Fault analysis: throw, heave, dip, and seal

The four fault measurements

• Throw $T$ is the vertical component of the displacement. Pick one horizon where the fault cuts it on each side: if it sits at depth $z$ at its footwall cutoff and at $z + T$ at its hangingwall cutoff, $T$ is the throw. Units: metres, or milliseconds if you have not depth-converted yet.
• Heave $H$ is the horizontal component: how far apart the same two cutoffs are across the section. It is hard to read directly from a seismic section and is usually computed from throw and dip.
• Slip $S$ is the displacement along the fault plane, the distance between the two cutoffs measured along the fault: the hypotenuse of the right triangle with throw and heave as its legs. A section cut along the direction of slip shows all of it; any other section shows less.
• Dip $\theta$ is the angle of the fault plane measured from horizontal. Normal faults usually dip 50 to 70°; thrusts dip 20 to 40°; strike-slip faults are nearly vertical (80 to 90°).

The four quantities are related by trigonometry of the fault-displacement right triangle:

$T = S \sin\theta$     $H = S \cos\theta$     $\tan\theta = T/H$

Given any two of the four, the others follow. Real interpretation usually measures throw directly from the seismic (vertical reflector separation) and measures dip from the fault’s angle on the section, then computes heave and slip from the equations above.

Planar vs listric faults

Real faults are not always straight in cross-section:

• Planar faults maintain a constant dip with depth. The dip angle you measure at the top of the fault is the same at the bottom. Typical of small-scale faults (< 1 km offset) in competent rock and of basement-involved faults.
• Listric faults curve from steep at the top (typically 60-70°) to shallow or flat at depth, where they merge into a horizontal detachment. Typical of large-scale extensional systems and gravity-driven growth faults. The transition from steep to shallow happens over a few kilometres of depth.

The geometry matters kinematically:

• On a planar fault the hangingwall can move as a rigid block, so every horizon records the same throw.
• On a listric fault the hangingwall has to deform internally to stay on the curved surface. In the simplest model, vertical simple shear, every horizon shares one heave, so the throw is roughly the heave times the tangent of the local dip and shrinks downward where the fault flattens; the beds sag into the fault as a rollover anticline.

Production interpretation uses both. If you interpret a fault as planar when it is listric, your throw maps will be wrong at every level but the one you measured, because on a listric fault the throw changes with depth.

Shale Gouge Ratio (SGR): the fault-seal calculation

A fault that offsets a stratigraphic section produces a fault rock, the pulverized material smeared along the fault plane as the rocks slid past each other. The composition of this fault rock determines whether the fault seals hydrocarbons (retains them on one side) or leaks (lets them migrate through). Before the fault rock matters, though, ask what faces the reservoir across the fault. A sand against shale is sealed by juxtaposition, because the shale itself is the seal; only where sand faces sand does the fault rock decide.

Shale Gouge Ratio (SGR, Yielding et al. 1997) is the simple and widely-used approximation for fault-rock composition:

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where the sum runs over the beds that slid past the point at depth $z$ on the fault, the window from $z$ minus the local throw to $z$ (on a planar fault, from $z - T$ to $z$), and $T$ in the denominator is that local throw; $V_{\mathrm{sh},i}$ is the shale fraction of bed $i$ and $\Delta z_i$ its thickness inside that window. In words, SGR is the thickness-weighted shale fraction of the rock that slid past the point: the shale log averaged over a window one throw long. It runs from 0 (all sand) to 100% (all shale).

The sealing threshold is empirical and basin-specific but typically:

• SGR below about 15 to 20%: the fault rock is sand-rich and permeable, and the fault leaks.
• SGR above about 20%: the fault rock is clay-rich enough to seal (Yielding et al. 1997 put the threshold near 15 to 20%).
• Higher SGR, taller column: above the threshold the pressure the fault rock can hold rises steadily with SGR. Bretan et al. (2003) calibrate it as $\log_{10} P_{\mathrm c} = \mathrm{SGR}/27 - C$, with $P_{\mathrm c}$ in bar and $C = 0.5$ at burial under 3 km; the oil column it holds is $P_{\mathrm c}/(\Delta\rho\,g)$.

Why this works geologically: shale minerals (mostly clay particles) are soft and deform by smearing, producing a continuous clay-rich layer along the fault. Sand grains fracture rather than smear, leaving the fault rock granular and permeable. A high-SGR fault has continuous clay drape; a low-SGR fault has interrupted, sand-rich granular fault rock.

Exercise, measure the fault and judge its seal

Figure 3.2 opens on a planar normal fault dipping 60° with 150 m of throw on the top of the Reservoir sand. Plate (a) is the section at true scale, (b) the seismic that section would give, and (c) the shale fraction along the fault, where the gouge is computed.

1. Read the triangle in (a). The two cutoffs of the top of the Reservoir fix every number in the table: the Reservoir drops 150 m, the cutoffs are 87 m apart horizontally and 173 m apart along the fault, so $T = S\sin\theta$ and $H = S\cos\theta$. In (b) the same step is what you would measure on data: you never see the fault plane, only where the reflectors stop and reappear lower down. At a 32 m wavelength the tuning thickness $\lambda/4$ is 8 m, so 150 m of throw is 18.8 times tuning and unmissable; at the 10 m minimum it is 1.25 times, and two interpreters could argue about it.
2. Read the headline. Across the fault the top 20 m of the Reservoir faces Floodplain shale, which seals it by juxtaposition, but the lower 30 m faces Channel sand. There only the gouge can stop oil, and plate (c) shows why it does: SGR is the shale log averaged over a window as long as the throw, and a 150 m window takes in the Mudstone and the Heterolithics. Its weakest value on that face is 34%, above the 20% threshold, and by the Bretan et al. (2003) calibration its gouge could support a column of about 190 m of oil.
3. Drop the throw to 30 m, less than the Reservoir is thick. The sand now faces the Heterolithics and its own upper part, and at the base of that face everything that slid past was clean Reservoir sand: the SGR falls to 5% and oil leaks, although the column as a whole is about 40% shale. At 70 m the sand faces the Heterolithics and the weakest SGR is 12%, still a leak.
4. Raise the throw to 190 m. Every metre of the Reservoir now faces Floodplain shale, so the fault seals by juxtaposition and there is no sand-on-sand face left to judge. More throw did not improve the gouge; it moved a different bed opposite the sand.
5. Back at 150 m, raise the threshold to 35%. The fault and its 34% gouge are unchanged, but the verdict flips to a leak. The threshold is a calibration from the basin’s own wells, and a prospect’s risk can hinge on it as much as on the geometry.
6. Switch the fault to listric. It now flattens toward a detachment, and the hangingwall deforms to stay on it: every horizon shares one heave, 157 m, so the throw falls with depth, from 231 m at the top of the column to 150 m on the Reservoir and 81 m on the 520 m horizon, whose hangingwall cutoff lies below the section, and the beds roll over into the fault. The rock beside the Reservoir slid down the steeper upper fault, so it faces 8 m of Shelf sand and then Floodplain shale, and the weakest SGR rises to 52%: gouge that could support about 880 m of oil, more than the whole section is deep, so the trap’s closure, not the fault, would limit the column.
7. The hatched unit at the top of the hangingwall is post-fault fill: it filled the space the fault made after the fault stopped moving. The fault never cut it, so plate (c) computes no gouge where the fault faces it. On a low-angle listric fault with a large throw (40° and 200 m) the fill reaches below the top of the Reservoir, and the figure counts that part of the face as open: the unconsolidated fill is credited with no seal and there is no gouge, so oil leaks there even where the rest of the face seals.

Common fault-analysis pitfalls

• Throw in time vs throw in depth. If you pick a fault in two-way time on seismic, your "throw in ms" is not the depth throw. Converting requires velocities at both sides of the fault and can change the apparent throw by 20-40%. Report throws in metres (depth-converted) whenever possible.
• Picking the fault dip from a section that is not perpendicular to fault strike. Any seismic line that is oblique to the fault strike shows apparent dip, always shallower than the true dip. True dip requires a line perpendicular to the fault strike, or a correction using the strike angle.
• SGR is a gross simplification. Real fault rocks have more complex fabric, mineralogy, and cementation history than the shale-fraction-weighted average captures. SGR is a useful screening tool, not a definitive seal predictor. Rely on well-calibration wherever possible.
• Small faults matter. A 10 m throw may be below seismic resolution, but it can be critical for field compartmentalization. Production reservoir models often include sub-seismic fault populations derived by extrapolation from the observable larger faults (using fractal displacement-length relationships).
• Fault seal is a geological property, not just a geometric one. SGR alone doesn't capture the stress state acting on the fault, which affects current-day permeability. A fault that was sealing at the time of hydrocarbon migration might leak today if stress changes have caused it to reactivate. Integrate with in-situ stress analysis for critical decisions.
• Throw is sometimes measured wrong. The common mistake: measuring the vertical distance between two reflectors that are not correlative across the fault. Always verify correlation using adjacent lines or distinctive marker horizons; a miscorrelation introduces a throw error equal to one bed spacing.

From fault analysis to trap evaluation

A quantitative fault analysis feeds directly into prospect evaluation:

• Measure throw and dip on the fault from seismic sections, creates the fault geometry.
• Tie fault throws to stratigraphy at nearest wells, identifies which layers juxtapose across the fault at each depth.
• Compute SGR along the fault plane, identifies sealing and leaking segments.
• Map fault throw and seal status in 3D, produces fault-seal maps for the prospect.
• Compare with structural trap outlines, identifies which portions of the closure are fault-sealed and therefore capable of trapping hydrocarbons.
• Estimate hydrocarbon column height supported by the seal, uses the buoyant pressure a fault can hold (calibrated from capillary entry pressure of the fault rock).

This pipeline is the modern standard for structural-trap prospect evaluation. Section 3.6 will integrate fault-seal analysis with structural closure definition to produce complete prospect assessments.