Downward continuation can enhance small‐scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability. We derive the mean‐value theorem for potential fields, which could be the theoretical basis of some data processing and interpretation. Based on numerical solutions of the mean‐value theorem, we present the convergent and stable downward continuation methods by using the first‐order vertical derivatives and their upward continuation. By applying one of our methods to both the synthetic and real cases, we show that our method is stable, convergent and accurate. Meanwhile, compared with the fast Fourier transform Taylor series method and the integrated second vertical derivative Taylor series method, our process has very little boundary effect and is still stable in noise. We find that the characters of the fading anomalies emerge properly in our downward continuation with respect to the original fields at the lower heights.

Qiongheba is a polymetallic ore concentration area located in the east margin of the Junggar Basin in Xinjiang, Northwest China. Because all three main types of metal deposits (porphyry-type copper, skarn-type iron-copper, and structural altered rock-type gold deposits) in this area are controlled strictly by fault structures and intrusions buried under the Quaternary sediments, the detection of concealed faults and intrusions is of great significance for mineral prospecting. We aim to make clear the faults and intrusions based on the high-precision gravity and magnetic data set. First, multiscale edge detection of gravity and magnetic data is used to distinguish and divide the faults system. Second, 3D recognition of concealed intrusions combining with 3D inversion and multiscale edge detection of gravity and magnetic is carried out to construct the 3D formation of concealed intrusions. Last, seven prospecting targets are proposed based on our research and existed regional geologic and geochemical information, and two of them have been confirmed to be rich in polymetal (Cu-Fe-Mo-Au in the Layikeleke deposit and Cu in the Baxi deposit) by drilling. Our research results not only proved the effectiveness of the combination method of 3D inversion and multiscale edge detection of gravity and magnetic data in the prospecting of concealed faults and intrusions, but they also provide abundant information for mineral exploration prediction in the Qiongheba area.

Elastic-wave migration in anisotropic media is a vital challenge, particularly for areas with irregular topography. Gaussian-beam migration (GBM) is an accurate and flexible depth migration technique, which is adaptable for imaging complex surface areas. It retains the dynamic features of the wavefield and overcomes the multivalued traveltimes and caustic problems of Kirchhoff migration. We have extended the GBM method to work for 2D anisotropic multicomponent migration under complex surface conditions. We use Gaussian beams to calculate the wavefield from irregular topography, and we use two schemes to derive the down-continued recorded wavefields. One is based on the local slant stack as in classic GBM, in which the PP- and PS-wave seismic records within the local region are directly decomposed into local plane-wave components from irregular topography. The other scheme does not perform the local slant stack. The Green’s function is calculated with a Gaussian beam summation emitted from the receiver point at the irregular surface. Using the crosscorrelation imaging condition and combining with the 2D anisotropic ray-tracing algorithm, we develop two 2D anisotropic multicomponent Gaussian-beam prestack depth migration (GB-PSDM) methods, i.e., using the slant stack and nonslant stack, for irregular topography. Numerical tests demonstrate that our anisotropic multicomponent GB-PSDM can accurately image subsurface structures under complex topography conditions.