The edge depth of geological bodies plays a critical role in the semi-quantitative interpretation of gravity and magnetic field data. Since gravity and magnetic anomalies and their derivatives of all orders satisfy the Euler homogeneous equation, the tilt-Euler method is favored for inversion of edge depth. However, it is found that when the total horizontal derivative or the total gradient mode of gravity or magnetic anomalies is equal to zero, the first-order derivative of the tilt angle cannot be calculated, resulting in the tilt angle cannot satisfy the Euler equation, and the tilt-Euler method cannot be used. In order to solve this problem, based on the regularization idea, we modified the first-order derivative of the tilt angle, so that the first-order derivative of the tilt angle can still be calculated when the total horizontal derivative or the total gradient mode of gravity or magnetic anomalies is equal to zero, and the modified derivatives of the tilt angle still satisfy the Euler equation. We call the improved method the rtilt-Euler method. At the same time, the normalized vertical derivative of the total horizontal derivative (NVDR-THDR) with higher edge recognition accuracy was used to constrain the inversion results and eliminate the bad points deviating from the edge position. The results of the model test show that the improved method eliminates the problems that the tilt angle derivative cannot be calculated and the instability of the inversion restults when the total horizontal derivative or the total gradient mode of gravity or magnetic anomalies is zero or very small.   This method was applied to the edge depth inversion of iron oxide, copper-gold (IOCG) deposit of the Olympic Dam in Australia. The results show that the edge depth of the iron oxide, copper-gold deposit is mainly concentrated in the depth ranges of 0-100 m and 100-200   m, which is consistent with the edge depth of 0-200 m shown by the sedimentary profile, proving the effectiveness of the method.