An inversion procedure is described wherein microseismic data recorded by a network of three component geophones are assumed to be represented as the sum of a compressional (P) and one or two shear (S) arrivals. The inversion operates in the frequency-space domain and includes a linear inversion for source waveforms and a nonlinear inversion for model properties or source locations. The linear inversion effectively reverses time using a ray trace Green function to recover the source-time functions. For the nonlinear inversion two waveform fitting functionals are constructed; one captures moveout and polarization information through a reconstructed data misfit, another captures information from arrival time differences through a spectral coherence functional. The two may be scaled and summed to form a joint X2 misfit which may be combined with soft prior information in a Bayesian posterior. This is then maximized using global search techniques. Model calibration is accomplished by inverting waveform data from known locations (e.g. perforation shots) for anisotropy and optionally for model smoothness and Q. Micro-earthquake event locations are determined by inverting waveform data given the calibrated model.
Since the procedure involves fitting waveforms, time picking is not required. The beam-forming property of the receiver array and the complete polarization vector are used to enhance the signal to noise ratio of arrivals. The presence of a P arrival is not necessary to determine a location. The algorithm implementation uses layered VTI models, includes losses due to spreading, transmission and Q and handles an arbitrary distribution of receivers (e.g. from horizontal or multiple wells or surface locations). The inversion permits automated, objective data analysis with quantified uncertainties in estimated unknowns.
A wavefield separation method using parametric inversion and decomposition is developed for data acquired for a borehole acoustic reflection survey (BARS). We start by estimating parameters describing the propagation along the wellbore of compressional, shear, and Stoneley waves, including geometric spreading and complex-valued velocities. We find and subtract the maximum portion of the measured wavefields, compatible with these estimated parameters. A further attenuation of the direct waves are obtained using median filters along the estimated propagation velocities. After removing the direct waves, we are left with a relatively larger presence of components of the wavefield possibly reflected in the formation. The effectiveness of the method is confirmed by application to the real field data. INTRODUCTION
Borehole Acoustic Reflection Surveys (BARS) are performed for the characterization of local geology (Hornby, 1989; Esmersoy et al., 1998), validation of geosteering (Borland et al., 2007) and detection of fractures (Yamamoto et al., 1999). The acquired sonic waveforms are processed and migrated to obtain images up to about 10 to 20 m away from the borehole. Fig. 1 shows the schematic illustration of the survey. As the reflected (p-to-p, p-to-s and s-to-p) and refracted (p-to-s and s-to-p) waves are usually weak compared to the direct compressional, shear and Stoneley waves, wavefield separation to extract the reflected and refracted signals is important and crucial. The adaptive interference canceler (AIC) filter and median velocity filters in common offset gathers (gathers of traces recorded by common receiver stations of the sonic array tool) are known to be effective methods for this purpose (Haldorsen et al., 2006), but event signals whose apparent velocity is slower than the direct P-waves may be removed and the amplitudes, especially for events from layers which are parallel to the well, tend to become weaker. Therefore a separation method which conserves amplitudes of event signals better is desired. Wavefield separation using parametric inversion (Leaney and Esmersoy, 1989; Leaney, 1990), based on the work of Esmersoy (Esmersoy, 1988, 1990) was used for vertical seismic profile (VSP) data. We describe a separation method for sonic data following their work. The sonic problem differs from that of VSP in that the waves to be estimated and removed are three (P-, S- and Stoneley), all have the same sign of moveout and the input data are not multi-component. Additionally, amplitude variations within the array are significant and the waves may be dispersive. Our development is focused on thesepoints.
Wavefields recorded by the array of receivers are assumed to be expressed by the phase shift due to the difference of arrival times and a function of geometrical spreading; they are decomposed as estimated amplitudes of angular frequency components. By using the estimated amplitudes, the reconstructed data, which only contain the decomposed wavefields are generated. If the decomposed wavefields are accurate extractions, the reflected and refracted event signals are separated out by subtraction of the reconstructed data from the input data. First parameters of geometrical spreading and complex-valued slowness of the direct compressional, shear and Stoneley waves are inverted by minimizing the errors between the input and reconstructed waveforms.