Application of Helbig integrals to magnetic gradient tensor multi-target detection

•We extended the magnetic gradient tensor Helbig integrals (MGTHI) from the classical Helbig integrals (HI), so that the advantages of the magnetic gradient tensor (MGT) can be applied to the method.•The two-dimensional trapezoidal rule method can be used to estimate the MGTHI well, and help to find the total magnetization direction and horizontal positions of multiple targets.•The invariant-improved tilt angles can well identify the distribution area and number of multiple targets, and further improve the positioning accuracy.•Magnitude magnetic anomalies and their transformation variables are used to estimate buried depths and magnetic moment magnitude of multi-target objects.