Time-domain induced polarization (TDIP) data are often perturbed by undesired electrical and electromagnetic responses, i.e., powerline harmonics, spikes etc., which along with the random noise from the instrument mask the measured IP data. This limits access to the spectral content, which is vital for characterizing the electrical properties of rocks, soil and minerals in the subsurface. Therefore, mitigating noise responses is key to gaining access to the spectral content. To this end, existing literature assumes prior noise models to deal with the harmonic, spike, and random noises whereby errors in the estimated model parameters can leave residuals, which are significant enough to question the reliability of the inversion results. To address this problem, we employ variational mode decomposition (VMD) that uses a data driven approach to decompose a TDIP signal into its intrinsic oscillatory modes, i.e., amplitude modulated-frequency modulated (AM-FM) sinusoids. The optimization based decomposition framework in VMD dynamically adjusts filtering properties according to the nature of the input TDIP signal. Since IP decays and noise have different spectral properties, we employ a multi-stage VMD operation to gradually isolate the signal of interest from noise. Through simulations and field examples we demonstrate that the proposed VMD based approach enhances the reconstruction of the IP decay and hence improves its inversion and interpretation.

Surface nuclear magnetic resonance (NMR) measurements are notorious for their low signal-to-noise ratio (SNR). Powerlines are probably the most common source of noise and give the greatest contribution to noise levels. The noise from powerlines manifests itself as sinusoidal signals oscillating at the fundamental powerline frequency (50 or 60 Hz) and at integer multiples of this frequency. Modeling and subtraction of the powerline noise have been demonstrated as a highly applicable method for improving SNR and are common practice today. However, the methods used to determine the parameters of the powerline noise are computationally expensive. Consequently, it is difficult to do real-time noise removal during the acquisition of field data and, therefore, also difficult to do a real-time quality inspection of data. Here, we demonstrate how the removal of powerline noise in surface NMR data can be significantly faster. We obtain this through two new developments. First, we apply a projection-based method to determine the powerline model, which is twice as fast as the commonly applied least-squares solution of a matrix equation. Second, we obtain a further 10–25 times speed-up by exploiting the high-performance parallel computations offered by graphical processing units (GPUs). We demonstrate the method on a noise-only field dataset with an embedded synthetic NMR signal.

Inversion of large-scale time-domain transient electromagnetic (TEM) surveys is computationally expensive and time-consuming. The calculation of partial derivatives for the Jacobian matrix is by far the most computationally intensive task, as this requires calculation of a significant number of forward responses. We propose to accelerate the inversion process by predicting partial derivatives using an artificial neural network. Network training data for resistivity models for a broad range of geological settings are generated by computing partial derivatives as symmetric differences between two forward responses. Given that certain applications have larger tolerances for modeling inaccuracy and varying degrees of flexibility throughout the different phases of interpretation, we present four inversion schemes that provide a tunable balance between computational time and inversion accuracy when modeling TEM datasets. We improve speed and maintain accuracy with a hybrid framework, where the neural network derivatives are used initially and switched to full numerical derivatives in the final iterations. We also present a full neural network solution where neural network forward and derivatives are used throughout the inversion. In a least-squares inversion framework, a speedup factor exceeding 70 is obtained on the calculation of derivatives, and the inversion process is expedited ~36 times when the full neural network solution is used. Field examples show that the full nonlinear inversion and the hybrid approach gives identical results, whereas the full neural network inversion results in higher deviation but provides a reasonable indication about the overall subsurface geology.

In efforts to map water at depth, steady-state free-precession (SSFP) sequences promise to rapidly increase data acquisition rates in the practice of surface nuclear magnetic resonance (NMR). Unlike conventional surface NMR excitation schemes, pulses in SSFP are transmitted so frequently that the nuclear magnetization of hydrogen in water can not return to its natural alignment with the earth’s ambient magnetic field, and instead achieve a steady-state; a dynamic equilibrium between pulses. Unfortunately, the traditional formulations of SSFP sequences and the full surface NMR forward models are not immediately compatible with each other. Firstly, the traditional analysis of SSFP sequences assume that relaxation during pulse (RDP) effects are negligible, which is not always valid in surface NMR. Secondly, even for single pulse measurements, the surface NMR forward model can be computationally demanding; this challenge scales with the number of pulses. Here we investigate the incorporation of RDP effects on the dynamic equilibrium of SSFP measurements. This is then incorporated into the full surface NMR forward model by deriving analytical expressions to directly predict processed surface NMR data. The model is validated by jointly inverting an extensive and diverse suite of SSFP measurements; 12 distinct sequences each with 16 pulse moments. The inverted model has a data misfit of 0.99 and is consistent with models derived from standard NMR data. The ability of our forward model to reproduce diverse signals and jointly invert them is a strong indication of its validity.

A common noise source in surface nuclear magnetic resonance (NMR) is narrowband noise sources that occur at frequencies close to the Larmor frequency, such as power-line harmonics or other sinusoidal signals of unknown origin. These noise sources can lead to significant perturbation on the estimated NMR signal and degrade the accuracy of subsurface characterizations. We demonstrate that the spectral analysis envelope detection scheme, where the envelope is estimated using the discrete Fourier transform for a suite of sliding windows, can be modified to mitigate the effect of narrowband noise sources. Selection of an appropriate length rectangular window is shown to allow one to effectively place a stopband at frequencies very close to the Larmor frequency, where the stopband may be selected to coincide with narrowband noise sources. The result is a significant reduction in the influence of the narrowband noise source on the estimated envelope, without introduction of distorting transients on the signal. Synthetic and field results are presented to illustrate the effectiveness of the proposed approach, as well as identify limits on the required resolution of the narrowband noise source's frequency.

Powerline harmonics are often the primary noise source in surface nuclear magnetic resonance (NMR) measurements. State-of-the-art techniques, such as notch filtering, Wiener filtering, and model-based subtraction, have been demonstrated to greatly mitigate powerline harmonic noise, but these approaches break down when one of the powerline harmonics has a frequency close to or coincident with the Larmor frequency fL, referred to as a co-frequency harmonic. We propose a hybrid scheme where model-based subtraction of powerline harmonics is coupled with data from a synchronous reference coil to specifically subtract the co-frequency harmonic component. In standard model-based subtraction of powerline harmonics, a sinusoidal model of all harmonic components is fit to the data and subtracted. In the new approach, the amplitude and phase of the co-frequency harmonic are determined by a sinusoidal model fit to the synchronous noise-only data recorded in a reference coil. From the reference coil co-frequency model, the co-frequency harmonic in the primary coil is estimated using relationships between the amplitude and phase of the co-frequency harmonic in the two coils established during noise-only segments. By utilizing data from the reference coil to model the co-frequency harmonic, accidental fitting of the surface NMR signal is avoided. We investigate the efficiency of the method using a synthetic surface NMR signal embedded in noise-only data recorded in Denmark. Our results demonstrate that the co-frequency powerline harmonic can be removed efficiently without distorting the surface NMR signal and the new method performs better than standard methods.