Joint inversion of gravity and magnetic can directly obtain the underground density and magnetic distribution by synthesizing the characteristics of gravity and magnetic data,and effectively reveal different lithology distribution and underground structure,which is an important means of mineral resources exploration. The actual surface of the earth and the observed surface of the airborne gravity and magnetic survey that fluctuates along the terrain are both undulating. In order to realize the highly efficient joint inversion of the undulating observation surfaces,we have established a fast joint physical inversion method for gravity and magnetic data under the constraints of undulating observation surfaces. Firstly,the data is flattened according to the maximum observed height. Then,Block-Toeplitz-Toeplitz-Block(BTTB)-FFT is used to achieve fast inversion,and the space between the converted observation plane and the actual observation plane is used as a constraint to eliminate the multiple solutions caused by the calculation of invalid grid cells. Therefore,this method can achieve high efficiency inversion without increasing the multiplicity of solutions due to additional partition elements. Model tests show that this method can effectively improve the computational efficiency by more than 32 times without losing the accuracy of inversion calculation,and has good stability for noisy data inversion. Finally,we applied this method to Sankeshu Depression,Tonghua Basin,eastern Jilin Province,China,and obtained the distribution of basement and igneous rocks in this area. The average depth of basin basement in this area is about 2.5 km,and the development of igneous rocks is mainly concentrated in the area with large basement depth,which provides important basic geological information for the next oil and gas exploration.It also provides important guiding significance for oil and gas exploration and deployment in the eastern peripheral new area of Songliao Basin.