Data examples of logarithm Fourier-domain bidirectional deconvolution

Trial and error on step length $\alpha$

Because the method above can lead to over-shooting on the step length $\alpha$ , it may lead to a blow-up problem. The Newton method requires a convex function, but for some field data sets that condition may not be met. To overcome this, we use trial and error to avoid step length $\alpha$ being too large. If the hyperbolic penalty function on new $r=r+\alpha\Delta r$ is greater than on original $r$ , the step length $\alpha$ is too large, and we overshoot; in that case, we reduce the step length $\alpha$ by half until the stability condition is met.