Merging airborne magnetic surveys into continental‐scale compilations

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 988-995 ◽  
Author(s):  
Brian R. S. Minty ◽  
Peter R. Milligan ◽  
Tony Luyendyk ◽  
Timothy Mackey

Regional compilations of airborne magnetic data are becoming more common as national databases grow. Grids of the magnetic survey data are joined together to form geological province‐scale or even continental‐scale compilations. The advantage of these compilations is that large tectonic features and geological provinces can be better mapped and interpreted. We take a holistic approach to the joining of survey grids. The leveling of the grids into a regional compilation is treated as a single inverse problem. We use the weighted least‐squares method to find the best adjustment for each survey grid such that the data value differences in the grid overlap areas are minimized. The method spreads any inconsistencies between grids among all of the grid overlap areas and minimizes the introduction of long‐wavelength errors into the composite grid. This is an improvement on the conventional approach of joining grids sequentially. A comparison of leveled data over Western Australia with diurnally‐corrected long aeromagnetic traverses shows long‐wavelength errors of about 200 nT over distances of more than 5000 km. This is an improvement on the sequential grid‐joining method, which gives errors of about 450 nT over the same distance. The application of the method to a smaller area covered by good quality surveys resulted in long‐wavelength errors of about 30 nT over a distance of 1200 km. This is within the estimated accuracy of the original survey measurements. The new method is also fast—what used to take many weeks of effort can now be achieved in a matter of hours.

SAGE Open ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 215824402110269
Author(s):  
Lang Liang

The Bass model is the most popular model for forecasting the diffusion process of a new product. However, the controlling parameters in it are unknown in practice and need to be determined in advance. Currently, the estimation of the controlling parameters has been approached by various techniques. In this case, a novel optimization-based parameter estimation (OPE) method for the Bass model is proposed in the theoretical framework of system dynamics ( SD). To do this, the SD model of the Bass differential equation is first established and then the corresponding optimization mathematical model is formulated by introducing the controlling parameters as design variable and the discrepancy of the adopter function to the reference value as objective function. Using the VENSIM software, the present SD optimization model is solved, and its effectiveness and accuracy are demonstrated by two examples: one involves the exact solution and another is related to the actual user diffusion problem from Chinese Mobile. The results show that the present OPE method can produce higher predicting accuracy of the controlling parameters than the nonlinear weighted least squares method and the genetic algorithms. Moreover, the reliability interval of the estimated parameters and the goodness of fitting of the optimal results are given as well to further demonstrate the accuracy of the present OPE method.


2010 ◽  
Vol 7 (5) ◽  
pp. 7383-7416 ◽  
Author(s):  
S. Ly ◽  
C. Charles ◽  
A. Degré

Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (krigings) are widely used in spatial interpolation from point measurement to continuous surfaces. However, the majority of existing geostatistical algorithms are available only for single-moment data. The first step in kriging computation is the semi-variogram modelling which usually uses only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. In this study, we used daily rainfall data from 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, Cressie's Approximate Weighted Least Squares method was used to fit seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) to daily sample semi-variogram on a daily basis. Seven selected raingages were used to compare the interpolation performance of these algorithms applied to many degenerated-raingage cases. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably interpolation with the Thiessen polygon that is commonly used in various hydrological models. Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) presented the highest Root Mean Square Error (RMSE) between the geostatistical and IDW methods. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases.


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