Study of land surface temperature and spectral emissivity using multi-sensor satellite data

In this study, an attempt has been made to estimate land surface temperatures (LST) and spectral emissivities over a hard rock terrain using multi-sensor satellite data. The study area, of about 6000 km², is a part of Singhbhum-Orissa craton situated in the eastern part of India. TIR data from ASTER, MODIS and Landsat ETM+ have been used in the present study. Telatemp Model AG-42D Portable Infrared Thermometer was used for ground measurements to validate the results derived from satellite (MODIS/ASTER) data. LSTs derived using Landsat ETM+ data of two different dates have been compared with the satellite data (ASTER and MODIS) of those two dates. Various techniques, viz., temperature and emissivity separation (TES) algorithm, gray body adjustment approach in TES algorithm, Split-Window algorithms and Single Channel algorithm along with NDVI based emissivity approach have been used. LSTs derived from bands 31 and 32 of MODIS data using Split-Window algorithms with higher viewing angle (50°) (LST1 and LST2) are found to have closer agreement with ground temperature measurements (ground LST) over waterbody, Dalma forest and Simlipal forest, than that derived from ASTER data (TES with AST 13). However, over agriculture land, there is some uncertainty and difference between the measured and the estimated LSTs for both validation dates for all the derived LSTs. LST obtained using Single Channel algorithm with NDVI based emissivity method in channel 13 of ASTER data has yielded closer agreement with ground measurements recorded over vegetation and mixed lands of low spectral contrast. LST results obtained with TIR band 6 of Landsat ETM+ using Single Channel algorithm show close agreement over Dalma forest, Simlipal forest and waterbody with LSTs obtained using MODIS and ASTER data for a different date. Comparison of LSTs shows good agreement with ground measurements in thermally homogeneous area. However, results in agriculture area with less homogeneity show difference of LST up to 2°C. The results of the present study indicate that continuous monitoring of LST and emissivity can be undertaken with the aid of multi-sensor satellite data over a thermally homogeneous region.     

重庆綦江地质公园地质遗迹特征及其地质意义

綦江地质公园发育木化石、恐龙足迹、恐龙骨骼化石、鱼化石、沉积构造、丹霞地貌等地质遗迹景观,木化石和恐龙足迹为园区的导向型景观。木化石分布在侏罗系中统沙溪庙组(J2s)上部砂岩层中,砂岩层含钙质结核,在约300×200m2的砂岩层内共埋藏有60多根木化石,其中一半木化石为钙化作用形成。恐龙足迹集中分布在白垩系上统夹关组(K2j)砂泥岩层中,岩层发育交错层理、波痕和泥裂。在夹关组的3个层位中共发现329个恐龙足迹,其分别属于甲龙类、鸟脚类和兽脚类。园区地质遗迹分布在一套河湖相沉积层中,其形成于内陆河湖网形成之时(如木化石),并随着四川盆地周围的湖泊系统解体而发展(如恐龙足迹),最终随着河流由堆积作用为主的阶段转变为以侵蚀作用为主的阶段而减弱(如丹霞地貌)。白垩纪上统夹关组的恐龙足迹群形成于干热的环境,多类型的恐龙足迹集中分布反映了白垩纪晚期(夹关期)恐龙种群的丰富,恐龙足迹的发现为区域内寻找白垩系地层的恐龙骨骼化石提供了依据。     

Fission-track ages of four meteorites

A method for selective annealing of cosmic-ray tracks has been developed, permitting determination of fission-track ages in the presence of a large background of cosmic-ray tracks. The mesosiderite Bondoc contains 41 fission tracks/cm², of which about 75% are due to neutron-induced fission of U²³⁵ during cosmic-ray exposure. Its net fission-track age is 140 ± 40 Myr, nearly identical to its cosmic-ray exposure age of 150 Myr. The mesosiderite Mincy has a fission-track age of 1500 ± 400 Myr.Nakhla (nakhlite) contains an excess of apparent fission tracks, which may be either genuine fission tracks from Pu²⁴⁴ or etch pits mimicking fission tracks in length, thermal stability, random orientation, and other characteristics. On the assumption that they are fission tracks, the Pu²⁴⁴/U²³⁸ ratio at the onset of track retention in Nakhla was (3.1 ± 1.3) × 10^?3, nearly an order of magnitude lower than the initial solar system ratio. This may reflect a chemical fractionation of Pu and U, or a late impact or magmatic event. Different minerals of the Washougal howardite have different Pu²⁴⁴/U²³⁸ ratios, from (24 ± 7) × 10^?3 to (2.3 ± 0.7) × 10^?3. This may imply a succession of impacts over a period of time. Additionally, Pu and U may have been chemically fractionated from each other in this meteorite.Shocked meteorites show no consistent pattern in the retentivity of fission tracks and of fissiogenic or radiogenic noble gases. Some meteorites, e.g. Bondoc, Serra de Magé, and Mincy, retain gases more completely than tracks; others, e.g. Nakhla and Allende, retain them less completely.Uranium was determined in feldspar and/or pyroxene from 19 Ca-rich achondrites and mesosiderites. For most, only upper limits of 0.01–0.03 ppb were obtained. Apparently the uranium in these meteorites resides almost exclusively in minor phases, as in terrestrial and lunar rocks.     

Integrating Seismic Data for Lithofacies Modeling: A Comparison of Sequential Indicator Simulation Algorithms

Clastic reservoir characterization starts typically with modeling lithofacies distribution and geometry. The architecture of the reservoir, governed by the lithofacies geometry, is a major source of heterogeneity in such clastic systems. Seismic data provide potentially valuable information about the areal distribution of different lithofacies, such as the averaged prior proportion of each lithofacies. However, seismic data are available only at coarse vertical resolution rather than the fine lithofacies sampling along wells, hence seismic is considered equivalent to 2D data while building 3D geological models. This scale difference between the seismic data and the lithofacies data available along the wells makes direct integration difficult. Different algorithms have been proposed to integrate the seismic data: (1) duplicate seismic data along the vertical line and use the prior proportions provided by the seismic data as prior local means; (2) integrate the 2D seismic data as collocated block averages; and (3) duplicate seismic data along the vertical line and integrate them using a Markov-Bayes algorithm. These three algorithms are applied on a data set originating from a real clastic reservoir. The results are compared with regard to how much kriging weight is applied to the seismic data and how well the information from seismic data is honored.     

A Spatial-Temporal/3-D Model for Volcanic Hazard Assessment: Application to the Yucca Mountain Region, Nevada

We present a 3-D Poisson model that permits identification and quantification of volcanic phenomena distributed through space and evolving in time (i.e., spatiotemporal data). Specifically, the model: (1) is volcanologically informative in solving problems of volcanic risk/hazard which depends on the location and time of future events; (2) contains model fitting computation algorithms that are efficient; and (3) is flexible enough to handle a large class of volcanic risk/hazard studies. Furthermore, we apply the model fitting techniques developed in this paper to the volcanic data from the Yucca Mountain project to demonstrate a unified volcanic hazard analysis. This study also evaluates the sensitivity of the statistical models developed by experts who have addressed the volcanic hazard/risk assessment problem near the Yucca Mountain region.     

Mapping and attenuation of surface waves side scattered by near-surface diffractors

Near-surface diffractors are one of the problems in land seismic exploration. They can scatter the surface wave energy emanating from the seismic source and contaminate the signal received by seismic receivers. The scattered energy from the near-surface diffractors manifests itself on seismic shot gathers as strong hyperbolic events, called diffractions, masking the weakly reflected body waves. Diffractions present complications to most of surface-wave suppression schemes, especially when they have been scattered by scatterers outside the receiver line. Different methods have been used to eliminate diffractions from seismic data, including geophone arrays, filtering, and inverse scattering. Each of those methods has its own limitations. In this study, we present processing algorithms to map and attenuate near-surface diffractors of surface waves in seismic shot gathers. The mapping algorithm is based on semblance measurements and time–offset relations, while the attenuation algorithm is based on the least-square fitting of a source wavelet. The algorithms are applied on synthetic data from two different models. The first model has three near-surface diffractors, while the second model has three clusters of near-surface diffractors. Each cluster consists of three near-surface diffractors with a different geometry for each cluster. The results show that the proposed algorithms are successful in locating and attenuating most near-surface diffractors, except when the separation between individual diffractors is below the wavelength of the diffracted surface wave.     

A Method for Modeling of a Creeping Slope with a Visco-Hypoplastic Material Law

This paper presents the numerical simulation of a creeping slope in Upper Austria, using a visco-hypoplastic material law which describes the mechanical behavior of cohesive soils allowing for viscous effects, i.e. creep and relaxation. The method consists of: (1) determination of the parameters of the material law, based on laboratory tests on soil samples taken from the slope; (2) simulation of the laboratory tests with an element test program in which the used material law was implemented, in order to test whether the model holds for the soils studied; and (3) simulation of slope movements at different sections along the slope, assuming an infinite slope. The simulation results fit well with the field measurements. This demonstrates that despite strongly simplified boundary conditions and limited availability of subsurface data (e.g. density) the visco-hypoplastic law is a promising tool for predicting creep movements.     

u‐p semi‐Lagrangian reproducing kernel formulation for landslide modeling

This paper presents a u‐p (displacement‐pressure) semi‐Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi‐Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u‐p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the u‐p semi‐Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide.     

土壤水分特征曲线模型模拟性能评价

土壤水分特征曲线模型作为实验测定土壤水分特征数据的一种替代方法,因其具有计算方便快捷和便于嵌入数值模拟程序的优点,开始受到越来越广泛的关注。虽然文献中存在众多的土壤水分特征曲线模型,但是这些模型的适用范围及拟合性能尚不明确。为了获得更加准确适用的土壤水分特征曲线,在实际应用中通常需要花费大量时间和精力去测试各种模型。为了解决上述问题,在国内外研究成果的基础上收集整理了12种典型的土壤水分特征曲线模型,并利用包含不同质地、有机质含量及容重的8种土壤的实测土壤水分特征数据来评估比较这些模型的模拟性能。模型性能通过均方根误差（RMSE）、平均偏差（AD）、AIC准则（Akaike Information Criterion）和纳什效率系数（NSE）4个指标评估。研究结果表明：大部分的模型能够提供比较接近于实际的拟合结果,评价指标值也比较相近。其中,KCGS2006（包含3个参数）和K1999模型（包含2个参数）拟合效果最好,而Gregson1987（包含1个参数）的拟合效果最差。该研究可以深入了解各种土壤水分特征曲线模型的适用性与局限性,更好地为生态环境建设和农业可持续发展研究中土壤水力参数的选取提供依据和参考。     

Stress determination by back-analysis of excavation-induced stress changes — a case study

Summary An Underground Research Laboratory (URL) has been constructed by Atomic Energy of Canada Limited (AECL) to study various aspects of disposing of nuclear fuel waste in the Canadian Shield. In order to ensure good quality and long life of the construction, one important factor to be considered is the in situ stress field. As part of the research program, stress changes have been measured during the advance of a tunnel to monitor the stress response to excavation. It is desirable to estimate the state of in situ stress from these stress change measurements and to compare the results with overcoring data. This paper describes the application of a recently developed stress change fitting technique for stress determination. The basic principle and the fitting procedure are briefly summarized and the back-analysis process for the data collected at the URL is presented in detail. A boundary element model was used to predict the stress changes as required by the fitting approach. This new method of in situ stress determination was successfully applied in this case. The back-analyzed stresses agree very well with those determined from overcoring tests. The quality of individual measurements was assessed and the required minimum number of measurements for a conclusive data interpretation is evaluated.     

土壤呼吸中根系与微生物呼吸的区分方法与应用

土壤呼吸中根系呼吸和微生物呼吸的区分在研究生态系统碳循环和土壤碳储量时具有重要意义。较系统地介绍了各种区分方法,主要包括成分综合法、生物量外推法、根去除法、同位素标记法等。现国内研究中使用生物量外推法较多,但其相关性较差。根去除法又可分为根移除法、挖沟隔离法和林隙法,由于是就地测定,其数据可信度较高。同位素标记法包括脉冲标记法和连续标记法,该方法避免了大的干扰,数据较准确,缺点在于设备复杂、操作困难、分析费用高。同时对各种方法的原理和应用进行了介绍。     

The hyperpycnite problem

Sedimentologic, oceanographic, and hydraulic engineering publications on hyperpycnal flows claim that(1) river flows transform into turbidity currents at plunge points near the shoreline,(2) hyperpycnal flows have the power to erode the seafloor and cause submarine canyons, and,(3) hyperpycnal flows are efficient in transporting sand across the shelf and can deliver sediments into the deep sea for developing submarine fans. Importantly, these claims do have economic implications for the petroleum industry for predicting sandy reservoirs in deep-water petroleum exploration. However, these claims are based strictly on experimental or theoretical basis, without the supporting empirical data from modern depositional systems. Therefore, the primary purpose of this article is to rigorously evaluate the merits of these claims.A global evaluation of density plumes, based on 26 case studies(e.g., Yellow River, Yangtze River, Copper River,Hugli River(Ganges), Guadalquivir River, Rio de la Plata Estuary, Zambezi River, among others); suggests a complex variability in nature. Real-world examples show that density plumes(1) occur in six different environments(i.e., marine,lacustrine, estuarine, lagoon, bay, and reef);(2) are composed of six different compositional materials(e.g., siliciclastic,calciclastic, planktonic, etc.);(3) derive material from 11 different sources(e.g., river flood, tidal estuary, subglacial, etc.);(4) are subjected to 15 different external controls(e.g., tidal shear fronts, ocean currents, cyclones, tsunamis, etc.); and,(5) exhibit 24 configurations(e.g., lobate, coalescing, linear, swirly, U-Turn, anastomosing, etc.).Major problem areas are:(1) There are at least 16 types of hyperpycnal flows(e.g., density flow, underflow, high-density hyperpycnal plume, high-turbid mass flow, tide-modulated hyperpycnal flow, cyclone-induced hyperpycnal turbidity current, multi-layer hyperpycnal flows, etc.), without an underpinning principle of fluid dynamics.(2) The basic tenet that river currents transform into turbidity currents at plunge points near the shoreline is based on an experiment that used fresh tap water as a standing body. In attempting to understand all density plumes, such an experimental result is inapplicable to marine waters(sea or ocean) with a higher density due to salt content.(3) Published velocity measurements from the Yellow River mouth, a classic area, are of tidal currents, not of hyperpycnal flows. Importantly, the presence of tidal shear front at the Yellow River mouth limits seaward transport of sediments.(4) Despite its popularity, the hyperpycnite facies model has not been validated by laboratory experiments or by real-world empirical field data from modern settings.(5) The presence of an erosional surface within a single hyperpycnite depositional unit is antithetical to the basic principles of stratigraphy.(6) The hypothetical model of "extrabasinal turbidites", deposited by river-flood triggered hyperpycnal flows,is untenable. This is because high-density turbidity currents, which serve as the conceptual basis for the model, have never been documented in the world's oceans.(7) Although plant remains are considered a criterion for recognizing hyperpycnites, the "Type 1" shelf-incising canyons having heads with connection to a major river or estuarine system could serve as a conduit for transporting plant remains by other processes, such as tidal currents.(8) Genuine hyperpycnal flows are feeble and muddy by nature, and they are confined to the inner shelf in modern settings.(9) Distinguishing criteria of ancient hyperpycnites from turbidites or contourites are muddled.(10) After 65 years of research since Bates(AAPG Bulletin 37: 2119-2162, 1953), our understanding of hyperpycnal flows and their deposits is still incomplete and without clarity.     

Analysis and Improvement of Fitting Models for Predicting Subsidence Under High-Speed Railway Lines

A number of methods for predicting land subsidence and monitoring deformation under high-speed railway tracks exist, and are divided into three categories: layer-wise summation, numerical calculations based on consolidation theory, and curve fitting. One of these, curve fitting, including the hyperbola, expanded hyperbola, three-point fitting and Asaoka methods, is widely used because it is computationally simple and applicable in many situations. In this paper, we analyze the performance of the four classical curve fitting methods using field data and propose a novel approach to estimate land subsidence. The new method integrates three-point fitting, which is computationally simple whilst stringent in terms of correlation restrictions, with the Asaoka method to significantly improve performance in practical applications. Our experimental results indicate the average relative error of the modified method is reduced by 35.3 % than that of three-point fitting, and the mean correlation coefficient remains within acceptable bounds and even was enhanced by 1.48 %, so that this modified method can substantially improve prediction precision.     

Holocene relative sea-level change, isostatic subsidence and the radial viscosity structure of the mantle of northwest Europe (Belgium, the Netherlands, Germany, southern North Sea)

A comprehensive observational database of Holocene relative sea-level (RSL) index points from northwest Europe (Belgium, the Netherlands, northwest Germany, southern North Sea) has been compiled in order to compare and reassess the data collected from the different countries/regions and by different workers on a common time–depth scale. RSL rise varies in magnitude and form between these regions, revealing a complex pattern of differential crustal movement which cannot be solely attributed to tectonic activity. It clearly contains a non-linear, glacio- and/or hydro-isostatic subsidence component, which is only small on the Belgian coastal plain but increases significantly to a value of ca 7.5 m relative to Belgium since 8 cal. ka BP along the northwest German coast. The subsidence is at least in part related to the Post-Glacial collapse of the so-called peripheral forebulge which developed around the Fennoscandian centre of ice loading during the Last Glacial Maximum. The RSL data have been compared to geodynamic Earth models in order to infer the radial viscosity structure of the Earth's mantle underneath NW Europe (lithosphere thickness, upper- and lower-mantle viscosity), and conversely to predict RSL in regions where we have only few observational data (e.g. in the southern North Sea). A very broad range of Earth parameters fit the Belgian RSL data, suggesting that glacial isostatic adjustment (GIA) only had a minor effect on Belgian crustal dynamics during and after the Last Ice Age. In contrast, a narrow range of Earth parameters define the southern North Sea region, reflecting the greater influence of GIA on these deeper/older samples. Modelled RSL data suggest that the zone of maximum forebulge subsidence runs in a relatively narrow, WNW–ESE trending band connecting the German federal state of Lower Saxony with the Dogger Bank area in the southern North Sea. Identification of the effects of local-scale factors such as past changes in tidal range or tectonic activity on the spatial and temporal variations of sea-level index points based on model-data comparisons is possible but is still complicated by the relatively large range of Earth model parameters fitting each RSL curve, emphasising the need for more high-quality observational data.     

Persisting effects of armored military maneuvers on some soils of the Mojave Desert

Soil compaction and substrate modification produced during large-scale armored military maneuvers in the early 1940s were examined in 1981 at seven sites in California’s eastern Mojave Desert Recording penetrometer measurements show that tracks left by a single pass of an M3 “medium” tank have average soil resistance values that are 50% greater than those of the surrounding untracked soil in the upper 20 cm At one site, measurements made along short segments of track that have been visually eliminated by erosion and deposition processes show a 73% increase in penetrometer resistance over adjacent, undisturbed soils Dirt roadways at three former base camp locations could not be penetrated below 5–10 cm because of extreme compaction Soil bulk density was not as sensitive an indicator of soil compaction as was penetrometer resistance Density values in the upper 10 cm of soil are not significantly different between tank tracks and undisturbed soils at most sites, and roadways at two base camps show an average increase in bulk density of only 12% over adjacent soils. Trench excavations across tank tracks show that physical modifications of the substrate can extend vertically beneath a track to a depth of 25 cm and outward from a track’s edge to 50 cm These soil disturbances are probably major factors that encourage accelerated soil erosion throughout the manuever area and also retard or prevent the return of vegetation to pre-disturbance conditions     

Groundwater flow underneath mound spring tufas from geophysical surveys in the southwestern Great Artesian Basin,Australia

Artesian springs, which form carbonate mounds at the surface, occur in groups along the southwestern edge of the Great Artesian Basin (GAB), in northern South Australia. Their underground structure and relationship to faulting are not well understood. This study investigated four mound spring groups (Beresford Spring, Warburton Spring, the Bubbler Spring group, and Freeling Springs), which have different geological settings, using a range of geophysical techniques: self-potential (SP), magnetotellurics (MT) and time-domain electromagnetics (TEM). The results confirmed that despite generally similar mound morphologies at the surface, spring vents in different groups have different mechanisms for sourcing water from the GAB aquifer. SP measurements effectively showed where most of the vertical flow occurs at all groups, while MT and TEM models identified the location of faults, other geological structures and the thickness of the Bulldog Shale aquitard. Beresford and Warburton springs are similar in that the spring locations at both are directly related to points on a regional-scale fault, which appears to provide a low permeability pathway to the surface. At the Bubbler Springs group, a regionally aligned fault identified in MT data seems to be bounding an area where the aquifer is much closer to the surface (and the overlying aquitard has been thinned) where the spring abundance is highest. SP responses indicate that shallow flow paths feeding individual vents are unrelated to the fault. At Freeling Springs, the SP suggests that groundwater is flowing up within shallow aquifers, and that spring location is offset from this upward flow, instead located on range-front faults that provide the final conduit to the surface.     

Neogene kinematics of the Giudicarie fault (Central-Eastern Alps, Italy): new apatite fission-track data

The Neogene kinematics of the Giudicarie fault (part of Periadriatic lineament, NE Italy) have been re-examined using apatite fission-track analysis. Twenty samples were collected along two geological sections; the first one crossing the Tertiary Corno Alto pluton (Adamello batholith) and the Variscan basement (Southalpine domain) adjacent to the South Giudicarie fault, the second one close to the North Giudicarie fault, in the Variscan basement of the Tonale nappe (Austroalpine system). Samples from the southern section show short tracks and ages between 14.7±1.2 Myr and 22.5±2.2 Myr along 1570 m of the profile; samples from the northern profile present long tracks and ages between 11.3±1.3 Myr and 14.7±3.4 Myr along 1225 m of the vertical profile. In the former, the presence of short tracks might indicate either a long permanence of the rocks in the apatite partial annealing zone, or a more complex thermal history; in the latter case we are dealing with rocks which experienced more rapid cooling.
  The two differing segments of the Giudicarie fault can be explained either as two completely independent tectonic features or, more likely, by hypothesizing a single fault active in its southern and northern parts at different times. Fission track data support a first exhumation of this single fault c. 15 Ma along the North Giudicarie, with a final exhumation towards the south, in the Adamello area, at c. 8–10 Ma (Mid Tortonian). This age fits with the so-called 'Giudicarie' phase, during which σ₁ in the stress field was orientated N280–290°.     

FuzzyKrig: a comprehensive matlab toolbox for geostatistical estimation of imprecise information

Using kriging has been accepted today as the most common method of estimating spatial data in such different fields as the geosciences. To be able to apply kriging methods, it is necessary that the data and variogram model parameters be precise. To utilize the imprecise (fuzzy) data and parameters, use is made of fuzzy kriging methods. Although it has been 30 years since different fuzzy kriging algorithms were proposed, its use has not become as common as other kriging methods (ordinary, simple, log, universal, etc.); lack of a comprehensive software that can perform, based on different fuzzy kriging algorithms, the related calculations in a 3D space can be the main reason. This paper describes an open-source software toolbox (developed in Matlab) for running different algorithms proposed for fuzzy kriging. It also presents, besides a short presentation of the fuzzy kriging method and introduction of the functions provided by the FuzzyKrig toolbox, 3 cases of the software application under the conditions where: 1) data are hard and variogram model parameters are fuzzy, 2) data are fuzzy and variogram model parameters are hard, and 3) both data and variogram model parameters are fuzzy.     

A robust cylindrical fitting to point cloud data

Environmental, engineering and industrial modelling of natural features (e.g. trees) and man-made features (e.g. pipelines) requires some form of fitting of geometrical objects such as cylinders, which is commonly undertaken using a least-squares method that—in order to get optimal estimation—assumes normal Gaussian distribution. In the presence of outliers, however, this assumption is violated leading to a Gaussian mixture distribution. This study proposes a robust parameter estimation method, which is an improved and extended form of vector algebraic modelling. The proposed method employs expectation maximisation and maximum likelihood estimation (MLE) to find cylindrical parameters in case of Gaussian mixture distribution. MLE computes the model parameters assuming that the distribution of model errors is a Gaussian mixture corresponding to inlier and outlier points. The parameters of the Gaussian mixture distribution and the membership functions of the inliers and outliers are computed using an expectation maximisation algorithm from the histogram of the model error distribution, and the initial guess values for the model parameters are obtained using total least squares. The method, illustrated by a practical example from a terrestrial laser scanning point cloud, is novel in that it is algebraic (i.e. provides a non-iterative solution to the global maximisation problem of the likelihood function), is practically useful for any type of error distribution model and is capable of separating points of interest and outliers.