Jean-Baptiste Tary

Spectral estimation—What is new? What is next?

Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

Interpretation of resonance frequencies recorded during hydraulic fracturing treatments

Hydraulic fracturing treatments are often monitored by strings of geophones deployed in boreholes. Instead of picking discrete events only, we here use time-frequency representations of continuous recordings to identify resonances in two case studies. This paper outlines an interpretational procedure to identify their cause using a subdivision into source, path, and receiver-side effects. For the first case study, two main resonances are observed both at depth by the downhole geophones and on the surface by two broadband arrays. The two acquisition networks have different receiver and path effects, yet recorded the same resonances; these resonances are therefore likely generated by source effects. The amplitude pattern at the surface arrays indicates that these resonances are probably due to pumping operations. In the second case study, selective resonances are detected by the downhole geophones. Resonances coming from receiver effects are either lower or higher frequency, and wave propagation modeling shows that path effects are not significant. We identify two possible causes within the source area, namely, eigenvibrations of fractures or non-Darcian flow within the hydraulic fractures. In the first situation, 15–10 m long fluid-filled cracks could generate the observed resonances. An interconnected fracture network would then be required, corresponding to mesoscale deformation of the reservoir. Alternatively, systematic patterns in non-Darcian fluid flow within the hydraulic fracture could also be their leading cause. Resonances can be used to gain a better understanding of reservoir deformations or dynamic fluid flow perturbations during fluid injection into hydrocarbon and geothermal reservoirs, CO2 sequestration, or volcanic eruptions.

Body Wave Separation in the Time-Frequency Domain

Separation of a seismogram into its individual constitutive phases (Pand S-wave arrivals, surface waves, etc.) is a long-standing problem. In this letter, we use a high-resolution time-frequency transform to achieve this and reconstruct their individual waveforms in the time domain. The procedure is illustrated using microseismic events recorded during a hydraulic fracturing treatment. The synchrosqueezing transform is an extension of the continuous wavelet transform combined with frequency reassignment. Its high-resolution time-frequency decompositions allow for separation and identification of Pand S-waves with subtly different frequency contents that would not be recoverable using short-term Fourier transforms due to its smearing in the frequency domain. It is an invertible transform, thus allowing for signal reconstruction in the time domain after signal separation. The same approach is applicable to other seismic signals such as resonance frequencies and long-period events and offers promising new possibilities for enhanced signal interpretation in terms of underlying physical processes.

Attenuation estimation using high resolution time–frequency transforms

Abstract Wave attenuation is often measured using spectral techniques such as the spectral ratio method and the frequency shift method, comparing the spectral content of pairs of waveforms along the ray path. The recent introduction of novel highly-localized time–frequency transforms leads to high-resolution but discontinuous spectra. It prevents the use of these time–frequency transforms with conventional attenuation measurement methods. We show how three highly-localized time–frequency transforms, namely basis pursuit, the synchrosqueezing wavelet transform, and complete ensemble empirical mode decomposition, can still be used to estimate attenuation using the peak frequency method. Assuming a Ricker source wavelet, the decrease in peak frequency of a wave spectrum as it propagates in a given medium is used to estimate attenuation. When applied to a synthetic benchmarking signal corrupted by Gaussian white noise, the three transforms show different degrees of performance and robustness for different signal-to-noise ratios. The developed methodology is suitable for geophysical investigations, but may also find application in other fields such as biomedicine, acoustics and engineering.

Characteristics of fluid‐induced resonances observed during microseismic monitoring

Three groups of resonances are observed during a two-stage hydraulic experiment recorded by 12 three-component geophones. The injected fluid is composed of a slurry of mostly water and proppant plus some supercritical nitrogen. Resonance characteristics are estimated using an autoregressive model. Three resonance models are investigated: fluid-filled cracks, nonlaminar fluid flow, and repetitive events in terms of anticipated resonance frequencies, quality factors, and amplitudes. The observed resonances are very stable and positively correlated with either the slurry flow or the nitrogen injection rate, which is in contradiction with the repetitive events and fluid-filled crack models, respectively. Resonances obtained by numerical simulations of an unstable jet agree with the main characteristics of most observed resonances. Our observations suggest that variations in resonance frequencies are mainly driven by variations in fluid flow, whereas quality factors are more sensitive to the fluid composition through variations in nitrogen injection rate. This study also suggests that resonance frequencies and quality factors can provide complementary information for real-time monitoring of fluid injection into reservoirs, for hydraulic stimulations, geothermal operations, carbon capture, and storage or fluid movement during volcano eruptions.

Low-Frequency Tremor Signals from a Hydraulic Fracture Treatment in Northeast British Columbia, Canada

The Rolla Microseismic Experiment (RME) was undertaken by the Microseismic Industry Consortium August 7-28, 2011 to record a multistage hydraulic fracture stimulation of a Triassic unconventional gas reservoir in northeastern British Columbia, Canada. The microseismic deployment included a 6-level downhole toolstring with low-frequency (4.5 Hz) geophones, a set of 21 portable broadband seismograph systems, and a 12-channel surface array comprised of 10-Hz geophones. Although we did not observe LPLD events based on how they have been previously described, our data exhibit high-amplitude signals in the 8-15 Hz band. These signals are monotonic and have been interpreted as resonance of fluid-filled cracks or successions of small repetitive events. We have also detected several instances of discrete microseismic events with unusually low frequency. An apparent tendency for low-frequency tremors to precede high-frequency microseismicity in our data provides a tantalizing suggestion that these processes may be genetically linked.

Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution. Yet, interpretation of the resulting spectral decomposition is often hindered by smearing and leakage of individual frequency components. Computation of instantaneous frequencies, combined by frequency reassignment, may then be applied by highly localized techniques, such as the synchrosqueezing transform and ConceFT, in order to reduce these effects. In this paper, we present the synchrosqueezing transform together with the CWT and illustrate their relative performances using four signals from different fields, namely the LIGO signal showing gravitational waves, a ‘FanQuake’ signal displaying observed vibrations during an American football game, a seismic recording of the Mw 8.2 Chiapas earthquake, Mexico, of 8 September 2017, followed by the Irma hurricane, and a volcano-seismic signal recorded at the Popocatépetl volcano showing a tremor followed by harmonic resonances. These examples illustrate how high-localization techniques improve analysis of the time-frequency information of time-varying signals. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

Interpretation of Resonance Frequencies Recorded during Hydraulic Fracturing

The frequency content of continuous passive seismic recordings of hydraulic fracturing are sometimes used to gain information on the numerous microseismic events occurring during the fluid injection. In addition, resonance frequencies are frequently recorded as well. Resonances can be used in many ways due to their multiple origins possible. In every circumstance, all possible sources have to be reviewed to define their respective influence. We present two different experiments showing resonances with presumably different origins. For the first experiment, the low-frequency resonances (5-50 Hz) are only recorded by downhole geophones and broadband stations on the surface that are close to the injection well. For the second experiment, four resonances at 17, 35, 51 and 60 Hz are detected. The fluid injection being at approximately the same depth as the receivers, the path effect influence will be limited and the resonances coming from receiver effects are anticipated to be outside the frequency range of the observed resonances. A possible source would be the resonance of fluid-filled cracks. The size of a crack corresponding to a resonance of 17 Hz is calculated to be 17 m. These resonances would then correspond to mesoscale deformation of the reservoir.

Gas and seismicity within the Istanbul seismic gap

Understanding micro-seismicity is a critical question for earthquake hazard assessment. Since the devastating earthquakes of Izmit and Duzce in 1999, the seismicity along the submerged section of North Anatolian Fault within the Sea of Marmara (comprising the “Istanbul seismic gap”) has been extensively studied in order to infer its mechanical behaviour (creeping vs locked). So far, the seismicity has been interpreted only in terms of being tectonic-driven, although the Main Marmara Fault (MMF) is known to strike across multiple hydrocarbon gas sources. Here, we show that a large number of the aftershocks that followed the M 5.1 earthquake of July, 25th 2011 in the western Sea of Marmara, occurred within a zone of gas overpressuring in the 1.5–5 km depth range, from where pressurized gas is expected to migrate along the MMF, up to the surface sediment layers. Hence, gas-related processes should also be considered for a complete interpretation of the micro-seismicity (~M < 3) within the Istanbul offshore domain.

The Synchrosqueezing Transform for High-resolution Time-frequency Representation of Microseismic Recordings

SUMMARY The analysis of the frequency content over time is essential to identify resonance frequencies. The ShortTime Fourier Transform (STFT), based on the Fourier spectra, is the most common transform despite its familiar problems: spectral leakage and signal windowing. The resulting noise can make the identification of a particular frequency component difficult. A new transform called synchrosqueezing (SST) was developed to improve the accuracy of wavelet-based transforms for frequency content estimation, by using the reassignment method which collapse averaged values to their center of gravity. When challenged by a synthetic signal with sharp onsets and a microseismic dataset exhibiting resonance frequencies, the SST is able to detect all frequency components with a better precision than the STFT. In fact, some hidden spectral lines on the STFT representation are identifiable on the SST representation. An accurate determination of the time-frequency content of microseismic recordings is indispensable to separate the different resonance frequencies. The study of these resonances may bring new information on the deformation of the reservoir during hydraulic fracturing experiments.