Aquifer Heterogeneity Characterization with Oscillatory Pumping: Sensitivity Analysis and Imaging Potential

[1] Periodic pumping tests, in which a fluid is extracted during half a period, then reinjected, have been used historically to estimate effective aquifer properties. In this work, we suggest a modified approach to periodic pumping test analysis in which one uses several periodic pumping signals of different frequencies as stimulation, and responses are analyzed through inverse modeling using a “steady-periodic” model formulation. We refer to this strategy as multifrequency oscillatory hydraulic imaging. Oscillating pumping tests have several advantages that have been noted, including no net water extraction during testing and robust signal measurement through signal processing. Through numerical experiments, we demonstrate additional distinct advantages that multifrequency stimulations have, including: (1) drastically reduced computational cost through use of a steady-periodic numerical model and (2) full utilization of the aquifer heterogeneity information provided by responses at different frequencies. We first perform fully transient numerical modeling for heterogeneous aquifers and show that equivalent results are obtained using a faster steady-periodic heterogeneous numerical model of the wave phasor. The sensitivities of observed signal response to aquifer heterogeneities are derived using an adjoint state-based approach, which shows that different frequency stimulations provide complementary information. Finally, we present an example 2-D application in which sinusoidal signals at multiple frequencies are used as a data source and are inverted to obtain estimates of aquifer heterogeneity. These analyses show the different heterogeneity information that can be obtained from different stimulation frequencies, and that data from several sinusoidal pumping tests can be rapidly inverted using the steady-periodic framework

Smoothing-based Compressed State Kalman Filter for Joint State-parameter Estimation: Applications in Reservoir Characterization and CO2 Storage Monitoring

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman-filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one-step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing-based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high-dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one-step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real-time characterization and monitoring of large-scale hydrogeological systems with sharp moving fronts

The Compressed State Kalman Filter for Nonlinear State Estimation: Application to Large-Scale Reservoir Monitoring

Reservoir monitoring aims to provide snapshots of reservoir conditions and their uncertainties to assist operation management and risk analysis. These snapshots may contain millions of state variables, e.g., pressures and saturations, which can be estimated by assimilating data in real time using the Kalman filter (KF). However, the KF has a computational cost that scales quadratically with the number of unknowns, m, due to the cost of computing and storing the covariance and Jacobian matrices, along with their products. The compressed state Kalman filter (CSKF) adapts the KF for solving large-scale monitoring problems. The CSKF uses N preselected orthogonal bases to compute an accurate rank-N approximation of the covariance that is close to the optimal spectral approximation given by SVD. The CSKF has a computational cost that scales linearly in m and uses an efficient matrix-free approach that propagates uncertainties using N + 1 forward model evaluations, where . Here we present a generalized CSKF algorithm for nonlinear state estimation problems such as CO2 monitoring. For simultaneous estimation of multiple types of state variables, the algorithm allows selecting bases that represent the variability of each state type. Through synthetic numerical experiments of CO2 monitoring, we show that the CSKF can reproduce the Kalman gain accurately even for large compression ratios (m/N). For a given computational cost, the CSKF uses a robust and flexible compression scheme that gives more reliable uncertainty estimates than the ensemble Kalman filter, which may display loss of ensemble variability leading to suboptimal uncertainty estimates

Flow convergence routing hypothesis for pool-riffle maintenance in alluvial rivers

The velocity reversal hypothesis is commonly cited as a mechanism for the maintenance of pool-riffle morphology. Although this hypothesis is based on the magnitude of mean flow parameters, recent studies have suggested that mean parameters are not sufficient to explain the dominant processes in many pool-riffle sequences. In this study, two- and three-dimensional models are applied to simulate flow in the pool-riffle sequence on Dry Creek, California, where the velocity reversal hypothesis was first proposed. These simulations provide an opportunity to evaluate the hydrodynamics underlying the observed reversals in near-bed and section-averaged velocity and are used to investigate the influence of secondary currents, the advection of momentum, and cross-stream flow variability. The simulation results support the occurrence of a reversal in mean velocity and mean shear stress with increasing discharge. However, the results indicate that the effects of flow convergence due to an upstream constriction and the routing of flow through the system are more significant in influencing pool-riffle morphology than the occurrence of a mean velocity reversal. The hypothesis of flow convergence routing is introduced as a more meaningful explanation of the mechanisms acting to maintain pool-riffle morphology

3-D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle: III. Thermochemical tomography in the Western-Central U.S.

Acknowledgments We are indebted to F. Darbyshire and J. von Hunen for useful comments on earlier versions of this work. This manuscript benefited from thorough and constructive reviews by W. Levandowski and an anonymous reviewer. We also thank J. Connolly, M. Sambridge, B. Kennett, S. Lebedev, B. Shan, U. Faul, and M. Qashqai for insightful discussions about, and contributions to, some of the concepts presented in this paper. The work of J.C.A. has been supported by two Australian Research Council Discovery grants (DP120102372 and DP110104145). Seismic data are from the IRIS DMS. D.L.S. acknowledges support from NSF grant EAR-135866. This is contribution 848 from the ARC Centre of Excellence for Core to Crust Fluid Systems (http://www.ccfs.mq.edu.au) and 1106 in the GEMOC Key Centre (http://www.gemoc.mq.edu.au).Peer reviewedPublisher PD

A unified approach to the parameter estimation of groundwater models

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Civil Engineering.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.Bibliography: leaves 134-138.by Peter Kitanidis.M.S

Geostatistical inversing for large-contrast transmissivity fields

The estimation of field parameters, such as transmissivity, is an important part of groundwater modeling. This work deals with the quasilinear geostatistical inverse approach to the estimation of the transmissivity fields from hydraulic head measurements. The standard quasilinear approach is an iterative method consisting of successive linearizations. We examine a synthetic case to evaluate the basic methodology and some modifications and extensions. The first objective is to evaluate the performance of the quasilinear approach when applied to strongly heterogeneous (or "high-contrast") transmissivity fields and, when needed, to propose improvements that allow the solution of such problems. For large-contrast cases, the standard quasilinear method often fails to converge. However, by introducing a derivative-free line search as a polishing step after each Gauss-Newton iteration, we have found that convergence can be practically assured. Another issue is that the quasilinear procedure, which uses linearization about the best estimate to evaluate estimation variances, may lead to inaccurate estimation of the variance of the estimated variable. Our numerical results suggest that this may not be a particularly serious problem, though it is hard to say whether this conclusion will apply to other cases. Nevertheless, since the quasilinear approach is an approximation, we propose a potentially more accurate but computer-intensive Markov Chain Monte Carlo (MCMC) procedure based on conditional realizations generated through the quasilinear approach and accepted or rejected according to the Metropolis-Hastings algorithm. Six transmissivity fields with increasing contrast were generated and one thousand conditional realizations were computed for each studied case. The MCMC procedure proposed in this work gives an overall more accurate picture than the quasilinear approach but at a considerably higher computational cost