Modified Rankine-Hugoniot shock fitting technique: Simultaneous solution for shock normal and speed

We introduce a modification of the nonlinear least squares fitting technique of Vinas and Scudder and Szabo (VSSz) with simultaneous determination of the shock normal direction (theta and phi) and propagation speed O(V-S). Similar to the 2D case of the VSSz technique, the uniqueness of the solution can still be graphically demonstrated in the 2D space of the unknown variables. The modified technique is validated through the analysis of synthetic shocks and is also applied to an interplanetary shock observed by Wind. Our technique provides self-consistent 3D confidence regions for the parameters while the VSSz technique assumes the independence of the V-S confidence interval from theta and phi. The 3D confidence region is highly dependent on V-S resulting in theta and phi joint confidence regions that are generally significantly larger and oriented differently than those obtained by the VSSz technique. This also leads to significantly larger confidence intervals for the individual parameters determined by our modified technique. While the best fit values provided by the two techniques are usually close to each other, we also demonstrate the advantage of the V-S best fit value determination with our technique in the case when a small density jump is combined with significant density fluctuations. The agreement between the best fit solutions of the techniques can also be used as a test for the correctness of the chosen upstream and downstream intervals.