Generation of High Spatial Resolution Terrestrial Surface from Low Spatial Resolution Elevation Contour Maps via Hierarchical Computation of Median Elevation Regions

We proposed a simple yet effective morphological approach to convert a sparse Digital Elevation Model (DEM) to a dense Digital Elevation Model. The conversion is similar to that of the generation of high-resolution DEM from its low-resolution DEM. The approach involves the generation of median contours to achieve the purpose. It is a sequential step of the I) decomposition of the existing sparse Contour map into the maximum possible Threshold Elevation Region (TERs). II) Computing all possible non-negative and non-weighted Median Elevation Region (MER) hierarchically between the successive TER decomposed from a sparse contour map. III) Computing the gradient of all TER, and MER computed from previous steps would yield the predicted intermediate elevation contour at a higher spatial resolution. We presented this approach initially with some self-made synthetic data to show how the contour prediction works and then experimented with the available contour map of Washington, NH to justify its usefulness. This approach considers the geometric information of existing contours and interpolates the elevation contour at a new spatial region of a topographic surface until no elevation contours are necessary to generate. This novel approach is also very low-cost and robust as it uses elevation contours.Comment: 11 pages, 6 figures,1 table, 1 algorith

Interpolation of Subsurface Isopach Maps Using Mathematical Morphology

Isopach maps have great importance in geological mapping for oil and gas exploration which consist of contour lines of equal thicknesses over an area. Isopach mapping is primarily based on information from outcrop rocks and data obtained from borehole surveys during oil-well drilling. One of the major limitations in preparing such geological maps is the sparse distribution of outcrops and the limited number of exploratory wells. Therefore, getting information in between such wellbore locations for the preparation of a representative subsurface isopach map is a big challenge. On the other hand, an accurately mapped subsurface geology is very essential to identify important structural features which could be the potential accumulations of hydrocarbon and also for the placing well locations. The accuracy of mapping can be improved by the use of spatial interpolation. Interpolation can reduce spatial uncertainty and improve the interpretation of spatial distribution. There are several methods available for such interpolation e.g kriging, triangulation, closest distance to point, inverse distance, etc. In interpolation of such geologic maps, retaining geometric information of the existing contours plays a major role in accurately identifying subsurface structural features. However, the majority of available methods use distance-based principles for point interpolation. From the literature, it is evident that mathematical morphological operators such as dilation and erosion are very powerful tools for shape-based feature extraction from topographic surfaces. Mathematical morphology is the first consistent non-linear theory used for image processing and several other applications. In this paper, we have proposed a method for interpolation of intermediate isopach contour lines between existing contours using two morphological operators: dilation and erosion. The proposed method first extracts the threshold regions and then considers them as discrete sets which will serve as input towards the prediction of intermediate regions. The contours are extracted from the gradient of these regions. This process is repeated until no new intermediate contours can be created. To the best of our knowledge interpolation of subsurface contour maps by using mathematical morphology has not been performed earlier and this method can significantly assist in the construction of more representative subsurface geological models for petroleum exploration