An iterative regularized inversion method of fracture width and height using cross-well optical fiber strain

The forward model of optical fiber strain induced by fractures, together with the associated model resolution matrix, is used to demonstrate the interpretability of fracture parameters once the fracture intersects the fiber. A regularized inversion framework for fracture parameters is established to evaluate the influence of measured data quality on the accuracy of iterative regularized inversion. An interpretation approach for both fracture width and height is proposed, and the synthetic forward data with measurement error and field examples are employed to validate the accuracy of the simultaneous inversion of fracture width and height. The results indicate that, after the fracture contacts the fiber, the strain response is strongly sensitive only to the fracture parameters at the intersection location, whereas the interpretability of parameters at other locations remains limited. The iterative regularized inversion method effectively suppresses the impact of measurement error and exhibits high computational efficiency, showing clear advantages for inversion applications. When incorporating the first-order regularization with a Neumann boundary constraint on the tip width, the inverted fracture-width distribution becomes highly sensitive to fracture height; thus, combined with a bisection strategy, simultaneous inversion of fracture width and height can be achieved. Examination using the model resolution matrix, noisy synthetic data, and field data confirms that the iterative regularized inversion model for fracture width and height provides high interpretive accuracy and can be applied to the calculation and analysis of fracture width, fracture height, net pressure and other parameters.