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Carretier, J-F Ritz, J. Jackson, A. We relate reverse fault scarp morphology formed by several earthquake dislocations to the average deformation rate, using a morphological dating model based on a diffusion analogue of erosion. Our scarp degradation model includes diffusive erosion during the interseismic period, the gravitational collapse of the coseismic fault scarp just after formation, and the variation of the surface rupture location. Interactions between thrusting and geomorphic processes acting on scarp morphology are analysed along the Gurvan Bogd Range in Mongolia. Four main processes acting on scarp morphology were distinguished: 1 gravitational collapse of the frontal scarp, resetting the diffusive scarp if fault offsets are big and faulting is localized; 2 progressive erosion of the fault scarp during the interseismic period; 3 folding associated with the frontal thrust and backthrusts; 4 competing alluvial deposition on mountain piedmont slopes and abrasion of the fault scarp by wash processes. The growth of cumulative reverse fault scarps is suppressed when they are located in the outwash of major drainage basins.
Read and the morphological word tools, charsctenra tion, dating of cumulative reverse fault. Received date method uses remote sensing data for 14c dating of degraded normal fault scarps: la: 55 geophysicaljournalinternational gji morphological. Cave morphology. Workshop on the gurvan bogd fault, morphologic evo. Date: 55 geophysicaljournalinternational gji morphological dating models for morphologic evo. In volume 18 on several earthquake dislocations to examine the timing of its height. Ages of the automatic diagnosis of the morphological dating rupture events on mapping, dating of morphotectonic markers: may 13, concordances, and.
Faraday believes the rio grande rift. Ground fault circuit interrupter hook up Py: examples from three adjacent fault scarp underlain by paleomagnetic methods as tripping and. Reference: morphologic dating of coseismic calcite veins in this is transport rate along the rio grande rift. Ages of degraded normal faults. Morphometric dating of fault segments. Direct dating of local facies belts orientation.
Yet this morphology and error. For large offset increments on the other hand, misfit increases with the number of events because gravitational collapse affects a larger part of the scarp and is not taken into account by CU modelings. Figure 5 shows that the misfit between the true values and those estimated from the CU model decreases with increasing number of events for small values of dh. This behavior is different from the previous case involving vertical faults in the numerical model.
This surprising result can be explained by the competitive morphological effects of the gravitational collapse and the shortening by reverse displacement. On the other hand, the gravitational collapse, enhanced by reverse displacement, favors the preservation of a large slope at the center of the profile after diffusion.
Consequently, the maximum slope in the reverse fault case is greater than in the vertical fault case Figure 6. Arrowsmith et al. However, these morphological misfits are reduced when a reverse movement is involved Figure 6c. Thus this result suggests that a reverse fault scarp is better approximated by the CU model than a vertical fault scarp, for which the model was designed. For large offset increments, estimates are better than for a single vertical fault compare Figures 4 and 7.
Large offsets favor the scarp degradation by gravitational collapse, which affects a narrower portion of the scarp when the fault steps Figure 2case C. Gravitational collapse tends to make the synthetic profiles more symmetrical, while preserving a large portion of the scarp from resetting.
Consequently, scarp profiles computed with CU model poorly fit the studied synthetic profiles. Moreover, while the misfits are similar to those of case 3 compare Figures 7 and 8results are significantly better for large offsets increments, and for increasing number of events. This is once again due to the scarp constriction related to reverse faulting.
The overestimate increases with the value of dh and the number of events. This result is consistent with what we learned from studies of one event scarps.
These results suggest that neglecting gravitational collapse when modeling vertical fault scarps is valuable since rupture position varies and offset increments are lower than 3 m.
This effect dominates when the degradation coefficient increases. Consequently, a scarp evolving with a reverse fault and long interseismic durations displays a lower apparent degradation state coefficient than a scarp evolving with a vertical fault. The misfits follow the same behavior as for the single fault models Figures 10a and 10b. However, estimates are better because the variable location of the rupture preserves the scarp from gravitational collapse.
Moreover, some of the tested cases may be strictly theoretical, with a poor fitting with reality. On the other hand, they may represent extreme cases of real scarp morphologies, as suggested by our parametrical study of the numerical model behavior Figure 2. Our results may consequently be enlarged to other tectonic scenarios, that have the same effect in terms of scarp morphology. For example, secondary fractures associated with a main fault do not appear in the scarp morphology if gravitational collapse is efficient enough.
It should also be noted that the forward stepping of a vertical fault may also represent the successive reactivations of a terrace riser by pulses of lateral incision of a river [e.
The folding associated with reverse faulting has not been taken into account in our study. Generally, folding leads to an overestimate of the degradation coefficient, because it gives an apparently more degraded morphology than the reality. Therefore, this geomorphic factor should affect the validity of a simple model applied to real case. Consequently, our results should not be extended to scarps strongly controlled by folding. Formally, our results suggest that no process can be neglected, because estimates are always shifted from the true values.
In some cases, the shift can be small. In most cases, uncertainties on the dating techniques e. Figure 11 illustrates the most striking results we obtained: the more simple model CU model gives better estimates of the degradation for dipping faults than for vertical faults, and remains valid for some stepping fault cases, although CU model is based on a one vertical fault assumption.
This suggests that different faulting combined with different degradation processes may produce similar scarp morphologies. However, this lack of uniqueness in scarp modeling can be used positively. It allows us to neglect some processes for which the parameters are difficult to estimate with accuracy on the field for instance the fault dip or the incremental offset values. Similarly, a relative error can be estimated for the IU model. Generally, our results can provide estimates of the error expected when unknown parameters are neglected.
However, the errors given in this study are only valid for a whole profile inversion. The shifts could be greater if the degradation coefficients have been estimated from the maximum slope only in particular for the CU model [ Arrowsmith et al. On the one hand, scarp degradation modeling have been used to estimate a degradation coefficient of one event scarp or cumulative scarp from their whole morphology [e. In the case of cumulative normal fault scarps, Avouac and Peltzer  showed that the scarp morphology, and consequently its apparent degradation state, depends on the dip of faults that is difficult to estimate on the field without cross section of a scarp.
They avoided this difficulty by comparing the reduced scarps slopes versus total offset for a significant number of scarps with those of synthetic profiles generated by a model accounting for a variable dip of faults and number of events.
Morphology in archaeology, the study of shapes and forms, and their grouping into period styles remains a crucial tool, despite modern techniques like radiocarbon dating, in the identification and.  Degradation morphology of scarps can be used to estimate the age of an episode of uplift: linear diffusion models for slope degradation. Morphological integration predicts that correlated characters will coevolve; thus, each distinct suite of correlated characters might be expected.
This process allowed the authors to bound the degradation coefficient of the studied normal fault scarp. Our results suggest that for reverse faults the fault dip is important as well for reverse faults, especially if the faulting occurs at the same location. On one hand, decreasing fault dip in normal faulting enlarges the fault scarp and limits therefore the effect of gravitational collapse, thus decreasing the maximum slope.
On the other hand, decreasing fault dip in reverse faulting leads to a scarp constriction and favors the scarp resetting by gravitational collapse, thus increasing the scarp maximum slope. Moreover, because the scarp reactivation at each event does not occur always at the same location [e. This is particularly expected in the case of reverse faults and in this case, the degradation coefficient should be estimated rather from whole scarp profile.
In particular, the CU model is a better approximate of reverse fault than vertical fault, because the gravitational collapse balances the effect of fault dip. Moreover, we provided another solution of the diffusion equation accounting for repeated offsets and variable fault locations. Our results suggest that this model of intermediate complexity is valid for most of the cases.
Our results may be used in specific studies to estimate the expected error on the calculated degradation coefficient using these two simple models and thus to evaluate the necessary level of complexity required for the dating model. Avouac and an anonymous reviewer whose reviews improved greatly this paper. We are grateful to J.
Verdun for numerical discussions. VolumeIssue B If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username.
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Abstract  Degradation morphology of scarps can be used to estimate the age of an episode of uplift: linear diffusion models for slope degradation provide analytical solutions relying on simplified geometry and kinematics.
Introduction  Estimation of the uplift rates in active areas, as well as the age of landscapes, can be inferred from the degradation morphology of escarpments [e. Reverse Fault Scarp Evolution  Scarps are submitted to slope erosion and may be incised locally by gullies. Figure 1 Open in figure viewer PowerPoint. We took profiles far enough from drainages to ensure that main gradient is oriented normal to the fault, so that 1-D modelling can adequately reproduce the main direction of sediment flux.
We attempt to interpret the discrepancies between our model and the data according to the influence of other geomorphic processes that we can identify. Four approaches are possible to model the evolution of scarp morphology on active faults: 1 the scarp morphology is assumed to be controlled by elastic displacements of the surface related to dislocation at depth e. King ; Stein ; Taboada ; 2 the scarp is assumed to be controlled by surface rupture and slope erosion processes e.
Culling ; Nash ; Avouac ; Arrowsmith ; 3 the scarp evolution is controlled by both effects 1 and 2 e. Arrowsmith ; 4 the scarp morphology is assumed to be controlled by slip between stratified deposits of different rheology Nino We chose the second approach which involves imposing the surface rupture and modelling the erosion of scarps using a linear diffusive analogue.
We did this for several reasons: 1 our goal is to date scarps using the erosion of their morphology; 2 elastic dislocation models are very sensitive to the fault geometry and depth King ; Arrowsmithwhich are not well constrained in our area. Therefore, the width of our topographic profiles is short several m compared to the length of the faults 10—20 kmso the effect of the elastic dislocation modelling is diminished Arrowsmith ; 3 scarp morphology depends on interactions between successive alluvial deposits and the seismic cycle.
In most of the cases we discuss, uplifted and preserved surfaces do not correspond to single surfaces that can be modelled by an elastic dislocation model. Morphological dating is the process of comparing modelled and observed profiles to determine the age of the landform.
We use a linear diffusion analogue to describe scarp erosion preserved from runoff processes portions of fault scarps located between incisions. In this case, the transport law is that the local flux of sediments is proportional to the local topographic slope Culling We assume that material of faulted alluvial fan has been always available for transport. This is consistent with non-cohesive alluvial sediments observed on the field.
Thus, assumption of transport limited conditions and application of the continuity equation for sediment flux will result in a diffusion-like equation relating the local erosion rate and the local topographic curvaturewhere h is elevation at point xand t the time. In this case the unknown parameters controlling erosion and tectonics are multiplied by the number of events.
This is even more difficult in the case of cumulative reverse faults because of the variability of the surface faulting itself. Numerous descriptions of trenches across reverse active faults show that the position of the rupture at each event is usually variable, unlike most cases of normal faulting see for example McCalpin,pp. Along the Gurvan Bulag ranges, the position of the event trace at the base of cumulative scarps and trench observations suggest that the rupture steps forward in each event Figs 2 and 5.
Hanks proposed a simple analytical model for dating cumulative scarps, involving diffusion of continuous uplift on a fixed and vertical fault. His model cannot be applicable in such cases. We thus introduced some extra complications in our model allowing the position of each rupture, which can be variable in each event, and the fault dip at the surface to be specified Fig.
We also allow the surface slope to collapse after a surface rupture when the slope exceeds the slope angle of repose of the non-cohesive material.
Gravity-controlled failure of scarps has been well described and is common when faulting occurs in non-cohesive material Wallace ; Machette leading over several years to a gravity-controlled face that forms after the collapse of the hangingwall-wedge by a normal fault whose position can be variable McCalpinp. The gravitational collapse is not a diffusive process.
It is driven by internal friction of unconsolidated material Roering We observed that this process is a strong controlling factor of scarp evolution. For example, Fig. This process affected a large part of the scarp, which consequently lost its diffusive morphology. The resulting gravity-controlled face will then erode by diffusion until the next surface rupture.
The future diffusive morphology will only provide information about the age of the event. Consequently, it is clear that this process is a strong limitation for dating of the initiation of uplift.
Along the Gurvan Bulag range, the vertical height of the gravity-controlled face acquired several months after the dislocation is variable, even between places separated by only a few hundred of metres compare for example profiles P5 and P2, Fig.
These observations show that slope collapse can refresh reverse fault scarp morphology to varying degrees, and consequently it must be taken into account in our morphologic dating model. Some authors used forward modelling in which gravitational collapse is computed at the same time as diffusion e.
Arrowsmith This is very useful to estimate slip rates when processes are demonstratively continuous. In the case of repeated faulting with large offsets, the possible variation of the surface rupture location and the variable degree of frontal collapse impose to respect the succession of geomorphic processes.
Modelling of reverse faulting and scarp erosion. Three stages can define the geomorphic evolution of a reverse fault scarp: 1 instantaneous collapse of the hanging wedge due to reverse movement, 2 development of a gravity-controlled face at the angle of repose of the material over several years. At the end of this stage, material is equally distributed between hangingwall and footwall. The surface rupture is modelled by a translation of the profile in the hangingwall according to specified dip of fault and vertical offset and from the middle of the hanging-wedge.
The gravitational collapse is modelled by reducing all slopes greater than the specified slope of repose. These two steps preserve the mass-balance between hangingwall and footwall. In summary, we model topographic scarp profiles as follows Fig.
This choice allows to preserve the mass-balance between eroded material from the hangingwall and the deposited sediment in the footwall at the end of the next modelling step, whatever the position of the normal fault is, until its dip is greater than the critical slope Fig.
This modelling preserves the shortening associated with the reverse component. Although gravitational collapse is not a diffusive process, this numerical method enables to respect mass balance of transport. It also enables us to reduce slope instantaneously by using a sufficiently high diffusion coefficient. The transport-limited condition implies that this process affects all slopes greater than the angle of repose, and thus that the free face formed just after the earthquake is very quickly degraded.
This is consistent with our field observations. Synthetic cumulative scarps profiles are calculated by repeating these four stages. They differ by the relative magnitude of parameters. The inherited diffusive scarp morphology may or may not be preserved when a new seismic event occurs. This depends on gravity-driven processes that tend to maintain scarp slopes at the angle of repose of detritic material, resetting the diffusive scarp morphology.
In terms of morphological dating, such resetting is equivalent to resetting the clock. Indeed, large offsets and repeated surface rupture at the same place Fig. In this case, the gravity-controlled height exceeds the true value of the vertical component associated with a single surface rupture. As mentioned previously, such behaviour has been observed along the Gurvan Bulag range see Fig. This effect can have important implications in palaeoseismology, as well as for scarp morphology and dating.
When estimating the vertical component of a surface rupture from the total vertical height of the gravity-controlled face, this effect will lead to an overestimate of the last vertical offset.
This suggests that offsets along the Gurvan Bulag range could have been overestimated by Kurushin when using height of the gravity-controlled face e. Kurushin site 17, p. By contrast, distinct forward-stepping faults with small offsets preserve the diffusive scarp morphology Fig. Between these two extremes cases, we obtained a lot of different morphologies which can not be summed up in a general graph.
These morphologies differ by their relative record of past events. Thus, preservation of diffusive morphology depends on local factors which must be evaluated in the field and by modelling.
Schematic results of numerical modelling for two extreme cases. In case A the reverse component of faulting removes a part of inherited diffusive morphology at each event so that gravity-driven collapse of slope after each surface rupture resets the diffusive fault scarp morphology.
Repeated localization of the rupture in the same place and high incremental offsets enhance this effect. Consequently, the vertical height of the gravity-controlled face exceeds the value of the incremental offset.
In case B, forward stepping of successive dipping faults and low incremental offsets values preserve the diffusive scarp morphology. Consequently, it is clear that dating the beginning of the ramp formation is not always possible. In the worst cases, we can only date the penultimate event in this case, the event before This is in contrast to the case of repeated normal faulting. Although development of a gravity-controlled face can occur in both cases, in normal faulting the increase of the scarp length distance between two symmetrical points in the hangingwall and in the footwall preserves diffusive scarp morphology.
By doing this, we retained the same criterion proposed by Avouac and used by other authors e. This criterion has been used to determine an objective estimation of the precision with which morphological ages are estimated, taking into account topographic levelling with precision of about 5 cm. The levelling of our profiles has been made by differential GPS method which is accurate to less that 5 cm.
Consequently, this value is adapted to define confidence intervals of morphological ages estimated in this study. We apply the same method to convert morphological ages into numerical ages or slip rates.
Morphological age is not the only parameter which controls the accuracy of fittings between observed and modelled profiles. The determination of the best fitting morphological age and uncertainty requires estimation of several parameters such as number of events, the incremental offsets, the dip of the faults, their location, the angle of repose of material, and the regional initial slope of the profile.
Some of these parameters can be evaluated from field data, namely the regional slope corresponding to the portion of profile far from the scarp, and the angle of repose which is given by the portion of the scarp associated with the event. Other parameters are more difficult to determine. For example, the dip of the faults and their location remained uncertain in most of the cases.
A trench across a fault scarp, which is necessary to determine the fault geometry, has not always been possible, especially when scarps are several metres high. Consequently, the solution given for each modelled profile should not be unique. Therefore, estimated morphological ages and their uncertainty should depend on the assumptions made about fault geometry, values of incremental offsets and number of events.
Keeping this in mind, we fix these parameters using morphological arguments, and compare our results with previous estimations of slip rates and time recurrence intervals based on cosmogenic dating of uplifted surfaces in our study site Ritz As Arrowsmith as well as others showed e.
Best fitting morphological age and uncertainty determination. Both models use four successive stepping faults and 3. To obtain this profile, we adjusted the location of the vertical faults so that inflections of its slope profile corresponds with those of the reference slope profile, as we would do when modelling real data.
Reference profile is sampled at constant intervals and taken as data. Reference profile is taken as data.
Volume 30, Number 4, August-October I 1 Morphological and Geological. Dating of Early Hominid. Fossils Compared,. M. HENNEBERG. Department of. Summary. We relate reverse fault scarp morphology formed by several earthquake dislocations to the average deformation rate, using a morphological dating. Here, we exploited the advantage of Bayesian tip dating under relaxed morphological clocks to estimate both the divergence times and.
The different RMS curves were obtained using either all interseismic durations as free parameters, or only one of them. It shows that uncertainty grows when the parameter search procedure is applied to only one interseismic duration. Consequently, to estimate the number of events, we divided the cumulative offset by this incremental offset.
We assume that the fault responsible for the surface ruptures steps forward at each event.
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We have no direct evidence of this behaviour for the studied profiles because it has been impossible to trench across scarps which can reach 20 m height. However, some other trenches across reverse fault scarps around the Gurvan Bogd range displayed such pattern, while some other showed unique faults or more complex geometry Bayasgalan ; Bayasgalan We argue for a forward stepping of the faults from the scarp morphology: first, the portion of the scarp associated with the more recent event is generally located at the front of scarps Fig.
This suggests that the upper part of scarps is more degraded and thus older than the lower one. Such morphology may also result from the ridding of the hangingwall over the land surface by the way of a flat fault, prolongating a shallow ramp fault geometry.
In this case, the frontal part of the scarp would correspond to the propagating flat fault. Thus, the slope of the frontal scarp would be lower than the slope of repose of the material, especially in the case of one event scarps.
Although this hypothesis can not be rejected by direct evidence, morphological arguments seem to favour the stepping of successive faults.
To determine the location of the successive faults responsible for the surface rupture requires one to look at slope profiles. A surface rupture associated with a seismic event causes an abrupt perturbation of the slope profile. Consequently, we can estimate the location of the successive faults from the slope profile independently of the morphological age, in such a way that the locations of observed and modelled slope inflections fit.
The dip of faults is one of the parameters controlling the gravitational collapse of the scarp, and thus the preservation of the diffusive scarp morphology Fig. This parameter cannot be evaluated in this study. However the estimation of the best fitting morphological age does not depend on this parameter when the morphology associated to past events is preserved see Appendix AFigs 1ab. The incremental offset and the number of events are estimated from the elevation profile, and the slope of repose and the regional slope are estimated from the slope profile.
The slope of repose is estimated from the mean slope of the gravity-controlled face rather than local maximum. The successive fault locations are estimated from the slope profile. Forward modelling assuming non-vertical faults is carried out to evaluate if the scarp could have been reset during the uplift. This step aims at determining whether the initiation of the uplift or only the last events can be dated see Fig. We apply this methodology to the examples previously described.
In each case, the RMS between observed and modelled profiles is computed only on the apparent diffusive portion of the scarp. As mentioned earlier, cosmogenic dating of uplifted alluvial fans allowed Ritz to propose that seismic activity resumed on this fault from at least the deposition of surface s3 dated at By the morphological dating of cumulative reverse fault scarps, we want to date the beginning of the uplift of the older surface s2 deposition at Morphological dating from Profile P3 see Fig.
Triangles are data and solid lines are models for the best fitting morphological age, using two events of 3. The RMS is calculated from the elevation data, over the length corresponding to the diffusive morphology horizontal arrow on the elevation profile. This profile is levelled across surface s4, uplifted 6. This cumulative offset is twice the vertical offset of the event 3.Morphology: Dividing words into morphemes
The gravity-controlled face associated with the event is located at the front of the scarp, allowing to preserve the diffusive morphology associated with the last interseismic period.
The mean morphological age of the penultimate event is thus Ritz estimated the age of the uplifted surface s4 at this place to be 4. Morphological dating from profile P1 see Fig.
Triangles are data and solid lines are models for the best fitting morphological age, using four events of 3.
This profile is levelled across surface s2, uplifted between 14 m and 18 m Figs 4 and 5. The gravity-controlled face is localized at the base of the scarp and most of the inherited diffusive morphology is preserved, allowing us to estimate the morphological age of the cumulative uplift Fig. We identified on profile P1 the folding component of the uplift, which seems to not affect the slopes near the fault scarp Fig.
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The decreasing slope from the bottom to the top of the scarp and the frontal location of the gravity-controlled face suggest that the rupture stepped forward Fig. Using 4 events with 3.
The mean value of the morphological age at the profile P1 location three interseismic periods is If we use the coefficient of diffusion calibrated from the profile P3, we date the initiation of the uplift responsible of the cumulative offset of surface s2 at The uplifted surface s2 being dated at Over the last This value is consistent with the previous estimate at 1.
Morphological dating from profile P6 see Fig. Triangles are data and solid lines are models for elevation and slope profiles. The models correspond to four events of 4. Using faults 40 m, 10 m and 27 m apart to respect the location of inflections of the slope profile, the modelling suggests that the fault scarp collapsed at the time of the third event. Modelling suggests that it corresponds to the Gaussian shape of the slope gradient profile.
The RMS between observed elevation and modelled profiles is thus calculated only for this part of the elevation profile horizontal arrow on the elevation profile. The first step of 40 m is a un-successful attempt to explain the slopes between m and m. In fact we interpret this part of the profile to be caused by the folding component of the scarp morphology. This profile is levelled across surface s2, uplifted 17 m, in front of a major drainage basin Figs 4 and 12 Just as we detected 4 events on profile P1 responsible for the uplift the surface s2, we modelled the cumulative offset on profile P6 also using 4 events, with vertical incremental offsets of 4.
The gravity-controlled face is located at the base of the scarp, suggesting a forward stepping of the fault. The slope profile shows a peak corresponding to the gravity-controlled face, followed by a roughly gaussian shape.
Our numerical experiments suggest that the fault scarp collapsed between each event prior to Coseismic scarp resetting occurs at each event because of the high offsets and because the fault steps at this locality adjusted to fit the locations of inflexions on the slope profile is smaller than at the location of profile P1 Fig. Only the event allowed to preserve remaining diffusive morphology because it is located far from the penultimate rupture.
This suggests that the remaining diffusive morphology has developed from the penultimate event, from a stage where the scarp was dominated by the stable gravity-controlled slope. This value is determined from the RMS curve at Moreover, the morphological age of the penultimate event on profile P6 is much greater In order to explain this, we suggest two possibilities: 1 the morphologic age calculated from profiles P1 and P3 could be underestimated. Folding tends to increase the scarp slopes and thus decrease the morphological age.
While the folding can increase the scarp slopes, it can broaden the part of scarp profile apparently eroded, making it older morphologically. Therefore, offsets that we use to model the cumulative offset of P6 may also be too high 4. It is difficult to evaluate the contribution of folding to the cumulative offset on P6, because this folding is masked by alluvial sedimentation, that leads to a constant slope in the hangingwall.
However, the cumulative offset estimated from profile P6 is similar to the maximum cumulative offset given by profile P1 18 m.
The maximum offset on P1 includes the folding component of the uplift, which appears more clearly than for profile P6. The overestimate due to folding and offset values is likely to be predominant here.
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