Quantitative evaluation of modeling error in Lg-wave attenuation model

In this study, we performed comprehensive statistical studies for the characteristics of the modeling error in Lg-wave attenuation model and obtained a two-dimensional crustal Lg-wave attenuation model. The amplitudes of Lg-wave can be strongly influenced by the geometrical spreading function and it is essential to reasonably evaluate the error of the inversion process if we use the inverted method under the meaning of least squares. Based on the modeling error samples collected in the Sichuan-Yunnan region and its adjacent areas, we use three statistical test methods, namely the K-S test, the Q-Q plot, and the normal distribution plot, to analyze the distribution characteristics of modeling errors in the input data of Lg- wave attenuation tomography inversion. We used both the SVD-based tomographic method and the back-projection method to invert for the Lg Q model of the Sichuan-Yunnan region and its adjacent area respectively. Then, we calculated the covariance matrix and the resolution matrix of the model and evaluated the resolution and error of each grid point in the Lg Q model quantitatively. Our results indicate that the modeling errors in the input data obeyed a normal distribution under first-order approximation. By using the data screening technique, we generated a new dataset with nearly perfect normally distributed for Q tomography. Compared with the result of back-projection, the SVD-based method could allow for obtaining a finer resolution of crustal Q value in the areas with dense ray path coverages, where the model resolution can be resolved within a range of 100 km with a relative error of less than 3%.