A marine VSP is designed to estimate the orientation and density of fracturing within a gas‐producing dolomite layer in the southern North Sea. The overburden anisotropy is firstly estimated by analysing shear waves converted at or just below the sea‐bed, from airgun sources at four fixed offset azimuths. Full‐wave modelling helps confirm that the background has no more than 3% vertical birefringence, originating from TIH anisotropy with a symmetry axis orientated perpendicular to the maximum horizontal compressive stress of NW–SE. This finding concurs with current hypotheses regarding the background rock matrix in the upper crust. More detailed anisotropy estimates reveal two thin zones with possible polarization reversals and a stronger anisotropy. The seismic anisotropy of the dolomite is then determined from the behaviour of locally converted shear waves, providing a direct link with the physical properties of its fractures. It is possible to utilize this phenomenon due to the large seismic velocity contrast between the dolomite and the surrounding evaporites. Two walkaway VSPs at different azimuths, recorded on three‐component receivers placed inside the target zone, provide the appropriate acquisition design to monitor this behaviour. Anisotropy in the dolomite generates a transverse component energy which scales in proportion to the degree of anisotropy. The relative amplitudes, for this component, between the different walkaway azimuths relate principally to the orientation of the anisotropy. Full‐wave modelling confirms that a 50% vertical birefringence from TIH anisotropy with a similar orientation to the overburden is required to simulate the field observations. This amount of anisotropy is not entirely unexpected for a fine‐grained brittle dolomite with a potentially high fracture intensity, particularly if the fractures contain fluid which renders them compliant to the shear‐wave motion.