Examples of two microseismic events used for source analysis. Top panel shows calculated signal and noise spectra. Middle panels show observed seismograms (vertical component). Lower panels show spectrograms, which show easily discernible P and S arrivals. 

Context in source publication

Context 1

... assumption is valid. Fig. 6 illustrates the sensitivity of magnitude and corner- frequency estimates to white noise and Q uncertainty. Model parameters for these tests are summarized in Tables 2 and 3. In Fig. 6(a), the reference S -wave model spectrum contains no noise and is computed for Q S = 150. The dashed curves show best-fitting model spectra, calculated using eqs (1) and (2) based on a priori assumptions of no attenuation ( Q S →∞ ), Q S too high (200) and Q S too low (100). The best-fitting curves were obtained by minimizing the misfit between model and reference spectra based on a least-squares criterion. Specifically, an exhaustive search procedure was used to select the parameter A 0 in order to minimize the least-squares misfit within a user-defined low-frequency band (50–100 Hz), followed by an exhaustive search to select ω c to minimize misfit in a user- defined high-frequency band (400–700 Hz). Although most curve fits appear reasonable, derived misfits in corner frequency are large (Table 2). In general, if a priori estimate of Q exceeds the correct value, the inferred corner frequency will be too low; conversely, if a priori estimate of Q is less than the correct value, the inferred corner frequency will be too high. As expected, uncertainties in Q have relatively little effect on the estimation of magnitude, which is estimated from the low-frequency displacement asymptote and does not depend on the corner frequency. To consider the effects of noise, a series of tests was conducted based on a modified spectral model | ν ( ω, r ) | = A ν 0 ( r ) exp( − α ν r ) + N 0 , (14) 1 + ( ω/ω c ν ) 2 i ω which differs from eq. (1) only by the inclusion of an additive noise parameter, N 0 to model constant background noise in the velocity spectrum. Parameters for the noise sensitivity tests are summarized in Table 3. Using the same least-squares fitting approach described above, model parameters A 0 and ω c were obtained using an exhaustive search procedure, based on prescribed values of Q and N 0 . Comparing Tables 2 and 3, we find that a factor of two uncertainty in noise has a less dramatic effect on inferred magnitudes and corner frequencies than a similar uncertainty in Q . Identical inferences can be derived for source-parameter estimation using P waves. Spectra for shear and tensile sources are used here to investigate source characteristics for a microseismic field experiment acquired in 2011 August in northwest Canada (Eaton et al . 2013). In this field data example, multistage hydraulic-fracture treatments in two horizontal wells at a depth of ∼ 1950 m were recorded using both surface and borehole sensors (Fig. 7). In this study, our analysis is confined to data from the borehole sensors, as relatively few events were detected at the surface. The borehole toolstring was deployed in a deviated well in a depth range of 1670–1830 m. The toolstring consisted of a six-level array of 4.5 Hz geophones with downhole digitization. Background velocities at the reservoir level are Vp ∼ 5 km s –1 and Vs ∼ 3 km s –1 . Most perforation shots were well recorded to distances of about 2 km. These signals were used to estimate Q P and Q S . In addition, numerous high-frequency ( > 100 Hz) microseismic events with moment magnitudes ranging from − 2.3 to − 0.3 were detected to distances of up to 1.5 km. Several examples of perf shots are shown in Fig. 8. The effects of attenuation are expressed as a reduction in amplitude coupled with relative loss of high-frequency content at greater observation distance. Signal and noise spectra were computed by windowing the desired waveform and pre-event noise. Pairs of perf shots were selected for Q determination based on similarity in ray azimuth for the distal and proximal perf shot locations (Fig. 9). As illustrated in Fig. 10, Q P and Q S values were determined using the spectral-ratio method described above. The spectra were computed by taking the Fourier transform, after isolating signals from P - and S -wave direct arrivals by applying a Gaussian windowing function with a standard deviation of 75 ms. The application of this windowing function has the effect of smoothing the computed spectrum, without affecting the overall amplitudes. Using all of the available high-quality perf-shot recordings, we found significant scatter in the results; we obtained average values of Q P = 109 ( N = 24) and Q S = 101 ( N = 16) with standard deviations of 49 and 46, respectively (see Supporting Information for complete results). These average Q values are used in the spectral calculations below, with the caveat that large scatter in Q estimates imply significant uncertainties in corner frequency. A subset of 20 events from the complete set of detected events was selected for further analysis, based on good signal to noise (S/N) and the discernibility of distinct P and S arrivals. Several examples of seismograms with corresponding spectrograms and amplitude spectra are presented in Fig. 11. The sample stage 1 event is located ∼ 358 m from the monitor well. The P -wave arrival is not visible (due to the plot scale, which is dominated by the S wave) in the seismogram, but it can be discerned in the spectrogram based on abrupt change in frequency content from the background levels. The S -wave arrival has high signal level to the Nyquist frequency (1000 Hz). The spectrum is dominated by the S wave and has good S/N > 20 dB) in the frequency range 100 < f < 1000 Hz. The sample stage 3 event is located ∼ 456 m from the geophone. Both P and S arrivals are clearly visible in the raw seismogram, and the spectrum has S/N ∼ 20 dB in the range 100 < f < 350 Hz. Brune source parameters for the analysed events were computed using a procedure similar to Abercrombie (1995). The overall workflow can be summarized as follows: (1) For each event, the three-component geophone with the high- est S/N is selected and used to pick P - and S -wave arrival times. P and S amplitudes are estimated using the maximum vector amplitude within two dominant periods following the picked arrival time. (2) A Gaussian windowing function with a standard deviation of 0.1 s is applied to isolate the desired arrival, as well as pre-event noise. (3) For each component (east, north and vertical), velocity spectra for signal and noise are computed by taking the Fourier transform of the windowed trace, normalized such that absolute units are preserved. Displacement spectra for individual components are then computed by dividing velocity spectra by i ω . Finally, scalar displacement spectra for signal and noise are calculated from the individual components based on the vector amplitude. (4) An initial estimate of the low-frequency plateau is obtained by taking the difference between the average signal and noise amplitude within a user-defined frequency range (here 200–300 Hz was used). (5) Corner frequency is determined by finding the optimum (least-squares) fit between observed and modelled displacement spectra, using an exhaustive search within the range 0 < f c < 10 000 Hz, where an obtained value of f c = 10 000 Hz is interpreted as undefined. The modelled spectrum is computed using eq. (14), with fixed values of Q and N 0 . Our method considers corner frequencies above the Nyquist frequency, since even at these higher values of corner frequency the effects on spectral shape remain significant. (6) The low-frequency plateau amplitude ( A 0 ) is adjusted and step 6 is repeated, as necessary, until misfit (variance) converges to a minimum value. Adjustment in low-frequency plateau involves a modest increase or decrease ( ± 50 per cent) to improve the fit of the modelled and observed spectrum. Fig. 12 shows an example fit obtained using this procedure. Although erratic fluctuations are evident in the observed spectrum, the Brune model provides a good overall fit. The corner frequency in this case is undefined, meaning that the effects of Q, rather than fall-off, dominate the high-frequency spectral decay. Table 4 summarizes inferred source parameters for the 20 analysed events. Observation distances sampled by this set of events span a range from ∼ 250 to ∼ 1500 m. Calculated moment magnitudes fall within the range − 2.06 ≤ M w ≤ − 0.34; this range likely reflects a sampling bias towards larger magnitudes, due to detection limits for this experiment (Eaton et al . 2013). As expected, based on uncertainty in Q from analysis of perf shots and background noise levels from the source analysis, inferred corner frequencies exhibit a high degree of scatter; where defined, they fall within the range 207 ≤ f c ≤ 1603 Hz. Measured S / P amplitude ratios vary from 1.13 to 8.91. 17 of the 20 events have an S / P amplitude ratio less than 5, which we consider to be indicative of tensile failure. In addition, four of the analysed events show source spectra characterized by quasi-periodic amplitude modulation above and below the best-fitting Brune spectrum. Fig. 13 shows an example of this type of source spectrum, which may be indicative of a complex source model such as several closely spaced events (Haddon & Adams 1997). As shown in Table 4, this set of four events is generally characterized by low value of S / P amplitude ratio, suggesting that a component of tensile failure may exists. For each of the four events with a complex source spectrum, we have performed a second analysis in which the filter defined by eq. (10) is applied the Brune source model. This represents a simplified model for rapid opening and closing of a tensile crack, defined by a time parameter τ that specifies delay time between two events of equal moment and opposite polarity. To obtain a model fit, step 6 in the workflow outlined earlier was amended to include adjustment to τ . As shown in Fig. 13, in this case this crack opening/closing model provides a better fit to the observed spectra than the con- ventional Brune model. We find an rms misfit of 5.7 × 10 − ...