We present three analyses that explore the behavior of the Cramer–Rao lower bounds (CRBs) on estimating a target’s relaxation frequency response from frequency-domain electromagnetic induction (EMI) data. In the first analysis, we show that the CRB on a given relaxation frequency is independent of the amplitudes of the other relaxations present in the target’s relaxation frequency response. In the second, we show that the presence of a second relaxation frequency closer than one decade in frequency greatly increases the CRB on that relaxation frequency. Finally, we illustrate the behavior of the minimum root-mean-square error (RMSE) per relaxation frequency as a function of the number of relaxation frequencies present in the target’s relaxation frequency response.

We derive the Cramer–Rao lower bounds (CRBs) for all target parameters associated with noisy measurements of a specific class of targets using a frequency-domain electromagnetic induction (EMI) system. The target parameters include the target tensors, the relaxation frequencies and their corresponding amplitudes, as well as the target location. We validate the derivation through Monte Carlo simulation. We then derive approximate CRB (ACRB) expressions based on a new low-rank model perspective for EMI data. These approximate expressions are significant simplifications over the full CRB expressions. They also facilitate the analysis and improve the understanding of the factors impacting the lower bounds on the target parameters. We demonstrate the utility and accuracy of the ACRB expressions for two example targets.

In the presence of background noise, arrival times picked from a surface microseismic data set usually include a number of false picks that can lead to uncertainty in location estimation. To eliminate false picks and improve the accuracy of location estimates, we develop an association algorithm termed RANSAC-based Arrival Time Event Clustering (RATEC) that clusters picked arrival times into event groups based on random sampling and fitting moveout curves that approximate hyperbolas. Arrival times far from the fitted hyperbolas are classified as false picks and removed from the data set prior to location estimation. Simulations of synthetic data for a 1-D linear array show that RATEC is robust under different noise conditions and generally applicable to various types of subsurface structures. By generalizing the underlying moveout model, RATEC is extended to the case of a 2-D surface monitoring array. The effectiveness of event location for the 2-D case is demonstrated using a data set collected by the 5200-element dense Long Beach array. The obtained results suggest that RATEC is effective in removing false picks and hence can be used for phase association before location estimates.

This work develops a model-based compression scheme for seismic data. First, seismic traces are modeled as multitone sinusoidal waves superposition. Each sinusoidal wave is regarded as a model component and is represented by a set of distinct parameters. Second, a parameter estimation algorithm for this model is proposed accordingly. In this algorithm, the parameters are estimated for each component sequentially. A suitable number of model components is determined by the level of the residuals energy. Next, the residuals are compressed using entropy coding or quantization coding techniques. The corresponding compression ratios are presented. Finally, the proposed model-based compression scheme is compared with the linear predictive coding (LPC) algorithm and the distributed principal component analysis (DPCA) algorithm on a real seismic database. The performance of the proposed model based is shown to be superior to that of the LPC and DPCA.

Although most topics in Digital Signal Processing (DSP) are highly mathematical, most experts possess knowledge of these concepts that is primarily graphical. Therefore, we have developed a variety of multimedia adjuncts for use in an introductory signal processing course at Georgia Tech to teach abstract concepts. These same multimedia tools are also valuable in senior-level and graduate DSP courses. Among the available resources are animations, demonstrations MATLAB GUIs that address nearly every major conceptual issue in a basic DSP course.

In this paper, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with two steps: first, wavelet estimation across all channels and second, refinement of the reflectivity estimate simultaneously in all channels using sparse deconvolution. The reflectivity update step is formulated as a basis pursuit denoising problem and a sparse solution is obtained with the spectral projected-gradient algorithm-faithfulness to the recorded traces is constrained by the measured noise level. Wavelet re-estimation has a closed form solution when performed in the frequency domain by finding the minimum energy wavelet common to all channels. Nothing is assumed known about the wavelet apart from its time duration. In tests with both synthetic and real data, the method yields sparse reflectivity series and stable wavelet estimates results compared to existing methods with significantly less computational effort.

We derive the Cramer-Rao lower bound (CRB) for target tensor amplitudes and target location parameters that can he estimated from electromagnetic induction (EMI) measurements of a target. In deriving the bound, no restrictions are placed on the target type, target orientation, quantity, or location of the measurement positions, nor the geometry of the EMI sensor or sensor array. The analysis is applicable to both a scanned sensor and a stationary array, as well as both time-and frequency-domain sensors. We show how the hound varies as a function of target type, orientation, depth, and signal-to-noise ratio. In addition, we illustrate the ways to use the CRB and the Fisher information matrix to analyze the relationships between the tensor amplitudes and location parameters. We show results of the CRB analysis applied to an experimental frequency-domain Georgia Tech sensor for a few target types for a nominal 2-D scan geometry as well as the Time-domain Electromagnetic Multi-sensor Towed Array Detection System. We also provide an algorithm for estimating the target location and tensor that achieves the CRB.

We address the problem of search-free DOA estimation from a single noisy snapshot for sensor arrays of arbitrary geometry, by extending a method of gridless super-resolution beamforming to arbitrary arrays with noisy measurements. The primal atomic norm minimization problem is converted to a dual problem in which the periodic dual function is represented with a trigonometric polynomial using truncated Fourier series. The number of terms required for accurate representation depends linearly on the distance of the farthest sensor from a reference. The dual problem is then expressed as a semidefinite program and solved in polynomial time. DOA estimates are obtained via polynomial rooting followed by a LASSO based approach to remove extraneous roots arising in root finding from noisy data, and then source amplitudes are recovered by least squares. Simulations using circular and random planar arrays show high resolution DOA estimation in white and colored noise scenarios.

A method for classifying targets using a low-rank representation of broadband electromagnetic induction data is presented. The method does not require position data, a sensor model, or a complex inversion so it is applicable to hand-held EMI systems or a simple vehicle based system. The low-rank representation is very straightforward to compute and does not require position significant computational resources. The method will be shown for data from a cart-based Georgia Tech EMI sensor that operates in the frequency domain and collects data at 15 logarithmically spaced frequencies from 1 kHz to 90 kHz. The data for several will be presented in the low-rank form to show that they are consistent within a target type and distinct for different targets. An example using the low-rank data to classify targets will be presented.

The increasing volume of seismic data from long-term continuous monitoring motivates the development of algorithms based on convolutional neural network (CNN) for faster and more reliable phase detection and picking. However, many less studied regions lack a significant amount of labeled events needed for traditional CNN approaches. In this paper, we present a CNN-based Phase-Identification Classifier (CPIC) designed for phase detection and picking on small to medium sized training datasets. When trained on 30,146 labeled phases and applied to one-month of continuous recordings during the aftershock sequences of the 2008 M-W 7.9 Wenchuan Earthquake in Sichuan, China, CPIC detects 97.5% of the manually picked phases in the standard catalog and predicts their arrival times with a five-times improvement over the ObsPy AR picker. In addition, unlike other CNN-based approaches that require millions of training samples, when the off-line training set size of CPIC is reduced to only a few thousand training samples the accuracy stays above 95%. The deployment of CPIC takes less than 12h to pick arrivals in 31-day recordings on 14 stations. In addition to the catalog phases manually picked by analysts, CPIC finds more phases for existing events and new events missed in the catalog. Among those additional detections, some are confirmed by a matched filter method while others require further investigation. Finally, when tested on a small dataset from a different region (Oklahoma, US), CPIC achieves 97% accuracy after fine tuning only the fully connected layer of the model. This result suggests that the CPIC developed in this study can be used to identify and pick P/S arrivals in other regions with no or minimum labeled phases.

Direction of Arrival (DOA) estimation using 1-bit analog-to-digital converters (ADCs) offers significant cost, power, and hardware complexity reduction for sensor arrays. We propose a 1-bit sparse super-resolution DOA method for coprime arrays to achieve search-free DOA estimation, under the assumption of uncorrelated sources. The approach extends gridless DOA estimation for coprime arrays based on sparse super-resolution (SR) theory to 1-bit measurements. Using the arcsine law, a scaled version of the full precision covariance matrix can be recovered from the 1-bit data. The vectorized covariance matrix becomes the effective measurements from the coprime virtual array, and then the DOA estimation problem is expressed as an infinite-dimensional atomic norm minimization problem in the continuous angle domain. The corresponding dual problem is converted to a finite semidefinite program with linear matrix inequality constraints, that is solvable in polynomial time. Finally, the search-free DOA estimates are obtained using the unit-circle zeros of a nonnegative polynomial formed from the dual polynomial, followed by an ℓ 1 norm minimization. The angular resolution and accuracy of the proposed method is compared to state-of-the-art approaches such as 1-bit and full-precision versions of spatially smoothed MUSIC and a discrete offgrid method, as well as the full-precision gridless SR method.

Machine learning algorithms have become a powerful tool in different areas of seismology, such as phase picking/earthquake detection, earthquake early warning and focal mechanism determination. Previously convolutional neural networks (CNN) have been applied to continuous seismic waveform recordings to perform efficient phase picking and event detection with good accuracy [Zhu et al., 2018]. However, the off-line training of current CNN requires at least a few thousands of accurately picked seismic phases, which makes it difficult to be applied to regions without sufficient picked phases. In this work, we will validate the transfer learning among different geographic regions. Our tests show that the phase picker trained on manually-labeled data acquired from Sichuan, China following the 2008 M7.9 Wenchuan earthquake [Zhu et al., 2018] works equally well on the continuous waveform acquired from Oklahoma, US [Zhu et al., 2018]. Specifically, using the CNN trained on the Wenchuan dataset, together with 895 local/regional catalog events recorded in central Oklahoma, we refine part of the networks to pick the arrival times of the local seismicity in Oklahoma. The refined CNN results are compatible with the matched filter results using the same catalog events as templates. Our next step is to extend our test to waveforms from different tectonic regions to demonstrate the generality of CNN-based phase picker. We plan to further use a New Zealand seismic dataset that includes more than 20 GeoNet stations in the North Island, where the matched-filter detected results are available to be compared with (Yao et al., 2018). Alternatively dataset include a subset of events in the waveform relocated catalog in Southern California. Updated results will be presented at the meeting.

Teaching is increasingly migrating to digital platforms, where relevant content can be quickly accessed and explored in small chunks within the appropriate context. A variety of on-line systems have been developed to cater to educational experience that is predominantly digital, contextually accurate, and personalized to learner's conceptual understanding and needs. In this paper, we provide an update on our continuing efforts at Georgia Tech to transform an undergraduate signal processing course into a data-mining teaching environment that structures student learning through concept driven content and personalized programmed instruction.

This work develops a multi tone modeling for seismic data compression. First, seismic traces are described as multitone decaying sinusoidal waves superposition. Each sinusoidal wave is regarded as a model component and is represented by a set of distinct parameters. Secondly, a novel parameter estimation algorithm for this model is proposed accordingly. In this algorithm, the parameters are estimated for each component sequentially. A suitable number of model components is determined by the level of the residuals energy. The proposed model-based compression scheme outperforms the Linear Predictive Coding (LPC) both analytically and experimentally in terms of compression ratio, reconstruction quality and convergence rate. Presentation Date: Wednesday, September 18, 2019 Session Start Time: 9:20 AM Presentation Time: 11:00 AM Location: Poster Station 11 Presentation Type: Poster

In this paper, we derive the Cramer-Rao Lower Bound (CRLB) for the unknown tensor amplitudes and target location parameters that can be estimated from electromagnetic induction (EMI) measurements of a target. In deriving the bound, no restrictions are placed on the target type, target orientation, measurement geometry, or the geometry of the electromagnetic induction sensor or sensor array. The analysis is applicable to both a scanned sensor and a stationary array. In doing so, we illustrate ways to use the CRLB to analyze the relationships between parameters and parameter sets. We then apply the analysis to an experimental Georgia Tech EMI sensor for a nominal 2-D scan geometry. We also identify additional considerations in designing EMI sensors and acquisition setups.

Current development of unconventional resources (such as shale gas, shale oil, and tight sands) requires hydraulic fracturing, which involves injecting fluid at high pressure into the subsurface reservoir. Such injections (or fluid production) cause stress changes in the reservoir. These stress changes often result in failure of the rocks with a concurrent release of seismic energy as seismic waves. The nature of seismic wave propagation in the subsurface media is complex. Based on the direction of propagation and the particle motion, body waves can be classified into P-waves (primary, compressional wave) and S-waves (secondary, shear wave). Passive seismic monitoring is based on recording these emitted waves and then using signal processing to extract characteristics such as amplitude, polarity, and arrival time, from which it is then feasible to estimate the location and character of the failure events.

Recent work with Wideband Electromagnetic Induction (WEMI) sensors has shown that a low-rank model can be used to exploit the measurements. The low-rank model has led to a new fi lterless processing framework for frequency-domain WEMI sensors, where projection operators can be used in both the frequency and spatial dimensions of the data. Previous work has used a single subspace from the projected measurements to perform target detection, classi fi cation, and localization. This work investigates the eight remaining measurement subspaces created by the projection operators and how they can be exploited to extract more information for WEMI processing.

Reliable detection and recovery of a microseismic event in large volume of passive monitoring data is usually a challenging task due to the low signal-to-noise ratio environment. The accuracy of weak microseismic event identification is a very important step in the analysis and interpretation of microseismic data. This paper introduces an approach for detecting (presence indication) and denoising (accurate recovery) microseismic events using tensor decomposition by considering the time-frequency representation of multiple traces as a 3-D tensor. A tensor is a multiway array having dimension greater than two, and recent signal processing techniques have been developed to manipulate such data by taking advantage of the multidimensional structure. With advances in technology and the availability of cheap memory, it is now possible to store and do mathematical operations, such as higher order singular-value decomposition or tensor decomposition, on multiway data. In active seismic, tensor decomposition has been used for multidimensional reconstruction via higher order interpolation to obtain missing observations. In this paper, we use 3-D tensor decomposition to process passive seismic data. Experiments performed on synthetic and field data sets show promising results achieved by these new methods.