高斯投影公式的机助推导

随着GPS应用的普及,高斯投影在测量中出现的机会越来越多。许多文献上都给出了推导过程,这个推导过程的运算量是非常大的,而且计算精度难于提高。经过研究,一种易于编程的递推公式被发现,虽然这个公式在计算量上没有减少,但是可以较好地解决精度问题。     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

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.     

Glacio-lacustrine stratigraphy,aquifer characterization and contaminant transport: a case study in South Lake Tahoe,California, USA

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.

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Electronic supplementary material   The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Changes in hydrogeological properties of the River Choushui alluvial fan aquifer due to the 1999 Chi-Chi earthquake, Taiwan

Changes in hydrogeological properties of the River Choushui alluvial fan aquifer before and after the 1999 Chi-Chi earthquake, Taiwan, have been identified using pumping tests. Three wells, SH2, YL2 and SC2, located in a compressional zone with high coseismic groundwater levels, were tested. The threshold of the aquifer deformation with respect to transmissivity (T) is greater than that with respect to storage coefficient (S). Decreases in the post-earthquake S are approximately 60% at SH2 and SC2, indicating aquifer compression after the Chi-Chi earthquake. Changes in the post-earthquake T range from 61% increase to 0.8% decrease. Moreover, results from anisotropy analysis of T at SC2 further illustrate that normal stresses induced by the Chi-Chi earthquake have consolidated soil particles. Soil particles dilated laterally after the earthquake, resulting in an increase of the equivalent T. The changes in hydrogeological properties have a considerable influence on spatiotemporal fluid pressure and horizontal groundwater movement, resulting in different amounts of drawdown during post-earthquake pumping.     

Estimates of heat flow and heat production and a thermal model of the São Francisco craton

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.     

Comparison of numerical models of two debris flows in the Cortina d’ Ampezzo area,Dolomites, Italy

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.     

(ϖμ/ϖT) P of the lower mantle

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.     

Rupture process of large earthquakes in the northern Mexico subduction zone

The Cocos plate subducts beneath North America at the Mexico trench. The northernmost segment of this trench, between the Orozco and Rivera fracture zones, has ruptured in a sequence of five large earthquakes from 1973 to 1985; the Jan. 30, 1973 Colima event (M _s 7.5) at the northern end of the segment near Rivera fracture zone; the Mar. 14, 1979 Petatlan event (M _s 7.6) at the southern end of the segment on the Orozco fracture zone; the Oct. 25, 1981 Playa Azul event (M _s 7.3) in the middle of the Michoacan gap; the Sept. 19, 1985 Michoacan mainshock (M _s 8.1); and the Sept. 21, 1985 Michoacan aftershock (M _s 7.6) that reruptured part of the Petatlan zone. Body wave inversion for the rupture process of these earthquakes finds the best: earthquake depth; focal mechanism; overall source time function; and seismic moment, for each earthquake. In addition, we have determined spatial concentrations of seismic moment release for the Colima earthquake, and the Michoacan mainshock and aftershock. These spatial concentrations of slip are interpreted as asperities; and the resultant asperity distribution for Mexico is compared to other subduction zones. The body wave inversion technique also determines theMoment Tensor Rate Functions; but there is no evidence for statistically significant changes in the moment tensor during rupture for any of the five earthquakes. An appendix describes theMoment Tensor Rate Functions methodology in detail.The systematic bias between global and regional determinations of epicentral locations in Mexico must be resolved to enable plotting of asperities with aftershocks and geographic features. We have spatially shifted all of our results to regional determinations of epicenters. The best point source depths for the five earthquakes are all above 30 km, consistent with the idea that the down-dip edge of the seismogenic plate interface in Mexico is shallow compared to other subduction zones. Consideration of uncertainties in the focal mechanisms allows us to state that all five earthquakes occurred on fault planes with the same strike (N65°W to N70°W) and dip (15±3°), except for the smaller Playa Azul event at the down-dip edge which has a steeper dip angle of 20 to 25°. However, the Petatlan earthquake does prefer a fault plane that is rotated to a more east-west orientation—one explanation may be that this earthquake is located near the crest of the subducting Orozco fracture zone. The slip vectors of all five earthquakes are similar and generally consistent with the NUVEL-predicted Cocos-North America convergence direction of N33°E for this segment. The most important deviation is the more northerly slip direction for the Petatlan earthquake. Also, the slip vectors from the Harvard CMT solutions for large and small events in this segment prefer an overall convergence direction of about N20°E to N25°E.All five earthquakes share a common feature in the rupture process: each earthquake has a small initial precursory arrival followed by a large pulse of moment release with a distinct onset. The delay time varies from 4 s for the Playa Azul event to 8 s for the Colima event. While there is some evidence of spatial concentration of moment release for each event, our overall asperity distribution for the northern Mexico segment consists of one clear asperity, in the epicentral region of the 1973 Colima earthquake, and then a scattering of diffuse and overlapping regions of high moment release for the remainder of the segment. This character is directly displayed in the overlapping of rupture zones between the 1979 Petatlan event and the 1985 Michoacan aftershock. This character of the asperity distribution is in contrast to the widely spaced distinct asperities in the northern Japan-Kuriles Islands subduction zone, but is somewhat similar to the asperity distributions found in the central Peru and Santa Cruz Islands subduction zones. Subduction of the Orozco fracture zone may strongly affect the seismogenic character as the overlapping rupture zones are located on the crest of the subducted fracture zone. There is also a distinct change in the physiography of the upper plate that coincides with the subducting fracture zone, and the Guerrero seismic gap to the south of the Petatlan earthquake is in the wake of the Orozco fracture zone. At the northern end, the Rivera fracture zone in the subducting plate and the Colima graben in the upper plate coincide with the northernmost extent of the Colima rupture zone.     

The “Zero-order Model” revisited: Paul Schindler's influence on the development of trace metal scavenging models

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.     

铁砚磨穿指蘸墨 不用扬鞭自奋蹄——志《山西地震》创刊20周年

回顾了《山西地震》创刊20年的历史,叙述了《山西地震》.编辑部在自身建设、执行科技期刊编排标准、为防震减灾事业默默奉献的情况,总结了经验、教训,指出了今后努力的方向.