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41.
On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms 总被引:2,自引:1,他引:1
The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E
Y
= (X−E
X
) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E
Y
and E
X
. Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation
matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix
X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem
by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative
algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition.
For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert
cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing
the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment
of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift
to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares
and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion
matrix of the estimated parameters. 相似文献
42.
Craig W. Morgan Graham M. Kent Gordon G. Seitz Michaela Novak 《Hydrogeology Journal》2008,16(5):981-994
A hydrogeologic model that has been used by many researchers and consultants to describe an area of South Lake Tahoe, California,
USA impacted by MTBE contamination describes a relatively homogeneous unconfined aquifer comprised of poorly sorted glacial
outwash deposits, within which water-supply wells are able to exert significant alteration in natural groundwater flow. A
re-examination of the area’s hydrogeology is presented, which supports a layered heterogeneous aquifer system constructed
of alternating fine and coarser-grained glacio-lacustrine depositional units. This re-evaluation was accomplished through
a review of lithologic logs across an area of approximately 1 km2, combined with observations of significant hydraulic head differences and knowledge of the depositional environments controlled
by Pleistocene Lake Tahoe high stands. Many of the fine-grained units observed at depths from 6 to 15 m, although relatively
thin, are generally continuous and serve as significant barriers to groundwater flow. The vertical migration of contamination
across these fine-grained units to deeper groundwaters was facilitated by cross-screened monitoring wells installed as part
of site investigation activities. This conclusion highlights the importance of geologic characterization and proper monitoring
well construction at contaminated site investigations.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.
相似文献
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.
Michaela NovakEmail: |
43.
An updated analysis of geothermal data from the highland area of eastern Brazil has been carried out and the characteristics of regional variations in geothermal gradients and heat flow examined. The database employed includes results of geothermal measurements at 45 localities. The results indicate that the Salvador craton and the adjacent metamorphic fold belts northeastern parts of the study area are characterized by geothermal gradients in the range of 6–17°C/km. The estimated heat flow values fall in the range of 28–53 mW/m2, with low values in the cratonic area relative to the fold belts. On the other hand, the São Francisco craton and the intracratonic São Francisco sedimentary basin in the southwestern parts are characterized by relatively higher gradient values, in the range of 14–42°C/km, with the corresponding heat flow values falling in the range of 36–89 mW/m2. Maps of regional variations indicate that high heat flow anomaly in the São Francisco craton is limited to areas of sedimentary cover, to the west of the Espinhaço mountain belt. Crustal thermal models have been developed to examine the implications of the observed intracratonic variations in heat flow. The thermal models take into consideration variation of thermal conductivity with temperature as well as change of radiogenic heat generation with depth. Vertical distributions of seismic velocities were used in obtaining estimates of radiogenic heat production in crustal layers. Crustal temperatures are calculated based on a procedure that makes simultaneous use of the Kirchoff and Generalized Integral Transforms, providing thereby analytical solutions in 2D and 3D geometry. The results point to temperature variations of up to 300°C at the Moho depth, between the northern Salvador and southern São Francisco cratons. There are indications that differences in rheological properties, related to thermal field, are responsible for the contrasting styles of deformation patterns in the adjacent metamorphic fold belts. 相似文献
44.
Comparison of numerical models of two debris flows in the Cortina d’ Ampezzo area,Dolomites, Italy 总被引:2,自引:0,他引:2
The accurate prediction of runout distances, velocities and the knowledge of flow rheology can reduce the casualties and property
damage produced by debris flows, providing a means to delineate hazard areas, to estimate hazard intensities for input into
risk studies and to provide parameters for the design of protective measures. The application of most of models that describe
the propagation and deposition of debris flow requires detailed topography, rheological and hydrological data that are not
always available for the debris-flow hazard delineation and estimation. In the Cortina d’Ampezzo area, Eastern Dolomites,
Italy, most of the slope instabilities are represented by debris flows; 325 debris-flow prone watersheds have been mapped
in the geomorphological hazard map of this area. We compared the results of simulations of two well-documented debris flows
in the Cortina d’Ampezzo area, carried on with two different single-phase, non-Newtonian models, the one-dimensional DAN-W
and the two-dimensional FLO-2D, to test the possibility to simulate the dynamic behaviour of a debris flow with a model using
a limited range of input parameters. FLO-2D model creates a more accurate representation of the hazard area in terms of flooded
area, but the results in terms of runout distances and deposits thickness are similar to DAN-W results. Using DAN-W, the most
appropriate rheology to describe the debris-flow behaviour is the Voellmy model. When detailed topographical, rheological
and hydrological data are not available, DAN-W, which requires less detailed data, is a valuable tool to predict debris-flow
hazard. Parameters obtained through back-analysis with both models can be applied to predict hazard in other areas characterized
by similar geology, morphology and climate. 相似文献
45.
We estimate (/T)
P
of the lower mantle at seismic frequencies using two distinct approaches by combining ambient laboratory measurements on lower mantle minerals with seismic data. In the first approach, an upper bound is estimated for |(/T)
P
| by comparing the shear modulus () profile of PREM with laboratory room-temperature data of extrapolated to high pressures. The second approach employs a seismic tomography constraint ( lnV
S
/ lnV
P
)
P
=1.8–2, which directly relates (/T)
P
with (K
S
/T)
P
. An average (K
S
/T)
P
can be obtained by comparing the well-established room-temperature compression data for lower mantle minerals with theK
S
profile of PREM along several possible adiabats. Both (K
S
/T) and (/T) depend on silicon content [or (Mg+Fe)/Sil of the model. For various compositions, the two approaches predict rather distinct (/T)
P
vs. (K
S
/T)
P
curves, which intersect at a composition similar to pyrolite with (/T)
P
=–0.02 to –0.035 and (K
S
/T)
P
=–0.015 to –0.020 GPa/K. The pure perovskite model, on the other hand, yields grossly inconsistent results using the two approaches. We conclude that both vertical and lateral variations in seismic velocities are consistent with variation due to pressure, temperature, and phase transformations of a uniform composition. Additional physical properties of a pyrolite lower mantle are further predicted. Lateral temperature variations are predicted to be about 100–250 K, and the ratio of ( lnp/ lnV
S
)
P
around 0.13 and 0.26. All of these parameters increase slightly with depth if the ratio of ( lnV
S
/ lnV
P
)
P
remains constant throughout the lower mantle. These predicted values are in excellent agreement with geodynamic analyses, in which the ratios ( ln / lnV
S
)
P
and ( / lnV
S
)
P
are free parameters arbitrarily adjusted to fit the tomography and geoid data. 相似文献
46.
Sergio E. Serrano 《Mathematical Geology》1996,28(6):701-721
A large body of existing theories of flow and contaminant transport in aquifers ignore the presence of recharge, eliminate the boundary conditions, neglect transient conditions in groundwater flow, conceive hydraulic gradients as linear, and require parameter variability to be stationary and Gaussian. The most outstanding and difficult to justify assumption is the subjective small size of the stochastic terms (i.e., small perturbation methods), which usually is forced by considering the logarithm of the hydraulic conductivity. Several problems in flow and contaminant subsurface hydrology, such as the enhanced dispersion parameters with plume size or time after injection, remain to be observed in the light of a stochastic theory that allows a more realistic consideration of physical and hydrologic properties. In this article, an attempt is made to reformulate a contaminant transport equation (the variable dispersion equation, VDE) with transport parameters in terms of regional hydrologic and aquifer hydraulic properties, such as recharge rate, spatially random transmissivity, hydraulic gradient, aquifer thickness, and soil porosity. Subsequently, a general analytic procedure, the method of decomposition, is used to derive a solution to the VDE. This procedure does not require small perturbation, logarithmic transformations, or specific probability law assumptions. Comparison tests with existing theoretical and field results are given. The tests illustrate the enhanced dispersion and shifting concentration effects produced by the variable dispersion equation. Finally a generalization of the method to nonstationary dispersion in three-dimensional domains is proposed. 相似文献
47.
Santschi Peter H. Honeyman Bruce D. Quigley Matthew S. 《Aquatic Sciences - Research Across Boundaries》1993,55(4):230-239
In 1975 Paul Schindler produced the first oceanic trace metal scavenging model to explicitly include the role of surface chemistry as a control on trace metal water column residence times. The eighteen years that have elapsed since the publication of Schindler's seminal paper have seen the development of a variety of oceanic scavenging models; yet, the fundamental insight of his Zero-order Model remains the benchmark. This paper describes the role of Paul Schindler's work on surface chemistry in providing a framework for the current generation of trace element scavenging models. 相似文献
48.
黄河下游断面形态与水沙输移关系及数学模拟方法 总被引:4,自引:0,他引:4
以前人对黄河下游的实测资料分析为基础,本文讨论断面形态与来水来沙关系、断面形态对输水输沙的影响,并根据实测资料,提出黄河下游弯段与直段断面冲淤变化的两种模式,建立了主流摆动及坍岸影响断面形态变化以及纵向冲淤量在断面的分布两种数学模拟方法。 相似文献
49.
Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (Xn, n 0) or (Xt, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Yn, n 0) or (Yt, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points. 相似文献
50.