Preface

Aster, R.; Borchers, Brian; Thurber, C. H.

doi:10.1016/s0074-6142(05)80014-2

Cited by 98 publications

(119 citation statements)

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“…From equation (5), we can estimate both the half-length (a) and the half maximum thickness (b) of a dike from the opening displacement, u y (q i ), where q i (0 ≤ q i ≤ 2a), observed at the dike tip. For these estimates, we must use a nonlinear least squares method (e.g., the Gauss-Newton method [Aster et al, 2005], which is used here, or the LevenbergMarquardt method [Aster et al, 2005] alternatively) because the parameter a is nonlinear in equation (5).…”

Section: Methodsmentioning

confidence: 99%

Aspect ratios and magma overpressures of non‐feeder dikes observed in the Miyake‐jima volcano (Japan), and fracture toughness of its upper part

Kusumoto

Geshi

Guðmundsson

2013

Geophysical Research Letters

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[1] We present a new method for estimating the length and maximum thickness (aperture) of a dike from the observed opening at one dike tip. We apply the method to 15 arrested non-feeder dikes (where the upper tip is known, the lower tip unknown) in the caldera walls of Miyake-jima, Japan, to estimate the length-thickness ratio, as well as the magma overpressure and fracture toughness. The calculated length-thickness ratio ranges from 61 to 246, with an average of 136. The ratios are low because the dikes are emplaced close to the surface in comparatively compliant (soft) rocks. Using these ratios and the appropriate elastic constants, the calculated magmatic overpressures of the dikes are between 2.3 and 8.9 MPa, and the stress intensity factors between 38 and 117 MPa m 1/2 . All these values are within the range of typical in situ estimates, supporting the validity of this new method. Citation: Kusumoto S., N.Geshi, and A. Gudmundsson (2013), Aspect ratios and magma overpressures of non-feeder dikes observed in the Miyake-jima volcano (Japan), and fracture toughness of its upper part,

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Section: Methodsmentioning

confidence: 99%

Aspect ratios and magma overpressures of non‐feeder dikes observed in the Miyake‐jima volcano (Japan), and fracture toughness of its upper part

Kusumoto

Geshi

Guðmundsson

2013

Geophysical Research Letters

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“…By applying this methodology, it is secured that uncertain data sets are down weighted when determining C p and that the uncertainty of the C p factor can be taken into account when determining T MRS . Subsequently, var½logðC p Þ can be determined for this simple case as (Aster et al, 2005) …”

Section: Uncertainty Of Mrs Transmissivities Wb65mentioning

confidence: 99%

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

2016

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The nuclear magnetic resonance sounding (MRS) method is used increasingly as a tool for hydrological investigations. Compared to other geophysical methods, the advantage of MRS is that it is directly sensitive to the presence of water in the subsurface. Data interpretations can also be used to get information about the subsurface pore structures, which under special conditions can be related to hydraulic properties such as aquifer transmissivity. However, to broaden the usage of this information in hydrological modeling, the uncertainties related to these transmissivity estimates must be determined. Otherwise, properly balanced weights cannot be given to the prior information obtained from MRS transmissivity estimates as compared to the hydrological data sets when used for groundwater model calibration. We have developed a methodology to estimate the uncertainties of MRS-based transmissivity estimates. Compared to previous studies, the methodology is well defined, and it takes into account important factors such as the uncertainties of the hydraulically estimated transmissivities, the uncertainty of the correlation factor in the petrophysical relation, and the uncertainties and correlations of the geophysically estimated parameters. We have determined the correlations and uncertainties of the geophysical parameters using a linear and a nonlinear method, and we find that the results are comparable.

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“…In the following Theorem and Corollary we give some well known properties about least squares functionals as random variables, see for example [1]. They will be used to show that even though the residual principle holds as the noise goes to zero, (11) may not be a good criteria from which to choose the regularization parameter.…”

Section: Relationship To Discrepancy Principlementioning

confidence: 99%

Discontinuous parameter estimates with least squares estimators

Mead

2013

Applied Mathematics and Computation

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We discuss weighted least squares estimates of ill-conditioned linear inverse problems where weights are chosen to be inverse error covariance matrices. Least squares estimators are the maximum likelihood estimate for normally distributed data and parameters, but here we do not assume particular probability distributions. Weights for the estimator are found by ensuring its minimum follows a χ 2 distribution. Previous work with this approach has shown that the it is competitive with regularization methods such as the L-curve and Generalized Cross Validation (GCV) [23]. In this work we extend the method to find diagonal weighting matrices, rather than a scalar regularization parameter. Diagonal weighting matrices are advantageous because they give piecewise smooth least squares estimates and hence are a mechanism through which least squares can be used to estimate discontinuous parameters. This is explained by viewing least squares estimation as a constrained optimization problem. Results with diagonal weighting matrices are given for a benchmark discontinuous inverse problem from [15]. In addition, the method is used to estimate soil moisture from data collected in the Dry Creek Watershed near Boise, Idaho. Parameter estimates are found that combine two different types of measurements, and weighting matrices are found that incorporate uncertainty due to spatial variation so that the parameters can be used over larger scales than those that were measured.

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Preface

Cited by 98 publications

References 0 publications

Aspect ratios and magma overpressures of non‐feeder dikes observed in the Miyake‐jima volcano (Japan), and fracture toughness of its upper part

Aspect ratios and magma overpressures of non‐feeder dikes observed in the Miyake‐jima volcano (Japan), and fracture toughness of its upper part

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

Discontinuous parameter estimates with least squares estimators

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