Hodogram

Key Takeaways

• Shear wave splitting (birefringence) analysis using hodograms is the primary borehole seismic method for characterizing fracture orientation and density in tight reservoirs: when a shear wave propagates through a vertically fractured formation, it splits into two orthogonally polarized shear waves -- the fast shear (S1, polarized parallel to the fracture strike direction) and the slow shear (S2, polarized perpendicular to fracture strike) -- that travel at different velocities and arrive at the receiver at different times; the time delay between S1 and S2 (the shear wave splitting time) is proportional to the fracture density and the degree of anisotropy, with typical splitting times of 1 to 20 milliseconds per kilometer of propagation in fractured tight reservoirs; before the splitting can be quantified, the coordinate system must be rotated from the acquisition geometry (inline and crossline components of the 3C geophone) to the natural splitting coordinate system aligned with the fast and slow shear directions; hodograms of the two horizontal shear components (H1 and H2) over the S-wave arrival window show an elliptical pattern when the geophone is not aligned with the symmetry axis, transitioning to two orthogonal linear traces (one for each shear) when the rotation angle aligns H1 with S1 and H2 with S2; the rotation angle that produces the two linear hodograms gives the fast shear azimuth (fracture strike direction), and the time delay between the arrival times of the two linear hodograms gives the shear wave splitting time (proportional to fracture density); this technique, validated against borehole image logs and core fracture orientation data in several carbonate and tight sand fields, provides a continuous depth profile of fracture orientation from VSP surveys.
• P-wave first-break polarization analysis using 3C VSP hodograms allows determination of the source-to-receiver azimuth and apparent angle of incidence at each depth level of a borehole seismic survey, providing the geometric data needed to compute borehole deviation and azimuth (if the source location and receiver depth are known) and to correct 3C VSP data for tool rotation between receiver stations: in a VSP geometry, the borehole geophone package (clamped against the borehole wall at successive depth intervals) may rotate azimuthally between stations if the borehole is not vertical and the tool has a preferred mechanical orientation; hodogram analysis of the P-wave first break (which is linearly polarized along the ray path from source to receiver) gives the apparent incidence vector in the geophone coordinate frame, which can be compared to the theoretical incidence vector computed from the source position and receiver depth to determine the tool rotation angle and correct the horizontal components to a consistent azimuthal orientation; without this rotation correction, the two horizontal components of the 3C VSP cannot be reliably converted to north-south and east-west components for P-to-S conversion analysis, azimuthal anisotropy study, or 3D VSP imaging; the hodogram-based rotation method is more reliable than magnetic tool-face measurements in wells with significant casing or drill collar magnetic interference.
• Surface wave (Rayleigh wave) hodogram geometry is retrograde elliptical near the Earth's surface, distinguishing surface waves from body waves (P and S) in seismic records: the particle motion of a retrograde Rayleigh wave traces an ellipse in the vertical plane containing the propagation direction, with motion retrograde to the propagation direction (i.e., the particle moves backward and downward as the wave crest passes, then forward and upward as the trough passes), creating an elliptical hodogram in the radial-vertical plane with the major axis tilted toward the propagation direction; this distinctive retrograde ellipse geometry allows surface waves to be identified and separated from body wave reflections in 3C land seismic data by hodogram-based filtering (also called polarization filtering), which suppresses arrivals with elliptical hodograms (ground roll) while passing arrivals with linear hodograms (P and S reflections); hodogram-based polarization filters can attenuate ground roll by 20 to 30 dB in areas where the ground roll and reflection signals overlap in both frequency and time (a common problem in shallow targets where the reflection two-way time is less than 100 to 200 ms), without the frequency-dependent attenuation that f-k filtering imposes; at greater depths, Rayleigh wave particle motion becomes more complex (transitioning toward linear at depths greater than approximately one wavelength below the surface), complicating hodogram-based surface wave identification.
• Microseismic event analysis uses hodograms to determine the particle motion direction and wave type classification for downhole geophone arrays monitoring hydraulic fracture propagation: during a hydraulic fracture treatment, microseismic events (small shear slippage events on natural fractures in the vicinity of the propagating hydraulic fracture) generate impulsive P and S waves that radiate outward and are recorded on downhole geophone arrays in offset monitoring wells; for each detected event, the hodogram of the P-wave window is linear and oriented along the source-to-receiver ray path (from the event location toward the monitoring array), providing a direct estimate of the event-to-receiver azimuth that can be combined with S-P time difference (for event depth estimation using velocity model) to locate the event in three dimensions; accurate hodogram analysis requires that the first-motion P-wave window is clearly identifiable above the background noise level, which in turn depends on the signal-to-noise ratio of the monitoring array (driven by monitoring well depth, offset from the treatment, and ambient noise), the magnitude of the microseismic event, and the frequency content of the P-wave relative to the dominant ground noise in the frequency range 100 to 1,000 Hz typical of microseismic events; in downhole arrays where the P-wave is visible above noise but below the minimum magnitude for reliable hodogram analysis, the S-wave (which has higher amplitude than the P-wave for typical double-couple shear source mechanisms) may still provide azimuth information from the tangential hodogram component.
• Multichannel hodogram analysis using 3D VSP or wide-azimuth borehole seismic data extends single-receiver hodogram interpretation to a spatially distributed picture of the wavefield polarization at each depth and azimuth, enabling mapping of anisotropy and fracture orientation variations that are not detectable from single-receiver analysis: in a walkaway VSP (where the surface source is moved progressively further from the wellhead along multiple azimuthal lines while the 3C receiver remains clamped at depth), the P-wave first-break hodogram at each source position gives the apparent polarization direction as a function of source azimuth, and the azimuthal variation of P-wave velocity (elliptical azimuthal anisotropy, AVAZ) can be fitted to determine the orientation and magnitude of horizontal stress anisotropy; the S-wave splitting parameters (fast azimuth and splitting time) determined from hodogram analysis at each source position form an azimuthal map that is sensitive to fracture strike and density around the well; integration of walkaway VSP hodogram-derived anisotropy parameters with borehole image log fracture orientation data and core plug velocity measurements provides the most complete characterization of near-wellbore fracture geometry available without drilling additional wells, and this characterization directly informs hydraulic fracture modeling (fracture azimuth prediction) and horizontal well landing zone selection in naturally fractured tight reservoir plays.