relative-error (the difference/the magnitude magnetic anomaly) reach 10% with spherical model. They suggest projection anomaly is not credible especially as high-precision of quantitative processing and interpretation are required and propose a method using the error yielded by the projection anomaly. Coleman and Li 29 studied the difference between the errors of the total-field anomaly and magnetic amplitude data and found that the errors in the three orthogonal components converted from the total-field anomaly had similar standard deviations. Based on the total magnetic anomaly is no longer approximately equal to projection anomaly in the highly magnetic environments, Sun et al. 30 used the information from the borehole data and structural orientation as constraints and get an acceptable result. In our study, we define the error between projection anomaly and observed modulus difference anomaly firstly and carefully discuss the error caused by amplitude, inclination and declination individually and together between the projection anomaly results (data processing, inversion and interpretation) with those of the modulus difference anomaly for strong magnetic anomalies. Second, we propose directly inverting for the modulus difference anomaly in strong magnetic bodies under Cartesian coordinate. Third, the operator, given by modulus difference anomaly, is nonlinear which is different with projection anomaly. Finally, the synthetic and field data are used to test the inversion method with two types of total field data.