Seismic monitoring is known as a method with an observation horizon that penetrates far deeper into a hydrocarbon reservoir than any other method employed in the oilfield industry.  It has been proposed to exploit the reach of seismic methods for the purpose of reservoir monitoring. 
In conventional seismic monitoring a seismic source, such as airguns, vibrators or explosives are activated and generate sufficient acoustic energy to penetrate the earth.  Reflected or refracted parts of this energy are then recorded by seismic receivers such as hydrophones and geophones. 
In passive seismic monitoring there is no actively controlled and triggered source.  The seismic energy is generated through so-called induced microseismic events caused by human activity or intervention. 
Apart from the problem of detecting the often faint microseismic events, their interpretation is difficult as neither the source location nor the source signature or characteristics are known a priori.  However knowledge of these parameters is essential to deduce further reservoir parameters knowledge of which would improve reservoir control. 
A specific field within the area of passive seismic monitoring is the monitoring of hydraulic fracturing.  To improve production or where reservoirs are used for storage purposes workers in the oil and gas industry perform a procedure known as hydraulic fracturing.  For example, in formations where oil or gas cannot be easily or economically extracted from the earth, a hydraulic fracturing operation is commonly performed.  Such a hydraulic fracturing operation includes pumping large amounts of fluid to induce cracks in the earth, thereby creating pathways via which the oil and gas may flow.  After a crack is generated, sand or some other material is commonly added to the crack, so that when the earth closes back up after the pressure is released, the sand helps to keep the crack open.  The sand then provides a conductive pathway for the oil and gas to flow from the newly formed fracture. 
However, the hydraulic fracturing process is difficult to monitor and control.  The hydraulic fractures cannot be readily observed, since they are typically thousands of feet below the surface of the earth.  Therefore, members of the oil and gas industry have sought diagnostic methods to tell where the fractures are, how big the fractures are, how far they go and how high they grow.  Thus, a diagnostic apparatus and method for measuring the hydraulic fracture and the rock deformation around the fracture is needed. 
In previous attempts to solve this problem, certain methods have been developed for mapping fractures.  For example, one of these methods involves seismic sensing.  In such a seismic sensing operation, micro-earthquakes generated by the fracturing are analyzed by seismic meters, for example, accelerometers. 
Known method of microseismic event location from a single vertical monitoring array used for example in the field of hydraulic fracturing monitoring (HFM) include the detection of arrivals of P- and S-waves, thus constraining the event depth and distance from the monitoring array.  The polarization of the P waves is then used to determine the vertical plane in which the source is located.  The vertical plane is often reduced to a single direction known as azimuth of the source or back-azimuth of the source.  The microseismic events are then located with the back-azimuth derived from P waves; distance and depth are constrained by the timing of arrivals of P- and S-waves. 
Details of these method can be found for example in the following publications:    Maxwell S. C., Urbancic T. I., Falls S. D., Zinno R.: “Real-time microseismic mapping of hydraulic fractures in Carthage”, Texas, 70th Annual International Meeting, SEG, Expanded Abstracts, 1449-1452 (2000).     Moriya, H., K. Nagano and H. Niitsuma: “Precise source location of AE doublets by spectral matrix analysis of the triaxial hodogram”, Geophysics, 59, 36-45 (1994).     Pearson, C: “The relationship between microseismicity and high pore pressures during hydraulic stimulation experiments in low permeability granitic rocks”, Journ.  Of Geophys Res.  86 (B9), 7855-7864 (1981).     Phillips W. S., T. D. Fairbanks, J. T. Rutledge, D. W. Anderson: Induced microearthquake patterns and oil-producing fracture systems in the Austin chalk.  Tectonophysics, 289, pp.  153-169 (1998). 
However the P-wave amplitudes are typically much smaller than the S-wave amplitudes of the same event.  Hence, the number of events that can be located is low compared to the number detected.  The radiation pattern of a source contributes further to the difficulty of determining the location of the event.  It is for example possible for a linear array of receivers to be located in the vicinity of the P-wave nodal line.  In such case the amount of energy detected and associated with the p-wave emission of an event tends to be very small, making the detection of the P-wave polarization a difficult task. 
A more recent study on the use of microseismic imaging for fracture stimulation was published as:    Rutledge, J. T. and Phillips, W. S. (2003): Hydraulic stimulation of natural fractures as revealed by induced microearthquakes, Carthage Cotton Valley gas field, east Texas.  Geophysics, 68, 441-452. 
In the publication, the authors measure the horizontal particle polarization of the S-waves signals and determine the direction perpendicular to the particle polarization as the back-azimuth of the source.  This approach can be seen as an approximation, as the polarization direction of the S-wave may be oriented in any orientation in the plane perpendicular to the slowness vector of S-wave. 
In Zheng X., I. Psencik (2002): Local determination of weak anisotropy parameters from qP-wave slowness and particle motion measurements.  Pure Appl.  Geophys.,  159, 1881-1905, there are described methods of determining local anisotropy from known source locations with general S-wave polarization. 
The present invention seeks to improve the methods for determining the back-azimuth or the full S-wave slowness vector of passive seismic events or sources, seismic events, or, more specifically, the fracture location or propagation in a hydrocarbon reservoir.