Reconstruction of discrete resistivity targets using coupled artificial neural networks and watershed algorithms

摘要

Estimating the dimensions (defined here as width, height and depth of burial) of discrete targets within resistivity models produced as a result of applying smoothness constraints in most inversion algorithms is difficult, especially when targets are closely spaced. Here we couple an image processing technique (watershed algorithm) with a trained Artificial Neural Network (ANN) model to arrive at predictions of the geometry and resistivity of discrete targets from an initial smoothness constraint resistivity model. These predictions are compared with those obtained from (1) applying the watershed algorithm alone, (2) inversion using the regular L1 norm and (3) when a smoothing disconnect is defined using image processing with data subsequently re-inverted to arrive at a revised model estimate. Synthetic studies were conducted on a single cavity model, a model for two widely spaced cavities (spacing ? unit electrode spacing), a model for two closely spaced cavities (spacing < unit electrode spacing) and a model for three closely spaced cavities (spacing < unit electrode spacing). In all model scenarios, the average root mean square (RMS) model error using our ANN approach is below 1 whilst the average combined RMS model error when including target resistivity is 35 for the single cavity, 30 for widely spaced targets and 75 for the closely spaced targets. Despite the higher errors in the closely spaced cavity models, application of the algorithm confirms the presence of multiple features, which is not ascertainable from the smooth inversion, or even when using a disconnect constraint. The ANN derived model significantly reduces the RMS misfit between synthetic and inverted models. We demonstrate the approach using field measurements collected over a precisely known void and also apply the method to smooth resistivity images obtained from measurements collected over an archaeological site at Qurnet Murai, Luxor city, Egypt.