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A B S T R A C TDuring seismic monitoring of hydraulic fracturing treatment, it is very common to ignore the deviations of the monitoring or treatment wells from their assumed positions. For example, a well is assumed to be perfectly vertical, but in fact, it deviates from verticality. This can lead to significant errors in the observed azimuth and other parameters of the monitored fracture-system geometry derived from microseismic event locations. For common hydraulic fracturing geometries, a 2 • deviation uncertainty on the positions of the monitoring or treatment well survey can cause a more than 20 • uncertainty of the inverted fracture azimuths. Furthermore, if the positions of both the injection point and the receiver array are not known accurately and the velocity model is adjusted to locate perforations on the assumed positions, several-millisecond discrepancies between measured and modeled SH-P traveltime differences may appear along the receiver array. These traveltime discrepancies may then be misinterpreted as an effect of anisotropy, and the use of such anisotropic model may lead to the mislocation of the detected fracture system. The uncertainty of the relative positions between the monitoring and treatment wells can have a cumulative, nonlinear effect on inverted fracture parameters. We show that incorporation of borehole deviation surveys allows reasonably accurate positioning of the microseismic events. In this study, we concentrate on the effects of horizontal uncertainties of receiver and perforation positions. Understanding them is sufficient for treatment of vertical wells, and also necessary for horizontal wells.

The paper is devoted to the numerical calculation of the frequency-dependent complexvalued vectorial amplitudes of S waves in weakly anisotropic media by the coupling ray theory. An efficient and accurate method of numerical integration of the coupling equation is proposed, and the accuracy of the method is estimated in order to control the integration step so that the relative error in the wavefield amplitudes due to the integration is kept below a given limit. Several quasi-isotropic approximations of the coupling ray theory are briefly discussed and a numerical example is presented.

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