The peak frequency of direct waves for microseismic events

Abstract

Direct seismic waves (P- or S-waves) are used to locate and further characterize microseismic events. The resolution of information obtained from direct waves depends on the peak frequencies of the waveforms. The peak frequency results from combination of the source, propagation, and the receiver effects. For frequencies below the corner frequency, propagation effects control the peak frequency in observed seismograms of microseismic events. The frequency dependence of direct body waves can be modeled by attenuation, specifically the global attenuation factor. This model is consistent with observed data along surface profiles explaining the difference between the peak frequencies of P- and S-waves. In addition, the model is consistent with the peak frequencies observed on downhole monitoring arrays. This can be used to invert effective attenuation providing additional unique measurement from microseismic events. The corner frequency can be estimated from the average stress drop and analytical source models such as a circular crack model. Typical stress drops for various magnitude ranges are discussed. The peak frequencies are usually below the corner frequencies of microseismic events smaller than moment magnitude 0.7 for surface monitoring and moment magnitude −0.5 for downhole monitoring. Understanding of the frequency dependence of the direct waves allows us to optimally design monitoring networks and mainly invert effective attenuation providing unique measurement from microseismic monitoring.

Attenuation from microseismic datasets by the peak frequency method benchmarked with the spectral ratio method

“…Using Eqs (2) and (3) we can define the effective quality factor Q as: Eisner et al (2013) used the above relations to estimate Q in a sedimentary basin from a surface monitoring array of several hundred receivers. However the results were questioned by Morozov (2014) as surface scattering might have influenced the results.…”

“…From the above listed effects, only attenuation affects amplitude spectra of the waves associated with rays. Assuming a shear source (see the definition above) with corner frequency and attenuation along ray paths, Eisner et al (2013) showed that the particle velocity amplitude spectra of a body wave can be approximated in the frequency domain as:…”

“…However, an attenuated signal has peak frequency controlled by the global absorption factor. Eisner et al (2013) using Eqs (1) showed that the peak frequency of the attenuated signal can be determined as:…”

“…Obviously, characterization of attenuation is important for microseismic monitoring especially since microseismic events radiate at high frequencies which are more attenuated. Eisner et al (2013) proposed a new method of the attenuation factor inversion based on the peak frequency of direct wave of a microseismic event. The technique assumes the knowledge of the shape of the source spectra and provides an easy and robust determination of the attenuation factor (Q).…”

“…1 . S o u r c e m e c h a n i s m a n d s p e c t r a Peak frequency method (Eisner et al, 2013) is based on a simple assumption of the source spectra of a microseismic event. Rutlege and Philips (2003) and Eisner et al (2010) argued that microseismic events are similar to a majority of earthquakes of bigger magnitudes, i.e.…”