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Soils are highly variable spatially due to soil forming and processes. Spatial variation of soil properties cause uneven patterns in soil fertility and crop growth, and use efficiency of externally applied resources. Application of variable rates of inputs needs partitioning of land units into homogenous land and management units (LMU), for production benefits and to minimize the adverse environmental impacts. The soil and site characteristics namely texture, depth and gravelliness, land use and climate are integrated to identify land units. Crop based production systems varied in different land units, production systems were super imposed on the delineated land units in GIS to identify the LMUs. Methodology was tested in Mysore district of Karnataka, where in 12 LMUs identified and delineated at district level. To verify the methodology, performance of crops vis-à-vis management practices followed in different LMUs was compared to plan appropriate land management decisions for current and future land use to ensure its sustainability.

A method of representing surfaces and volumes by a set of geometric points and a small set of auxiliary parameters, based on generalization of Bernoulli's notion of lemniscates is introduced. It provides for easy generation and modification of surfaces and volumes, which could be connected, disjoint or even with very irregular boundaries. This allows solving geophysical inversion problems, without constraining the anomalous volumes to some ideal or simple forms. This is illustrated by the example of joint inversion of gravity and magnetic data sets attributable to two-dimensional anomalous bodies. A nonlocal optimization algorithm called segmented Hamming scan is used for inversion. Comparison with nonlinear least-squares algorithm shows the advantages of the chosen approach. The concepts of desideratal and procedural detours are illustrated.

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