Noise suppression is significant for magnetotelluric (MT) data analysis, especially in the face of strong human electromagnetic interference. Variational mode decomposition (VMD) is a novel signal ...processing method, and the selection of proper decomposition layers plays a key role in its signal processing effects. In view of the fact that detrended fluctuation analysis (DFA) is an evaluation criterion capable of selecting the appropriate number of sub-signals, we propose a noise suppression method for MT by combing VMD with DFA. We firstly estimate the scaling exponent range of MT noisy data and decompose it into a given series of K-order intrinsic mode functions (IMFs). Then, a criterion based on DFA is designed to select the mode number K with the purpose to improve the decomposition accuracy of VMD. The scaling exponent of DFA is used to define the relevant modes for the construction of filtered signals. In this research, the MT data is collected from Qinghai test site and added with strong interference for comprehensive analysis by the remote reference method, VMD method, and the proposed VMD-DFA method. The results have shown that the proposed method could greatly improve the accuracy of signal decomposition and the reliability of the reconstructed signal by adaptively selecting suitable K-order IMFs for different types of interference. Consequently, strong interference is effectively eliminated, and the obtained apparent resistivity-phase curve is stable and smooth. Moreover, the denoised MT data will further strengthen the interpretability of geoelectric information.
•Noise suppression is significant for magnetotelluric (MT) data analysis.•We combine VMD and DFA to suppress magnetotelluric noise.•The method can improve the quality of magnetotelluric data in strong interference area.
Radar backscattering from human objects is subject to micro-Doppler modulations because of their flexible body articulations and complicated movement patterns, which can help identify the interested ...targets and provide valuable information about their motion dynamics. In this paper, a novel theoretical method to extract target micro-Doppler trajectories from continuous-wave radar echo is proposed with a united application of a modified high-order ambiguity function and an adaptive denoising technology. Through this method, multiple components corresponding to different target scattering parts and their micro-Doppler trajectories can be accurately extracted and estimated even in a time-varying low signal-to-noise ratio environment. Finally, a series of simulations is conducted to illustrate the validity and performance of the proposed techniques.
SUMMARY
To effectively and efficiently interpret or invert controlled-source electromagnetic (CSEM) data which are recorded in areas with the kind of complex geological environments and arbitrary ...topography that are typical, 3-D CSEM forward modelling software that can quickly solve large-scale problems, provide accurate electromagnetic responses for complex geo-electrical models and can be easily incorporated into inversion algorithms are required. We have developed a parallel goal-oriented adaptive mesh refinement finite-element approach for frequency-domain 3-D CSEM forward modelling with hierarchical tetrahedral grids that can offer accurate electromagnetic responses for large-scale complex models and that can efficiently serve for inversion. The approach uses the goal-oriented adaptive vector finite element method to solve the total electric field vector equation. The geo-electrical model is discretized by unstructured tetrahedral grids which can deal with complex underground geological models with arbitrary surface topography. Different from previous adaptive finite element software working on unstructured tetrahedral grids, we have utilized a novel mesh refinement technique named the longest edge bisection method to generate hierarchically refined grids. As the refined grids are nested into the coarse grids, the refinement technique can precisely map the electrical parameters of inversion grids onto the forward modelling grids so that the extra numerical errors generated by the inconsistency of electrical parameters between inversion grids and forward modelling grids are eliminated. In addition, we use the parallel domain-decomposition technique to further accelerate the computations, and the flexible generalized minimum residual solver (FGMRES) with an auxiliary Maxwell solver pre-conditioner to solve the final large-scale system of linear equations. In the end, we validate the performance of the proposed scheme using two synthetic models and one realistic model. We demonstrate that accurate electromagnetic fields can be obtained by comparison with the analytic solutions and that the code is highly scalable for large-scale problems with millions or even hundreds of millions of unknowns. For the synthetic 3-D model and the realistic model with complex geometry, our solutions match well with the results calculated by an existing 3-D CSEM forward modelling code. Both synthetic and realistic examples demonstrate that our newly developed code is an effective, efficient forward modelling engine for interpreting CSEM field data acquired in areas of complex geology and topography.
SUMMARY
Joint inversion of magnetotelluric (MT) and geomagnetic depth sounding (GDS) responses can constrain the crustal and mantle conductivity structures. Previous studies typically use either ...deterministic inversion algorithms that provide limited information on model uncertainties or using stochastic inversion algorithms with a predetermined number of layers that is generally not known a priori. Here, we present a new open-source Bayesian framework for the joint inversion of MT and GDS responses to probe 1D layered Earth’s conductivity structures. Within this framework, model uncertainties can be accurately estimated by generating numerous models that fit the observed data. A trans-dimensional Markov Chain Monte Carlo (MCMC) method is employed to self-parametrize the model parameters, where the number of layers is treated as an inversion parameter that is determined automatically by the data. This adaptability can overcome the under or over-parametrization problem and may be able to automatically detect the conductivity discontinuities in the Earth’s interior. To accelerate the computations, a large number of Markov chains with different initial states can be run simultaneously using the MPI parallel technique. Synthetic data sets are used to validate the feasibility of our method and illustrate how separate and joint inversions, as well as various priors affect the posterior model distributions. The trans-dimensional MCMC algorithm is then applied to jointly invert the MT and GDS responses estimated at the Tucson geomagnetic observatory, North America. Our results not only contain model uncertainty estimates but also indicate two distinct conductivity discontinuities at around 85 and 440 km, which are likely related to the lithosphere-asthenosphere boundary and the upper interface of the mantle transition zone, respectively.
During the last 15 years, more attention has been paid to derive analytic formulae for the gravitational potential and field of polyhedral mass bodies with complicated polynomial density contrasts, ...because such formulae can be more suitable to approximate the true mass density variations of the earth (e.g., sedimentary basins and bedrock topography) than methods that use finer volume discretization and constant density contrasts. In this study, we derive analytic formulae for gravity anomalies of arbitrary polyhedral bodies with complicated polynomial density contrasts in 3D space. The anomalous mass density is allowed to vary in both horizontal and vertical directions in a polynomial form of
λ
=
a
x
m
+
b
y
n
+
c
z
t
, where
m
,
n
,
t
are nonnegative integers and
a
,
b
,
c
are coefficients of mass density. First, the singular volume integrals of the gravity anomalies are transformed to regular or weakly singular surface integrals over each polygon of the polyhedral body. Then, in terms of the derived singularity-free analytic formulae of these surface integrals, singularity-free analytic formulae for gravity anomalies of arbitrary polyhedral bodies with horizontal and vertical polynomial density contrasts are obtained. For an arbitrary polyhedron, we successfully derived analytic formulae of the gravity potential and the gravity field in the case of
m
≤
1
,
n
≤
1
,
t
≤
1
, and an analytic formula of the gravity potential in the case of
m
=
n
=
t
=
2
. For a rectangular prism, we derive an analytic formula of the gravity potential for
m
≤
3
,
n
≤
3
and
t
≤
3
and closed forms of the gravity field are presented for
m
≤
1
,
n
≤
1
and
t
≤
4
. Besides generalizing previously published closed-form solutions for cases of constant and linear mass density contrasts to higher polynomial order, to our best knowledge, this is the first time that closed-form solutions are presented for the gravitational potential of a general polyhedral body with quadratic density contrast in all spatial directions and for the vertical gravitational field of a prismatic body with quartic density contrast along the vertical direction. To verify our new analytic formulae, a prismatic model with depth-dependent polynomial density contrast and a polyhedral body in the form of a triangular prism with constant contrast are tested. Excellent agreements between results of published analytic formulae and our results are achieved. Our new analytic formulae are useful tools to compute gravity anomalies of complicated mass density contrasts in the earth, when the observation sites are close to the surface or within mass bodies.
The magnetotelluric (MT) method is a mainstream geophysical exploration method widely used in deep mineral resource exploration and other fields. However, the MT signal is extremely vulnerable to ...noise since it employs natural electromagnetic fields as a source. In order to improve the signal-to-noise ratio, a novel MT noise suppression method based on impulsive atoms and a niche particle swarm optimization-orthogonal matching pursuit (NPSO-OMP) algorithm is proposed. First, an over-complete dictionary composed of impulsive atoms is well-developed to match different types of cultural noise. Then, the sparse decomposition process of OMP is optimized with NPSO. Finally, the original MT data are de-noised using the well-developed dictionary and the NPSO-OMP algorithm. By processing the synthetic and measured MT data, and comparing the experimental results with those by traditional methods, we found that the proposed method can effectively suppress the high-intensity impulsive noise in the MT signal under the premise of retaining useful information. The continuity of apparent resistivity and the phase curve are significantly improved, and the results are verified by the remote reference method and robust statistic estimation. When the observation data are subjected to persistent, strongly correlated noise pollution, our method can obtain better results than the remote reference method and robust statistic estimation. Thus, when it is difficult to obtain high-quality MT response curves through the remote reference method and robust statistic estimation, our method is a promising alternative.
Magnetotelluric (MT) method is widely used for revealing deep electrical structure. However, natural MT signals are susceptible to cultural noises. In particular, the existing data-processing methods ...usually fail to work when MT data are contaminated by persistent or coherent noises. To improve the quality of MT data collected with strong ambient noises, we propose a novel time-series editing method based on the improved shift-invariant sparse coding (ISISC), a data-driven machine learning algorithm. First, a redundant dictionary is learned autonomously from the raw MT data. Second, cultural noises are reconstructed using the learned dictionary and the orthogonal matching pursuit (OMP) algorithm. Finally, the de-noised MT data are obtained by subtracting the reconstructed cultural noises from the raw MT data. The synthetic data, field experimental data and measured data are tested to verify the effectiveness of the newly proposed method. The results show that our new scheme can effectively remove strong cultural noises and has better adaptability and efficiency than the predefined dictionary-based methods. The method can be used as an alternative when a remote reference station is not available.
In this study, we developed a novel 18-layers residual full convolutional neural network (18RFCN) for audio magnetotellurics (AMT) data inversion. Different from traditional inversion methods, the ...18RFCN-based inversion algorithm is based on big-data training rather than prior-information assumptions, and the prediction is almost no time-consuming after network training. The problem of gradient disappearance was solved by adding shortcut connections when training deep neural networks, and we proposed two novel methods to quickly generate millions of samples for network training to improve the network generalization. We first tested on four synthetic data sets with Gaussian noises, which are entirely different from the data of sample sets, and the inversion results showed that the deep learning algorithm could accurately recover the underground conductivity structure almost no time-consuming compared to the Gauss Newton (GN) algorithm. We further tested the inversion algorithm on a field AMT data set acquired in Qinghai province, China. The inversion results of the deep learning algorithm agree well with the GN algorithm and the drilling data.
•A new Convolutional Network for audio magnetotelluric inversion is presented.•Residual method is adopted to solve the problem of gradient disappearance.•A new method is adopted to generate 3 million samples for network training.•The trained network can get reliable conductivity model with no time-consuming.
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