Wavelet filtering of magnetotelluric data

The KRISP-94 magnetotelluric survey of early 1995: first results

SUMMARY The solution of the remote reference method, a frequently used technique in magnetotelluric (MT) data processing, can be viewed as a product of the two-input–multiple-output relationship between the local electromagnetic field and the reference field at a remote station. By applying a robust estimator to the two-input–multiple-output system, one can suppress the influence of outliers in the local magnetic field as well as those in the local electric field based on regression residuals. Therefore, this study develops a new robust remote reference estimator with the aid of robust multivariate linear regression. By applying the robust multivariate regression S-estimator to the multiple-output system, the present work derives a set of equations for robust estimates of the transfer function, noise variances, and the scale of the Mahalanobis distance simultaneously. The noise variances are necessary for the multivariate analysis to normalize the residuals of dependent variables. The Mahalanobis distance, a distance measure for multivariate data, is a commonly used indicator of outliers in multivariate statistics. By updating those robust estimates iteratively, the new robust remote reference estimator seeks the transfer function that minimizes the robust scale estimate of the Mahalanobis distance. The developed estimator can avoid bias in the MT transfer function even if there are significant noises in the reference magnetic field and handle outlying data more robustly than previously proposed robust remote reference estimators. The authors applied the developed method to a synthetic data set and real-world data. The test results demonstrate that the developed method downweights outliers in the local electric and magnetic fields and gives an unbiased transfer function.

Power-line interference is one of the most common noises in magnetotelluric (MT) data. It usually causes distortion at the fundamental frequency and its odd harmonics, and may also affect other frequency bands. Although trap circuits are designed to suppress such noise in most of the modern acquisition devices, strong interferences are still found in MT data, and the power-line interference will fluctuate with the changing of load current. The fixed trap circuits often fail to deal with it. This paper proposes an alternative scheme for power-line interference removal based on frequency-domain sparse decomposition. Firstly, the fast Fourier transform of the acquired MT signal is performed. Subsequently, a redundant dictionary is designed to match with the power-line interference which is insensitive to the useful signal. Power-line interference is separated by using the dictionary and a signal reconstruction algorithm of compressive sensing called improved orthogonal matching pursuit (IOMP). Finally, the frequency domain data are switched back to the time domain by the inverse fast Fourier transform. Simulation experiments and real data examples from Lu-Zong ore district illustrate that this scheme can effectively suppress the power-line interference and significantly improve data quality. Compared with time domain sparse decomposition, this scheme takes less time consumption and acquires better results.

Data processing is one of the essential steps to obtain optimum response function of the Earth’s subsurface. The MT Data processing is based on the Fast Fourier Transform (FFT) algorithm which converts the time series data into its frequency domain counterpart. The FFT combined with statistical algorithm constitute the Robust Processing algorithm which is widely implemented in MT data processing software. The Robust Processing has three variants, i.e. No Weight (NW), Rho Variance (RV), and Ordinary Coherency (OC). The RV and OC options allow for denoising the data but in many cases the Robust Processing still results in not so smooth sounding curve due to strong noise presence during measurement, such that the Crosspower (XPR) analysis must be conducted in the data processing. The XPR analysis is very time consuming step within the data processing. The collaboration of B-Spline algorithm and Qualitative Spectral Analysis in the frequency domain could be of advantages as an alternative for these steps. The technique is started by using the best coherency from the Robust Processing results. In the Qualitative Spectral Analysis one can determine which part of the data based on frequency that is more or less reliable, then the next process invokes B-Spline algorithm for data smoothing. This algorithm would select the best fit of the data trend in the frequency domain. The smooth apparent resistivity and phase sounding curves can be considered as more appropriate to represent the subsurface. This algorithm has been applied to the real MT data from several survey and give satisfactory results.

Wavelet de-noising method is often used in the processing of magnetotelluric (MT) signal, and the wavelet hard and soft threshold de-noising method are the most popular although there is much room for improvement in the threshold function selection and threshold determination. A new adaptive wavelet threshold de-noising method was proposed by selecting a new threshold function and presenting an adaptive method for obtaining optimal threshold based on the multi-resolution Stein unbiased risk estimation. New threshold function and an adaptive method to determine threshold were discussed, and the principle and implementation of the algorithm were given. The simulated signal and the measured MT data contaminated by impulse interference were analyzed, and the obtained results were compared with those of the conventional wavelet hard and soft threshold de-noising methods. The results show that the proposed method overcomes the defects of the traditional wavelet soft and hard threshold due to a new threshold function, and a new method to determine the threshold of each layer is applied and provides an adaptive method for filtering MT data in the wavelet domain that requires a minimum of human intervention. The presented de-noising method is very suitable for suppressing the impulse interference for MT data and can get higher signal-to-noise ratio than the traditional wavelet threshold de-noising methods. After de-noising, the accurate data is loaded for further impedance estimation and geological interpretation.

Comparison of stable maximum likelihood estimator with traditional robust estimator in magnetotelluric impedance estimation

Magnetotelluric data modeling was used for oil and gas exploration. The parameters are apparent resistivity and phase. The magnetotelluric data of this research were line JBS4 with 71 sounding sites and line JBS8 with 66 sounding sites. The magnetotelluric data was completed by remote reference data which used for reducing the noise so that good data could be gotten. The magnetotelluric data was proceed in stage as follow: time series selection, Fourier transform, robust processing, cross power selection, and 2 dimension inversion. The result of this research showed that magnetotelluric method can figured out the sub-surface model well. From the result of interpretation 2D inversion magnetotelluric and other geophysical data (gravity anomaly map), we can conclude that magnetotelluric modeling figured out 2 sub-basins. Those sub basins had thick sediment layer (4000 meter for Bantarkalong Basin and 3000 meter for Citanduy Basin) and the dominant resistivity value was 22-119 Ohm.meter.

The effects of the ocean coast on magnetotelluric (MT) data have been studied and results are described in this article. MT soundings from various sites along coastal plains of Kachchh were acquired where volcanic rocks overlie Mesozoic sediments having potential resource prospects. The region of our study lies in the proximity of Gulf of Kachchh and Arabian Sea. This article describes the effects the presence of a conductive body on the acquired MT data. With the help of synthetic MT modelling and induction arrows we demonstrate the influence of shallow conductive body on the MT data. The modelling results when compared to the field observations show that much of the high frequencies are unaffected by the coast, however low frequencies of the data do seem to be distorted by onshore–offshore resistivity contrasts. The least affect on high frequencies can be attributed to very shallow water depth as well as to the fact that the onshore–offshore resistivity contrasts are not large enough to influence the high frequency data badly. The results presented here report for the first time the effect of the coast on the analysis on MT data from Kachchh. Due to several academic as well as industrial onshore–offshore MT experiments presently being carried out to explore its hydrocarbon potential, our results have an important bearing on designing and acquisition of future MT surveys in this region.

Synthesis of natural electric and magnetic Time series using Interstation transfer functions and time series from a Neighboring site (STIN) is a new approach for recovering natural electric and magnetic fields and reduce the influence of anthropogenic noise. The proposed approach modifies the windows of the local electric and magnetic time series that are affected by noise with time series resulted from modifying the spectra of the magnetic time series from a neighboring site with the interstation transfer functions between the local and neighboring sites. The STIN method was tested with artificially contaminated electric and magnetic time series. Comparison between STIN‐corrected time series and original noncontaminated time series shows high similarity, both in the time and frequency domains. Differences were quantified using the normalized root‐mean‐square error, the correlation coefficient, and the signal‐to‐noise ratio. The STIN method was also applied to two sites affected by unconstrained anthropogenic noise, thus demonstrating the ability and accuracy of STIN in synthesizing natural electric and magnetic fields and reducing the influence of anthropogenic noise. The synthesized time series provided by STIN show the method to be valuable for magnetotelluric (MT) geophysical applications, by increasing the reliability when constrains the MT impedance tensor and by reducing the scatter of data points when the time series are affected by noise, particularly for longer periods. As STIN is based on interstation transfer functions, the electric and magnetic time series can be treated independently, enabling computation of the MT impedance tensor even when the electric and magnetic time series of the local site were recorded at different times.

While much of the workflow for geophysical data processing and analysis is automated, final quality assurance typically requires the decisions of skilled human analysts and interpreters. The quality and reliability of geophysical inverse models depends directly on the effectiveness of input data. The influence of spurious data on derived data products used in the inversion has been reduced by this effectiveness. Failure to identify and mitigate bias in data products can lead to costly errors. By applying supervised machine learning (ML), a neural network can be trained to recognize features in data that a human domain expert would identify as characteristic of poor data quality. In this study, we use magnetotelluric (MT) data as an example of a geophysical data set appropriate for such a training exercise. While MT data are used to estimate the resistivity structure of the subsurface, the concepts we discuss are universal to seismic, potential fields, and other geophysical data sets. We train a neural network, pyMAGIQ (Python-based magnetotelluric impedance qualifier), with multiple hidden layers and demonstrate that it successfully generates the nonlinear mapping function required to assess the quality of MT data. The training set is a large database of frequency-domain MT impedance tensors from the National Science Foundation-funded EarthScope MT project. A human-assigned quality index is associated with each impedance. We apply pyMAGIQ to unrated MT data from the United States and Canada and confirm that the ML-assigned quality factors are consistent with those assigned by trained human operators. We also apply sensitivity analysis to the trained neural network. This reveals that the human- and ML-assigned data quality index depends on the magnitude of the confidence limits on (1) the phases and (2) the continuity of the apparent resistivities and phases with respect to frequency.

SUMMARYSimulation-based probabilistic inversions of 3-D magnetotelluric (MT) data are arguably the best option to deal with the nonlinearity and non-uniqueness of the MT problem. However, the computational cost associated with the modelling of 3-D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT data sets. In this contribution, we present a novel and general inversion framework, driven by Markov Chain Monte Carlo (MCMC) algorithms, which combines (i) an efficient parallel-in-parallel structure to solve the 3-D forward problem, (ii) a reduced order technique to create fast and accurate surrogate models of the forward problem and (iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method. We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parametrizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3-D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.

SUMMARY Magnetotelluric (MT) data inversion seeks to recover resistivity models of the subsurface. Solving the inversion problem is a non-trivial task, as multiple plausible solutions can be recovered due to the nonlinearity of the problem. To reduce this nonlinearity, we propose a data-driven approach where a 1-D cumulative resistance model is estimated from MT data via a direct data transformation. We define the cumulative representation of layered models as the weighted sum of layer thickness divided by resistivity from surface to any depth level, which is the cumulative conductance. Its inverse, cumulative resistance, is directly related to the real part of the impedance computed from MT data. We train a neural network to transform the MT impedance into a resistance model. The corresponding 1-D resistivity model is obtained without a priori information. We validate our approach using synthetic and real data, opening the discussion for future developments of this new perspective.

Inversion is a fundamental step in magnetotelluric (MT) data routine analysis to retrieve a subsurface geoelectrical model that can be used to inform geological interpretations. To reduce the effect of non-uniqueness and local minimum trapping problems and improve calculation speeds, a data-driven mathematical method with a deep neural network was developed to estimate the subsurface resistivity. In this study, a deep learning (DL) inversion technique using a revised multi-head convolutional neural network (CNN) architecture was investigated for MT data analysis. We created synthetic datasets consisting of 100,000 random samples of resistivity layers to train the network’s parameters. The trained model was validated with independent noised datasets, and the predicted results displayed reasonable accuracy and reliability, which demonstrates the potential application of DL inversion for real-world MT data. The trained model was used to analyze MT data collected in the southwestern Athabasca Basin, Canada. The calculated results from the DL method displayed a detailed subsurface resistivity distribution compared to traditional iterative inversion. Since this approach can predict a resistivity model without multiple forward modeling operations after the CNN model is created, this framework is suitable to speed up the computation of multidimensional MT inversion for subsurface resistivity.

Controlled-source audio-frequency Magnetotellurics method (CSAMT) partially overcomes the drawbacks of weak natural field signals. However, substantial interference is an inevitable part of field surveys in practice, which negatively impacts signal quality. We require new denoising techniques since traditional techniques, such as Fourier transformation, which compute apparent resistivity directly from frequency-domain data, are insufficient in our situation. CSAMT denoising research is currently lacking, nevertheless. This research proposes the use of long short-term memory (LSTM) neural networks to denoise CSAMT signals in the time domain, given their good performance in processing Magnetotelluric (MT) data as shown by prior studies. We seek to directly extract the desired frequency signal for denoising from the time series data, in contrast to conventional denoising techniques. Since noise and target frequency signals are mixed together in MT data, the only way to suppress noise is to find the characteristics of the noise in the time series. CSAMT, on the other hand, differs from MT in that it uses an artificial transmitting source and fixes the valid signal frequency within a temporal window. This makes it possible to extract target frequency signals directly without taking into account the intricate properties of noise. In order to complete the noise suppression job, we created a neural network in this study that is based on bidirectional LSTM. This method was able to partially handle the difficulty of denoising when the data's SNR falls below 0 dB and, on average, enhance the signal-to-noise ratio (SNR) of CSAMT data by roughly 20 dB after executing both simulated and measured data testing.

A prominent TE and TM mode split is observed in magnetotelluric (MT) data below 0.5 Hz collected in the Perth Basin over the Harvey Ridge, Western Australia. We investigate the causes of mode splitting and consider implications on inversion of the MT data to subsurface electrical conductivity distribution. Twenty-five broad-band MT stations were acquired and remote reference processing was completed to arrive at a data set located midway between the Darling Fault and the Indian Ocean. We used forward modelling to test our strong suspicion that the Indian Ocean, Darling fault and architecture of the Granitic Basement were indeed the major contributors to mode splitting that we observed. Forward modelling of synthetic data was completed for comparison with the Harvey MT data. We were surprised at the match between synthetic and field data given the simplicity of the forward model and the considerable lateral distance between the MT soundings and the Indian Ocean or Darling fault. We were then able to make significant improvements to the MT inversion outcome by introducing a large scale geo-electrical architecture as the seed model for inversion. Our work demonstrates that large scale geo-electrical contrasts at considerable lateral distance from an MT transect, or the target zone need to be systematically introduced to the inversion if a quality outcome is to be achieved.