Quantifying tomb geometries in resistivity images using watershed algorithms

Quantifying the geometries (defined here as width, height and depth of burial) of archeological structures within resistivity models produced as a result of the regularization constraints used in most inversion algorithms is difficult, especially when structures are closely spaced. Here we apply the watershed by simulated immersion method of boundary detection to smooth 2D resistivity images generated for synthetic and field data over 3D targets. The synthetic studies include a single cavity model, a model for two widely spaced cavities (spacing ? unit electrode spacing) and a model for two closely spaced cavities (spacing < unit electrode spacing). We also examine a single-cavity model where a relatively resistive overburden, common at archaeological sites in Egypt, is included. In the case of the single cavity models, the maximum error for any geometries are 18% for the model without the resistive overburden and 10% for the model where the overburden is included, whereas it increases to 24% for the widely spaced model and 40% for the closely spaced model. Despite, the higher errors in the closely spaced cavity model, application of the algorithm confirms the presence of two features, which is not ascertainable from the smooth resistivity images. Boundaries detected with the watershed algorithm are subsequently used to define a disconnect in the regularization, resulting in a markedly improved estimate of the resistivity structure (particularly for the closely spaced cavity model) in a second inversion step using the model obtained from the smoothness constraint inversion as the starting model. This revised resistivity model also results in a lower root-mean-square (rms) misfit between measured and theoretical data, and between synthetic and inverted models. We demonstrate how the method can be applied on images from the archaeological site at Qurnet Murai, Luxor City Egypt.     

The Diurnal Cycle of Regional Commuter Systems: North Wales, 1991

Places of household residence and places of commuter destination are considered in a contiguous system of subareas constituting a region. An intrahousehold distribution of household members, by subarea of their commuting destination, is considered for each subarea of residence. A household composition matrix is constructed in reference to the average number of commuters to subareas of destination, per household at a subarea of residence, across all subareas. The matrix is a linear transformation from the spatial distribution of households onto the spatial distribution of daytime population, over all subareas of the region. Diurnal population change throughout the region is rendered by this transformation. A linear optimization model extending this transformation formalizes general conditions that relate the diurnal population system to household choice of residence and work. Further, the division of the region into subareas is assumed to be such that the average household in each subarea contains at least one person who remains in the subarea during day and night. Under these conditions, the diurnal system is shown to be analogous to the Leontief input‐output model. An example of eleven counties of North Wales, along with an exogenous area of northwestern England, drawn from the 1991 census of the United Kingdom, illustrates the formal relationships.