A new method to select reliable Euler solutions based on damping variation

Euler deconvolution is a common method to estimate the source position, but it generates spurious solutions in most cases. The Euler normal equations matrix is easy to become singular, which is a main cause for generating unreliable solution. Hence, we use the damped square method to obtain solutions. Previous research shows that the distance between the sliding window center and the source position is approximately correlated negatively with the stability of the normal equations matrix. We make a further research about that and propose a new method based on damping variation to select best Euler solutions. In our method, a set of damping factors ([0, df]) is used and the Euler solution which changes slightly is considered to be reliable. If the Euler solution is not sensitive to small variations in damping factor, the normal equations matrix is stable and the window is in the neighborhood of the highest values of the anomaly, but if small variations have great influence on the solution, the normal equations matrix is unstable and the window is at the anomaly borders. The damping factor df could be chosen from the eigenvalue of the normal equations matrix in all sliding windows. Our method is applied to synthetic and real data. And the results indicate that it could drastically reduce large numbers of invalid solutions.