In the oil and gas industry a crucial step for detecting and developing natural resources is to drill wells and measure miscellaneous properties along the well depth. These measurements are used to understand the rock and hydrocarbon properties and support oil/gas field development. The measurements are done at multiple times and using different tools. This introduces multiple disturbances
which are not related to physical properties of rocks or fluids themselves, and should be tackled before data is used to build subsurface models or take decisions. One important source of this disturbances is depth misalignment and in order to compare different measurements care must be taken to ensure that all measurements (log curves) are properly positioned in depth. This process is called depth matching. In spite of multiple attempts for automating this process it is still mostly done manually. This thesis addresses the automation problem and proposing a model based approach to solve it using Parametric Time Warping (PTW).

Based on the PTW, a parameterised warping function that warps one of the curves is assumed and its parameters are determined by solving an optimization problem maximizing the cross-correlation between the two curves. The warping function is assumed to have the parametric form of a piecewise linear function in order to accommodate the linear shifts that take place during the measurement process. This method, combined with preprocessing techniques such as an offset correction and low pass filtering, gives a robust solution and can correctly align the most commonly accruing examples. Furthermore, the methodology is extended to depth match logs with severe distortion by applying the technique in an iterative fashion. Several examples are given when developed algorithm is tested on real log data supplemented with the analysis of the computational complexity this method has and the scalability to larger data sets.