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Additional file 1: Table S1. Description of Cis-elements.

Gravity and magnetic measurement data often contain gaps and significant noise interference and must therefore be interpolated and border-padded prior to processing and transformation in the wavenumber domain. The primary cause of much processing and transformation instability is high-frequency noise interference. Conventional processing methods generally perform interpolation, border-padding, and denoising independently; in this study, we apply a unified approach to implement these three tasks and propose an iterative method for applying them based on the projection onto a convex sets method. The proposed iterative method first fills the vacancies and border of the original potential field data with zeros and determines a final cutoff wavenumber for the iteration by applying fractal model fits of the radial average power spectrum of the zero-padding data. The iteration steps are then performed by applying a simple ideal low-pass filter in the wavenumber domain until the predetermined iteration number is attained. Numerical examples involving synthetic gravity and real aeromagnetic data demonstrate that the proposed iterative method is simple in principle, easy to carry out, and has a high interpolation and denoising accuracy with smooth and distortion-free interfaces between the interpolation and border-padding results. The proposed method has evident advantages in terms of precision and speed relative to classical interpolation-based border padding, denoising, and combined methods.

There are many unstable linear transformations in the processing and interpretation of potential field data, such as, derivatives, reduction to the pole at low latitudes, and downward continuation. They all have the tendency to amplify the noise content in the original data. By means of the Wiener filter theory it is possible to derive optimum transformation filters for these processing technologies in the wavenumber domain. However, the realization of these optimum filters is difficult because they need to know the noise-to-signal power ratio. In this paper, we use iterative Wiener filter (IWF) to solve this problem. First, a noise variance estimation method is proposed based on the annular averaged power spectrum of potential field data. Then, we use the discrepancy principle to choose the regularization parameter for the regularized filter which is an approximation of Wiener filter. After that, the regularized transformation result is used as the initial value of IWF algorithm. Finally, a correction term is used to update the power spectrum estimation of the desired potential field data. Synthetic and field examples show that the proposed IWF algorithm yields better transformation results than the regularized method and has a stable convergence.

Downward continuation of potential field data plays an important role in interpretation of gravity and magnetic data. For its inherent instability, many methods have been presented to downward continue stably and precisely. In this manuscript, we propose an improved regularization operator for downward continuation of potential field data. First, we simply define a special wavenumber named the cutoff wavenumber to divide the potential field spectrum into the signal part and the noise part based on the radially averaged power spectrum of potential field data. Next, we use the conventional downward continuation operator to downward continue the signal and the Tikhonov regularization operator to suppress the noise. Moreover, the parameters of the improved operator are defined by the cutoff wavenumber which has an obvious physical significance. The improved operator can not only eliminate the influence of the high-wavenumber noise but also avoid the attenuation of the signal. Experiments through synthetic gravity and real aeromagnetic data show that the downward continuation precision of the proposed operator is higher than the Tikhonov regularization operator.

We have developed an improved adaptive iterative method based on the nonstationary iterative Tikhonov regularization method for performing a downward continuation of the potential-field data from a horizontal plane. Our method uses the Tikhonov regularization result as initial value and has an incremental geometric choice of the regularization parameter. We compared our method with previous methods (Tikhonov regularization, Landweber iteration, and integral-iteration method). The downward-continuation performance of these methods in spatial and wavenumber domains were compared with the aspects of their iterative schemes, filter functions, and downward-continuation operators. Applications to synthetic gravity and real aeromagnetic data showed that our iterative method yields a better downward continuation of the data than other methods. Our method shows fast computation times and a stable convergence. In addition, the [Formula: see text]-curve criterion for choosing the regularization parameter is expressed here in the wavenumber domain and used to speed up computations and to adapt the wavenumber-domain iterative method.

The work described herein discusses the application of generalized cross-correlation method to time delay estimation of infrasound signal. At present, the basic cross-correlation technique is mainly used to the time delay estimation of infrasound signal. However, the estimation accuracy based on this method is not high. In order to improve the accuracy, the generalized cross-correlation method is applied in this paper. The generalized cross-correlation method can be viewed as applying a weighting or a window function to the cross-power spectrum. An improved window function is given and compared with several other proposed processors of similar form. The result shows that the estimation accuracy by the improved window function is high and the performance is stable under different signal-to-noise ratio.

The variable geomagnetic field contains a variety of components from various sources. It has different variation characteristics at each time scale. In this paper, a method of modeling and forecasting the variable geomagnetic field at multiple time scales is presented. Firstly, we develop a magnetic trend variation model at day scale, a magnetic daily variation model at hour scale, and a short period variation model at minute scale, respectively. Then, we combine each model of different time scale to realize the modeling and forecasting of the variable geomagnetic field. The method combines the physical origin of the variable geomagnetic field and fuses multiple models to obtain both long forecasting time span and high forecasting precision.

Estimation of invariants plays a very important role in the analysis of chaotic time series. However, the length of tune series affects the quality of estimation directly. To estimate these invariants accurately, the length of time series must be very long, especially for the continuous chaotic systems. On the condition of keeping the total observation time-constant, the method of resampling is introduced to the analysis of chaotic time series, experimental results and corresponding analysis indicate that resampling can keep the good quality of original phase space, and reduce the total computation time quickly. This may be an efficient method to calculate the invariants of chaotic system by shortening time series.

Under the condition of the chosen structure of BP neural network, the underlying reason for the good accuracy in training and poor generalization performance in testing of BP network under the under-determined status is analyzed. A new BP network generalization learning algorithm based on suboptimal criterion of fitting error of random assistant samples is presented. Theoretic analysis and simulation results show that the method is practical and feasible.

Based on the attractor analysis approach in phase space, 7 kinds of general features are extracted from the Lorenz model system to compute the infimum of uncorrelated features in number by numerical experiments. This infimum indicates that the least number of features is feasible to classify samples of special target recognition completely. After the infimum is chosen, a new feature selection method - ordinal optimization is introduced and applied to the selection of the least and optimum feature group. Blind picking rule of ordinal optimization is tested in the experiments and the experimental results indicate that ordinal optimization can reduce the size of feature space quickly and efficiently, and is a feasible approach to search the satisfactory subset from huge feature combination space.

In this paper, the origin of feature phase space is presented, the construction method based on various features extracted from Lorenz model system is stated, and the validity of attractor analysis of feature phase space is tested by numerical experiments. Experimental results indicate that attractor analysis approach of feature phase space is an efficient way in pattern recognition, it determines the infimum of uncorrelated features in number, it has great immunity to noise, and it is very suitable to analyze the practical samples with noise and disturb. The practical application in the recognition of underground nuclear explosions from natural earthquakes has proved the validity of attractor analysis of feature phase space.

The article analyzes the chaotic dynamic characteristic of geomagnetic variation field mainly in two aspects: (1) analyzing the chaotic dynamic characteristic of the geomagnetic variation field data observed at the same period (both low geomagnetic disturbance period and high geomagnetic disturbance period) from a series of geomagnetic stations using multiple approaches, in order to get a sufficient proof to validate whether there is chaotic dynamic characteristic in geomagnetic variation field; (2) analyzing the chaotic dynamic characteristic of the geomagnetic variation field data observed at different periods from the same geomagnetic station, aiming at finding out whether there is a parameter-varying chaotic characteristic in the geomagnetic variation field. The results indicate: (1) There is definitely chaotic dynamic characteristic in the geomagnetic variation field time series. (2) In view of chaotic time series phase space reconstruction, the number of independent variables to simulate the geomagnetic variation field dynamical system is about 6. (3) Geomagnetic variation field time series shows not only chaotic dynamic characteristic but also parameter-varying dynamical chaotic characteristic.