## 4 Application to Real Data  
The study area (Figure 15), which straddles three major tectonic units, the Sino-Korean, Yangzi, and South China plates, underwent the consolidated diagenesis and reactivation of the Late Sibao Movement in the Mesoproterozoic Era and of the Jinning Movement in the Neoproterozoic Era, forming a two-layer crystalline basement of Meso-Neoproterozoicoic shallow metamorphic rock and Archean-Paleoproterozoic deep metamorphic rock [30; 31; 32]. Under the influence of the multi-period tectonic movement reformations and the action of various tectonic stresses, the study area has successively experienced tectonic activities of various natures, such as extensional fault depressions, and strike-slip subsidence [33]. It is a marine-continent multi-cycle superimposed petroliferous basin that has been formed based on the pre-Sinian metamorphic basement. Based on the collected density information about the study area [34; 35], vertically, the density decreases gradually from deep to shallow; horizontally, the density of different tectonic units varies. This density difference facilitates our use of gravity data to study the tectonic distribution of the zone. Figure 16 shows the Bouguer gravity map of the region. Figure 14: Time spent in each inversion process. Circles of different colors represent different mesh sizes. Figure 13: Filtered Euler solutions from different algorithms (The base map shows the distribution of magnetic anomalies). (**a**) Finite-difference Euler deconvolution algorithm. (**b**) Our algorithm. (**c**) Euler deconvolution algorithm based on DST. Figure 16: The Bouguer gravity map of the study area. Figure 15: Sketch map of the tectonic location of the northern basin of the south of the Yellow Sea and its adjacent area (modified from Xu [30]). Next, we apply the enhanced total horizontal derivative, improved logistic filter (IL, [36]), and the Euler deconvolution method to the gravity data in this area. The IL is based on the logistic function and the horizontal gradient amplitude and outlines the source horizontal boundaries more clearly and with high accuracy and resolution. Figure 17a is the enhanced total horizontal derivative of the data in Figure 16, and Figure 17b shows the IL. Figure 18 shows the final Euler solutions. Before performing Euler deconvolution, the selected sliding window size is 11 \(\times\) 11 (22 \(\times\) 22 km), and the SI is 1.5. The same distinguishing method is applied to select the results generated by the three Euler algorithms, and the Euler solutions with a small standard error of estimated depth (top 30%) are saved. In Figure 18, the depth of the solution is indicated by the color, so we do not ascribe much accuracy to these depths and prefer to use the descriptors'shallow' and 'deep'. By comparing Figure 18a and Figure 18b, we find that the distribution of Euler solutions generated from finite-difference Euler deconvolution and improved finite-difference Euler deconvolution is different, and our algorithm shows more detail. The depth range in Figure 18a is 0.1-21.9 km, and the depth range in Figure 18b is 0.4-22.8 km. By comparing Figure 18b and Figure 18c, we find that the distribution of Euler solutions generated from our method and DST Euler deconvolution is almost the same, including the estimated depth. By comparing the Euler solutions and the edge detection results, we find that their distribution patterns are very similar (Figure 19). Additionally, this fully demonstrates the effectiveness of our method. The distribution of the Euler soluitons and the peaks of the IL present a good correlation with some faults in the region, which are shown by Xu [32]. Based on the stratigraphic distribution, structural trend, geomorphological characteristics, and distribution of magmatic rocks [33], the Euler solutions (NE (NNE)) are consistent with the regional tectonic trend.