# Demodulation of EM Telemetry Data Using Fuzzy Wavelet Neural Network with Logistic Response
###### Abstract  
Data telemetry is a critical element of successful unconventional well drilling operations, involving the transmission of information about the well-surrounding geology to the surface in real-time to serve as the basis for geosteeringering and well planning. However, the data extraction and code recovery (demodulation) process can be a complicated system due to the non-linear and time-varying characteristics of high amplitude surface noise. In this work, a novel model fuzzy wavelet neural network (FWNN) that combines the advantages of the sigmoidal logistic function, fuzzy logic, a neural network, and wavelet transform was established for the prediction of the transmitted signal code from borehole to surface with effluent quality. Moreover, the complete workflow involved the pre-processing of the dataset via an adaptive processing technique before training the network and a logistic response algorithm for acquiring the optimal parameters for the prediction of signal codes. A data reduction and subtractive scheme are employed as a pre-processing technique to better characterize the signals as eight attributes and, ultimately, reduce the computation cost. Furthermore, the frequency-time characteristics of the predicted signal are controlled by selecting an appropriate number of wavelet bases \"N\" and the pre-selected range for \(p_{ij}^{\mathrm{s}}\) to be used prior to the training of the FWNN system. The results, leading to the prediction of the BPSK characteristics, indicate that the pre-selection of the N value and \(p_{ij}^{\mathrm{s}}\) range provides a significantly accurate prediction. We validate its prediction on both synthetic and pseudo-synthetic datasets. The results indicated that the fuzzy wavelet neural network with logistic response had a high operation speed and good quality prediction, and the correspondingly trained model was more advantageous than the traditional backward propagation network in prediction accuracy. The proposed model can be used for analyzing signals with a signal-to-noise ratio lower than \(1\) dB effectively, which plays an important role in the electromagnetic telemetry system. demodulation; EM telemetry; fuzzy wavelet neural network; logistic response +
Footnote †: journal: Medical  
of operation and the exploration depth increases [2]. The current frequency of operation is limited to the extremely low-frequency electromagnetic (ELF-EM) signal range, with values ranging from 10-20 Hz being commonly adopted as the center frequency. Hence, telluric and near-surface noise interference from field operations are of major concern and, therefore, affects decoding accuracy. To solve this challenge, new developments in EM telemetry have been more focused on increasing the telemetry signal strength via improvements in technology and modes of acquisition/acquisition design, with fewer reports on data processing and transmitted signal demodulation. An improvement in current signal processing capability is expected to help with the advancement of the technique by increasing the practical transmission depth, improving the signal-to-noise ratio (SNR), and reducing the error rate. Therefore, working out an effective method of removing the ELF-EM in-band noise has become key to the transmission of electromagnetic telemetry measurement while drilling (EM MWD). Traditionally, designed filtering bandwidth is applied to smooth out-of-band noise [3] but not the in-band noise. Relatively recent techniques with improved characteristics include the method of spectral subtraction applied to the EM MWD noise problem by [PERSON] [2], which addressed the receiver-filtering portion but not the decoder; the harmonic interference elimination algorithm based on parameter estimation [4] by [PERSON] et al., although it fails to filter out in-band noises and meet the real-time decoding requirement; the EM MWD receiver of the neural network algorithm proposed by [PERSON] et al.