems. Predictability of intermittent processes/system responses is inherently low for combinations of systems states and/or boundary conditions that push the system close to a threshold. Post hoc identification of "cause-effect relations" to explain when the system became critical is inherently difficult because of our limited ability to perform observations under controlled identical experimental conditions. In this review, we distinguish three forms of threshold behavior. The first one is threshold behavior at the Correspondence to: E. Zehe (e.zehe@bv.tum.de) process level that is controlled by the interplay of local soil characteristics and states, vegetation and the rainfall forcing. Overland flow formation, particle detachment and preferential flow are examples of this. The second form of threshold behaviour is the response of systems of intermediate complexity -e.g., catchment runoff response and sediment yield -governed by the redistribution of water and sediments in space and time. These are controlled by the topological architecture of the catchments that interacts with system states and the boundary conditions. Crossing the response thresholds means to establish connectedness of surface or subsurface flow paths to the catchment outlet. Subsurface stormflow in humid areas, overland flow and erosion in semi-arid and arid areas are examples, and explain that crossing local process thresholds is necessary but not sufficient to trigger a system response threshold. The third form of threshold behaviour involves changes in the "architecture" of human geoecosystems, which experience various disturbances. As a result substantial change in hydrological functioning of a system is induced, when the disturbances exceed the resilience of the geo-ecosystem. We present examples from savannah ecosystems, humid agricultural systems, mining activities affecting rainfall runoff in forested areas, badlands formation in Spain, and the restoration of the Upper Rhine river basin as examples of this phenomenon. This fun...

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Section: Need For Better "Observables"mentioning

confidence: 99%

Threshold behaviour in hydrological systems as (human) geo-ecosystems: manifestations, controls, implications

Zehe¹,

Sivapalan

2009

Hydrol. Earth Syst. Sci.

196

139

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“…In this study, we consider an example from GPR cross-borehole tomography. This method has become popular during the past few decades and has various applications, such as mapping of tunnels and voids (Moran and Greenfield, 1993), mapping of bedrock fractures and fracture zones (Olsson et al, 1992;Lane et al, 1998), estimation of hydrological parameters and delineation of flow paths in the unsaturated zone (Hubbard et al, 1997;Looms et al, 2008aLooms et al, , 2008b, and delineation of geologic structures and lithologies (Fullagar et al, 2000;Bellefleur and Chouteau, 2001;Tronicke et al, 2004).…”

Section: Modeling Errors In Cross-borehole Gpr Tomographymentioning

confidence: 99%

Accounting for imperfect forward modeling in geophysical inverse problems — Exemplified for crosshole tomography

et al. 2014

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Inversion of geophysical data relies on knowledge about how to solve the forward problem, that is, computing data from a given set of model parameters. In many applications of inverse problems, the solution to the forward problem is assumed to be known perfectly, without any error. In reality, solving the forward model (forward-modeling process) will almost always be prone to errors, which we referred to as modeling errors. For a specific forward problem, computation of crosshole tomographic first-arrival traveltimes, we evaluated how the modeling error, given several different approximate forward models, can be more than an order of magnitude larger than the measurement uncertainty. We also found that the modeling error is strongly linked to the spatial variability of the assumed velocity field, i.e., the a priori velocity model. We discovered some general tools by which the modeling error can be quantified and cast into a consistent formulation as an additive Gaussian observation error. We tested a method for generating a sample of the modeling error due to using a simple and approximate forward model, as opposed to a more complex and correct forward model. Then, a probabilistic model of the modeling error was inferred in the form of a correlated Gaussian probability distribution. The key to the method was the ability to generate many realizations from a statistical description of the source of the modeling error, which in this case is the a priori model. The methodology was tested for two synthetic ground-penetrating radar crosshole tomographic inverse problems. Ignoring the modeling error can lead to severe artifacts, which erroneously appear to be well resolved in the solution of the inverse problem. Accounting for the modeling error leads to a solution of the inverse problem consistent with the actual model. Further, using an approximate forward modeling may lead to a dramatic decrease in the computational demands for solving inverse problems.

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“…To determine petrophysical properties, state variables, and structural boundaries, it may be necessary to combine information provided by models obtained from different geophysical data (e.g., Tronicke et al, 2004;Bedrosian et al, 2007). Interpretation of several individually inverted data sets can be illuminating, but the results are usually affected by the resolution limitations of each model.…”

Section: Introductionmentioning

confidence: 99%

Joint inversion of crosshole radar and seismic traveltimes acquired at the South Oyster Bacterial Transport Site

et al. 2008

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Abstract:The structural approach to joint inversion, entailing common boundaries or gradients, offers a flexible way to invert diverse types of surface-based and/or crosshole geophysical data. The cross-gradients function has been introduced as a means to construct models in which spatial changes in two models are parallel or anti-parallel. Inversion methods that use such structural constraints also provide estimates of non-linear and non-unique field-scale relationships between model parameters. Here, we invert jointly crosshole radar and seismic traveltimes for structurally similar models using an iterative non-linear traveltime tomography algorithm.Application of the inversion scheme to synthetic data demonstrates that it better resolves lithological boundaries than the individual inversions. Tests of the scheme on observed radar and seismic data acquired within a shallow aquifer illustrate that the resultant models have improved correlations with flowmeter data than with models based on individual inversions.The highest correlation with the flowmeter data is obtained when the joint inversion is combined with a stochastic regularization operator, where the vertical integral scale is estimated from the flowmeter data. Point-spread functions shows that the most significant resolution improvements of the joint inversion is in the horizontal direction.2

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Multivariate analysis of cross‐hole georadar velocity and attenuation tomograms for aquifer zonation

Cited by 124 publications

References 59 publications

Threshold behaviour in hydrological systems as (human) geo-ecosystems: manifestations, controls, implications

Threshold behaviour in hydrological systems as (human) geo-ecosystems: manifestations, controls, implications

Accounting for imperfect forward modeling in geophysical inverse problems — Exemplified for crosshole tomography

Joint inversion of crosshole radar and seismic traveltimes acquired at the South Oyster Bacterial Transport Site

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