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Dip-slip faulting is relative motion on a geological fault predominantly along the steepest direction within the fault plane. That direction is perpendicular to the fault strike and follows the fault dip. It differs from strike-slip faulting, whose motion is mainly along strike.

For an inclined plane, normal faulting lowers the hanging wall relative to the footwall; reverse faulting raises it. The surface step is only a projection of the full fault slip, so vertical offset alone is not the total displacement unless the geometry is known. Mixed motion belongs to oblique-slip faulting, and an observed focal mechanism must be interpreted with independent evidence for the actual fault plane.

The fault dip is the angle between a fault plane and a horizontal plane, measured perpendicular to fault strike towards the descending side. It lies between $0$ and $90^{\circ }$.

The horizontal dip-direction component of displacement across a fault. The displayed expression assumes pure dip slip, with magnitude $D$ and fault dip $\delta$.

A fault plane is an idealized planar surface across which rock has slipped. A curved fault can be described by local fault planes. Its orientation is specified by fault strike and fault dip, and the slip direction within it by fault rake.

The vertical component of displacement between correlated markers across a fault. For pure dip slip of magnitude $D$ at fault dip $\delta$, the displayed formula applies. Erosion and ground slope can make surface fault scarp height different from throw.

A geological fault is a fracture or fracture zone across which rock has undergone relative displacement. Its local geometry is described by a fault plane, fault strike, fault dip and fault rake. A locked fault can store elastic strain while surrounding rock deforms; some faults also accommodate displacement by slow creep.

For a cohesionless, optimally oriented normal fault with vertical maximum compression and horizontal minimum compression,where $\delta$ is fault dip and $\phi$ the internal friction angle. This is a geometric inference under the model, not a measurement of friction from dip alone.

For a compression-positive Mohr circle, put $C=({\sigma }_1^{\prime }+{\sigma }_3^{\prime })/2$ and $R=({\sigma }_1^{\prime }-{\sigma }_3^{\prime })/2$. Tangency to the cohesionless Mohr-Coulomb failure criterion $\tau ={\mu }_f{\sigma }_n^{\prime }$ gives $R/C=\sin \phi$. The contact point is $({\sigma }_n^{\prime },\tau )=(C{\cos }^2\phi ,C\sin \phi \cos \phi )$. The physical plane-normal angle to ${\sigma }_1^{\prime }$ is half the corresponding central angle, giving the stated dip. Equivalently the plane itself makes $45^{\circ }-\phi /2$ with ${\sigma }_1^{\prime }$.

The associated stress ratio is ${\sigma }_1^{\prime }/{\sigma }_3^{\prime }=(1+\sin \phi )/(1-\sin \phi )$. A reactivated nonoptimal plane, nonzero cohesion or unknown principal stress directions defeats the simple dip-only inversion.

For a double-couple seismic source, measure P-wave first-motion polarity signs and use source-to-station takeoff angles from the location and velocity model to plot them on a focal sphere. Fit the alternating radiation-sign quadrants, optionally adding amplitude ratios and waveform information. The two nodal planes determine a focal mechanism, conventionally expressed by fault strike, fault dip and fault rake.

A more general waveform inversion fits a seismic moment tensor to several components and stations. Its double-couple part supplies candidate slip and normal vectors, but a general moment tensor should not be forced to be double-couple without justification. Polarity calibration, near-nodal observations, path effects and takeoff-angle errors limit the result.

Point-source radiation alone interchanges the fault plane and auxiliary plane without changing the double couple. Resolve this fault-plane ambiguity using mapped rupture, aftershock geometry, geodesy or finite-rupture directivity. A dense set of polarity picks does not by itself remove that fundamental ambiguity.

A fault plane represents the surface across which the two sides of a fault slip. A real fault need not be perfectly planar; these angles can describe a local planar segment. Its fault strike is the azimuth, measured clockwise from north, of its horizontal intersection. The line itself has a $180^{\circ }$ ambiguity; choose the direction for which the fault dips to the right. Its fault dip, $\delta$, is the angle below horizontal measured perpendicular to that fault strike, from $0^{\circ }$ for horizontal to $90^{\circ }$ for vertical.

The fault rake, $\lambda$, is the angle of the relative slip vector within the fault plane. State the sign convention: if $\mathbf{s}$ is the chosen strike direction and $\mathbf{d}$ points down dip, useThus $\lambda =0$ is slip along $\mathbf{s}$, $+90^{\circ }$ is up-dip slip and $-90^{\circ }$ is down-dip slip. This distinguishes the direction in which the fault is tilted from the direction in which it actually moves.

The hypocentre is the point where rupture begins within the Earth. The epicentre is the point on the surface directly above it. The hypocentre need not coincide with the centroid of the final rupture. Orientation uses strike and dip; motion additionally needs rake; epicentre and hypocentre locate the rupture's start.^[ref]

A numerical answer needs an assumption about fault orientation. For a cohesionless fault optimally oriented for Mohr-Coulomb failure criterion, with vertical ${\sigma }_1$, write $\phi$ for the internal friction angle and $\delta$ for the fault dip. The angle between the plane and ${\sigma }_1$ is $90^{\circ }-\delta$, so the optimal normal-fault dip relation givesHence ${\mu }_f=\tan 40^{\circ }=0.839\simeq 0.84$ under that model.

For the Mohr circle, plot effective compression ${\sigma }_n^{\prime }$ horizontally and shear stress $\tau$ vertically. Draw a circle with diameter $[{\sigma }_3^{\prime },{\sigma }_1^{\prime }]$ tangent to $\tau ={\mu }_f{\sigma }_n^{\prime }$. Its centre and radius obey $R/C=\sin \phi$. One illustrative normalization is ${\sigma }_3^{\prime }=1$, ${\sigma }_1^{\prime }=4.59891$, with tangency at the resolved stresses on the $65^{\circ }$ plane. Pore fluid pressure shifts the total-stress circle horizontally; the friction law uses effective stress.

The dip does not determine the actual sliding coefficient of friction without the optimal-orientation assumption. A reactivated inherited plane may be nonoptimal, cohesion may matter, and the stress ratio and pore fluid pressure are not measured. For an arbitrary compression-positive stress state,at cohesionless sliding. Thus the requested single value is a conditional inference, not a friction measurement.

The fault dips are approximately $90^{\circ }$. The mapped senses of fault slip are predominantly strike-slip faulting. In an Andersonian faulting regime, the intermediate principal stress ${\sigma }_2$ is vertical and the maximum and minimum principal stresses ${\sigma }_1,{\sigma }_3$ are horizontal, so the preferred fault planes are vertical. Local bends can introduce oblique-slip faulting without changing this first-order interpretation.

Put the reverse fault along the mountain-front trace identified in part (ii), with the mountainous southern/southwestern block as hanging wall and the central basin to its north/northeast as footwall. Draw teeth on the southern hanging wall side of the line. In the simplest cross-section the fault dips south and the southern block moves northward and up over the basin edge. The image constrains the surface trace and relative uplift more securely than its subsurface fault dip; the precise dip cannot be measured from this map alone.

A reverse or thrust fault earthquake is the expected end member: a hanging wall moves upwards relative to its footwall, accommodating north–south tectonic shortening. A plausible double-couple seismic source focal mechanism has an approximately east–west fault strike, a moderately north- or south-dipping fault plane, and up-dip fault slip. For example, right-hand-rule strike $090^{\circ }$, southward fault dip about $32^{\circ }$, and fault rake $+90^{\circ }$ specify a pure thrust mechanism.

In a lower-hemisphere equal-area plot, with shaded regions denoting compressional P first motions, this focal mechanism has a shaded central region and two unshaded outer lobes. The P axis is approximately horizontal north–south and the T axis approximately vertical for a symmetric idealization; for a single $32^{\circ }$ plane their axes are slightly tilted. The P and T axes of a double-couple seismic source need not exactly equal the regional principal stress axes. The nodal curves represent both the fault plane and its auxiliary plane; additional evidence is needed to choose between them.^[ref]

Assume an initially unfractured homogeneous isotropic material described by a linear Mohr-Coulomb failure criterion, with the given coefficient of friction ${\mu }_f=0.5$ representing the relevant internal friction angle. Use spatially uniform pore fluid pressure, effective stresses ${\sigma }_i^{\prime }={\sigma }_i-P_f$, and compression-positive signs. ThenThe Mohr circle in the ${\sigma }_1^{\prime },{\sigma }_3^{\prime }$ plane has centre $C=({\sigma }_1^{\prime }+{\sigma }_3^{\prime })/2$ and radius $R=({\sigma }_1^{\prime }-{\sigma }_3^{\prime })/2$. At first failure it is tangent to the failure envelope. The radius to the positive-shear tangent point is perpendicular to the line of slope $\tan \phi$, hence makes angle $90^{\circ }+\phi$ with the positive normal-stress axis.

If $\theta$ is the angle between the fault normal and ${\sigma }_1$, the stress transformation isThus $2\theta =90^{\circ }+\phi$, $\theta =58.2825^{\circ }$, and the angle of the fault itself to horizontal ${\sigma }_1$ isThe two conjugate thrust faults therefore strike approximately east–west and dip about $32^{\circ }$ north and $32^{\circ }$ south. This is the fault dip, not the $58.3^{\circ }$ fault-normal angle. Both sediments and basement have the same optimum orientation under these assumptions because their stipulated friction slopes are equal; their cohesion and absolute failure stresses could still differ.

The first two panels in solution give the labeled construction. Constant cohesion shifts the straight failure envelope without changing its slope, and uniform pore fluid pressure translates the Mohr circle in normal-stress coordinates; neither changes this tangency angle. In the illustrative cohesionless case, $R/C=\sin \phi$, giving ${\sigma }_1^{\prime }/{\sigma }_3^{\prime }=(1+\sin \phi )/(1-\sin \phi )\simeq 2.618$. Pre-existing weaknesses, a nonuniform stress field, anisotropic strength, or a nonlinear failure envelope invalidate the simple optimum-orientation prediction.^[ref]

The $31.7^{\circ }$ result predicts initial failure in a uniform material under the assumed principal-stress orientations. The actual Figure 3 is a present-day NW–SE cross section through a thick, heterogeneous Alpine stack, extending to about 50 km depth. It contains near-horizontal basal stretches, curved ramps, tightly bent contacts, and steep structures in the internal zones around Viso and the Dora Maira complex. It does not show a single undeformed conjugate pair newly formed in horizontal uniform rock.

Several processes explain the departures:

Finally, a section shows apparent dip unless it is perpendicular to fault strike. For an ideal plane, $\tan {\delta }_{\mathrm{app}}=\tan {\delta }_{\mathrm{true}}\sin \alpha$, where $\alpha$ is the angle between the section direction and fault strike. Obliquity can make a plane look shallower, but cannot on its own explain an apparent dip steeper than its true dip. Do not infer that each black curve is a currently active brittle earthquake fault.

The geomorphology of active normal faulting records a competition between accumulated tectonic displacement and the ability of erosion, transport and deposition to modify it. A hanging wall moves down relative to a footwall, producing a fault scarp, mountain-front relief, and accommodation space for a sedimentary basin. Repeated earthquakes can build a large front even though each individual surface break is much smaller.^[ref]

The principal controls and their observable effects are:

Useful observations therefore include scarp profiles, repeated offsets of dated surfaces, drainage organization, and continuity along strike. A high rugged front is not by itself evidence of a high present fault slip rate; conversely, a muted or buried scarp need not mark an inactive fault.

A fault on which the hanging wall moves up relative to the footwall, accommodating shortening. A low-angle reverse fault is a thrust fault. The fault dip is a geometric property and should be distinguished from the direction of fault slip.