The advance in obtaining fault slip rate of strike slip fault-A review

Jinrui Liu ,Zhikun Ren,＊ ,Wei Min ,Guanghao Ha ,Jinghao Lei

a State Key Laboratory of Earthquake Dynamics,Institute of Geology,China Earthquake Administration,Beijing,China

b Key Laboratory of Seismic and Volcanic Hazards,China Earthquake Administration,Beijing,100029,China

Keywords:Slip rate Strike-slip fault Active tectonics Monte Carlo Paleoslip analysis

ABSTRACT Slip rate along the major active fault is an important parameter in the quantitative study of active tectonics.It is the average rate of fault slip during a certain period of time,reflecting the rate of strain energy accumulation on the fault zone.It cannot only be directly applied to evaluate the activity of the fault,the probabilistic seismic hazard analysis,but also important basic data for the study of geodynamics.However,due to the nonstandardized process of obtaining fault slip rates for a given strike-slip fault,the results could be diverse based on various methods by different researchers.In this review,we analyzed the main advances in the approaches to obtain fault slip rate.We found that there are four main sources affecting the final results of slip rate:the displacement along the fault,the dating of the corresponding displacement,the fitting of the displacement and corresponding dating results,and paleoslip analysis.The main advances in obtaining fault slip rates are based on improving the reliability of the above four main factors.To obtain a more reasonable and reliable slip rate for a given fault,it is necessary to select a suitable method according to the specific situation.

1.Introduction

The slip rate of a strike-slip fault is the average slip of fault movement in a certain period of time,which reflects the rate of energy accumulation on a strike-slip fault zone,and can be applied to the probability evaluation of seismic risk (Molnar and Tapponnier,1978;Zhang et al.,2008).The fault movement is based on the elastic rebound theory conceptually(Reid,1910) where elastic strain energy accumulates across a locked fault until a critical threshold is reached,at which time the stored energy is‘instantaneously’released as seismic waves(Gold et al.,2017;Scholz,2019).During this process,the surface drainages,ridges,river terraces or their intervening risers,alluvial fans,moraines,shorelines,and other landforms crossing the fault will be displaced along the relative movement direction of the two walls of the fault.These offset geomorphic markers can be preserved for thousands of years or even longer under appropriate external conditions,to record the displacement and movement sense on the surface during the earthquake (Fig.1).Considering that the linear landform can be easily restored to its original shape and position,the identification of these linear geomorphic markers is an effective means to quantify the amount of seismic deformation (Dong,2015).At present,it is generally used to calculate the slip rate of active strike-slip faults based on the accumulated displacements of the offset landforms and the corresponding ages (Sieh and Jahns,1984;Weldon and Sieh,1985;Zhang et al.,2008).Because the corresponding cumulative time is difficult to measure directly,it is often constrained by the age of the geomorphic surface.

Fig.1.Linear offset geomoephic features of strike-slip fault,such as scarps,offset ridges,sag ponds,shutter ridges,and drainages,springs,and beheaded streams(Burbank and Anderson,2011).

The slip rate along the strike-slip fault is not only one important quantitative parameter to constrain the deformation of the block and the mechanism of continental dynamics,but also its patterns along fault strike are helpful for understanding the strain accumulation-release model (Resor et al.,2018;Zechar and Frankel,2009).The decreases of slip rate at the terminals of strike-slip faults are widely observed all over the world.The slip rate is relatively stable at～10 mm/yr along the main segment of the Altyn Tagh fault zone and rapidly decreases at 94°E,which is considered that the NW-trending mountains to absorb the left-lateral slip through crustal thickening(Meyer et al.,1998;Xu et al.,2005;Zheng et al.,2013).The crustal thickening of the Anyemaqen Mountain accommodating the eastern slip rate along the Kunlun fault lead to the decrease of the slip rate from～10 mm/yr to<1 mm/yr(Kirby and Harkins,2013).The Haiyuan fault also conforms to this situation,in which the uplift of Liupanshan-Madong mountain contributes to the decrease of the slip rates(Liu et al.,2018;Zheng et al.,2013).Similarly,the slip rate is relatively stable at～27 mm/yr along the central part of the Alpine fault zone and rapidly decreases from～27 mm/yr to～6.3 mm/yr at the end (Norris and Cooper,2001).The late Quaternary slip rates of the Death Valley–Fish Lake Valley fault decrease northward and southward from the central segment,which transfers into several normal faults(Frankel et al.,2007,2011).The slip rates of the Denali fault decrease from 13 mm/yr to 7 mm/yr towards the northwest and transfers into the active folds and thrust belts at the front of Alaska area (Fletcher and Freymueller,2003;Freymueller et al.,2008;Matmon et al.,2006;Mériaux et al.,2009).Therefore,the kinematic information of tectonic deformation contained in the fault slip rate is an important basis to restrict.

However,due to the non-standardized process of obtaining fault slip rates,for a given fault,the results could be diverse based on various methods used by different researchers.To improve the reliability of slip rate results,four factors need to be considered:the offset,the dating of the corresponding offset,the relationship between these two parameters,and paleoslip analysis.

Fig.2.Schematic diagrams showing high-resolution terrain data acquisition methods.

2.Advances in measurment of the displacement

2.1.High-resolution topographic data

With the rapid development of topographic data,such as highresolution digital elevation models (DEMs) derived from LiDAR (Light Detection and Ranging) data,UAV (Unmanned Airborne Vehicle) surveys,and stereo pairs of remote sensing imagery (Johnson et al.,2014;Mackenzie and Elliott,2017;Ren et al.,2013,2016;Stewart et al.,2018;Wang et al.,2019;Westoby et al.,2012;Zielke et al.,2010,2015),we can better constrain the offsets of terrace risers,channels,etc.,precisely in three dimensions (3-D) compared with using a simple tape measure in the field(Fig.2).

2.2.Lidar technology

In recent years,LiDAR technology has developed rapidly,with the advantages and characteristics of high spatial resolution,penetrating vegetation and directly acquiring real surface 3-D information.It provides a new technology means for fast acquisition of high-precision topographic and geomorphic data along active faults (Oskin et al.,2012;Ren et al.,2016;Zielke et al.,2010).Hudnut et al.(2002) firstly applied LiDAR topography in active tectonics to scan the surface rupture of 1999 Hector Mine,California earthquake.Since then,the pioneering B4 San Andreas fault system scan (Bevis et al.,2005) and the Geo-EarthScope project (Prentice et al.,2009) have been carried out successively,which is of milestone significance to the development of earth science.High-resolution 3-D data can provide basic data for the complexity of fault geometry and the details of offset geomorphic markers,which is very essential to constrain the slip rate of strike-slip faults.Lidar measurement technology,with its advantages of high-resolution,omnidirectional and direct and rapid acquisition of 3-D space information on the target surface,can provide high-precision basic data of geomorphic elevation along the whole fracture zone for the study of active structure.

2.3.UAV photogrammetry 3-D reconstruction

UAV photogrammetry and 3-D reconstruction use a large number of photos of a given target taken from multiple advantageous locations to estimate the scene structure and generate a seamless texture map.By measuring the length and displacement of the fault,rich deformation characteristics can be obtained,which can be used to study the seismic surface rupture style,fault kinematic parameters and geomorphic evolution process.Through UAV survey of typical displaced geomorphic units,DEM data with the resolution better than 0.1 m can be generated,and its vertical accuracy is about 10～15 cm.It can better reflect the fine structural deformation characteristics of typical offset geomorphology.According to the site conditions,the micro-topography survey can be carried out in a small area of 2 km2,which can accurately outline the terrain surface geometry,and accurately measure the vertical displacement of planar landform surface(terraces,fans,etc.) and the horizontal and vertical displacement of linear landform (gullies,rivers,etc.).

2.4.Stereo image pair method of high-precision DEM data

With the development of digital photogrammetry and image matching technology,high-resolution satellite images have the characteristics of large imaging range,short acquisition period and fast update.Combined with high spatial-temporal resolution remote sensing images,photogrammetry methods have become the development trend of fast acquisition of high-precision DEM (Liu et al.,2018;Ren et al.,2018;Wang et al.,2019).Only a small number of stereo pairs are needed to obtain the topographic data of the whole study area,which greatly reduces the cost and is more conducive to obtain the aerial image data of a specific period(Wang et al.,2019).Especially for the northwest of China,the harsh climate and complex terrain conditions bring great challenges to the traditional measurement and UAV methods.However,due to the lack of vegetation coverage,the photogrammetry method of obtaining DEM from high-resolution stereo pairs can solve this problem efficiently and quickly.

2.5.The method of displacement measurement

It is an important work in active tectonics to measure the latest coseismic displacement and cumulative displacement of multiple events along active faults,which can help researchers to better understand the kinematic process and mechanism of faults(Armijo et al.,1989;Klinger et al.,2011;Zielke et al.,2010).The traditional way to obtain displacement is to tape measure it in the field.With the acquisition of image data,the fault displacement markers were identified by satellite image interpretation for manual measurement(Frankel et al.,2007;Gold et al.,2009).However,the uncertainty and error of the results obtained by a visual interpretation will make the results controversial.We can also use different GPS to measure the contour map which may identify the edge of the displaced geomor phic body,but the measurement error is still given artificially (Fig.3a).With the application of DEM data,methods and equipments for offset measurements have been greatly improved over the past decades (Zielke et al.,2010,2015),such as the LaDiCaoz code proposed by Zielke et al.(2010)and the 3-D_Fault_Offsets code proposed by Stewart et al.(2018).

As a tool in displacement measurement of strike-slip,LaDiCaoz_v2 code is based on fitting the terrain profiles cutting through a linear landform(Fig.3b).This code is specially used for the measurement of the displacement quantity of strike-slip fault.The measurement object is high-resolution DEM data.Through the user's input of fault location and upstream and downstream profile location,the profile lines parallel to the fault on both sides of the fault can be automatically generated.The current gully center line of the gully is selected as the geomorphic reference,and according to the location of two gully center trend lines and their projection on the fault,The best horizontal displacement value is identified,and the reliability of displacement can be verified by restoring the original landform before displaced (Haddon et al.,2016;Zielke et al.,2010).

The offsets can also be measured from the LiDAR DEM using the 3-D_Fault_Offsets code(Stewart et al.,2018).Ideally,the 3-D_Fault_Offsets code can identify nine topographic data points of linear markers in 3D,including ridges or crests,top,free face and base of channel banks and streambeds.By fitting best lines through point clouds on each side of the fault,lateral displacements between the piercing points can be computed.Meanwhile,from various sources of error,the total uncertainty on each offset is also provided through the Monte Carlo approach.Further,the corresponding back-slip maps are provided in the results for checking the reliability of the offsets(Fig.3C).

However,Gold et al.(2017)argue that these codes can only identify the existing terrain,but some areas of local accumulation or erosion can not be identified,which will affect the measurement results.Sometimes,artificial identification is needed.The equipment development has experienced several stages,from tape measures and plane table surveys to total station,differential GPS,LiDAR and UAV surveys.Consequently,the resolution of topographic data surveyed in the field and the precision of offset measurements have also greatly improved(Johnson et al.,2014;Mackenzie and Elliott,2017;Ren et al.,2013,2016;Stewart et al.,2018;Wang et al.,2019;Westoby et al.,2012;Zielke et al.,2010,2015).Improvement of data resolution and the progress of measuring technology can help us identify and measure more detailed displaced landform features and make better interpretations.These codes can realize semi-automatic measurement and visually show the effect of displacement recovery.The progress of these methods has reduced the error of displacement measurement,and it is necessary to choose the appropriate measurement method for different geomorphic conditions.

Fig.3.Dispacement measurement methods.(a) Obtaining contour map by differential GPS (Zheng et al.,2013);(b) Dispacement measurement process using LaDiCaoz_v2 code (Zielke et al.,2010);(c) Dispacement measurement process using 3-D_Fault_Offsets code (Stewart et al.,2018).

3.Advance in dating of the geomorphological markers

In the study of the slip rate of strike-slip faults,the displacement accumulation time of a displaced marker is often limited by the age of offset landform,so the determination of landform formation age is a critical step(Burbank and Anderson,2011;Ren et al.,2018).Considering the temporal scope of Late Quaternary rate of strike-slip faults,the commonly used dating methods include AMS14C (Accelerator Mass Spectrometry Radiocarbon Dating),OSL (Optically Stimulated Luminescence) dating,IRSL (Infrared Stimulated Luminescence) and CRNs(in-situ cosmogenic radionuclides) dating.In recent years,the dating resolution has made significant progress,especially the improvement of the mass spectrometer,which can measure less nuclide concentration,thus increasing the number of data samples(Ren et al.,2013,2018;Zinke et al.,2017,2019).The principle and process of various dating methods have been reviewed in many researches (Ren et al.,2018;Yang et al.,2020).This study focuses on how to select appropriate dating methods according to different situations,in order to more accurately limit the formation age of the geomorphic surface.

Considering the sedimentary history of the landforms,taking the river terrace as an example(Fig.4),if the terrace is completely abandoned,the sedimentation will stop and the river terrace will form,and then loess will be deposited.Ideally,if there is no sedimentary discontinuity,the bottom age of loess will be close to the top age of river terrace deposition,which can represent the formation age of the river terrace.However,if there is sedimentary discontinuity,it is difficult to constrain the accurate terrace formation age by a single age.At this time,the terrace formation age is between the age of the bottom of loess and the age of the top of river sedimentation.Before determine the formation age of offset landform,it is necessary to verify whether there is sedimentary discontinuity in the landform(Hu et al.,2017).

Fig.4.Schematic representation of different dating methods.(a) Sampling locations of luminescence dating and radiocarbon dating on the sedimentary profile of river terrace.(b) CRNs (in-situ Cosmogenic Radionuclides) depth profile method is based on the interaction between cosmogenic rays and susceptible minerals,exposed at the surface or shallow underground,of which production rate and inheritance depend on depth (Ren et al.,2018).(c) Modeled gravel and sand samples ages from step 2 of the Bayesian Age Model approach (Zinke et al.,2019).

The principle of CRNs dating is the interaction between cosmogenic rays and susceptible minerals,exposed at the surface or shallow underground.The concentration of these cosmogenic nuclides generated in surface rocks is related to the time the rocks are exposed to cosmic rays(Fig.4b).The longer the exposure time,the higher the abundance of these nuclides in rock surface samples.Therefore,this process can be used to record the exposure history of rocks.Generally speaking,the geomorphic surface samples have a certain nuclide concentration before deposition.Therefore,to obtain a more reliable geomorphic surface formation age,it is necessary to eliminate the inherited nuclide concentration before sediment deposition.By measuring the nuclide content of debris samples from different sources at the same depth,the depth profile method can well average the rock debris with different transportation and deposition history,which can well control the inheritance concentration of geomorphic surface samples.For the geomorphic surfaces undergoing serious surface erosion,more reliable exposure age of geomorphic surface can be obtained by profile fitting.

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For the multi-level offset landforms at the same research location,the Bayesian Age Model approach can provide optimum age control for the preserved offset markers,which mainly is based on sedimentological and geomorphological interpretation of the site,and the lithostratigraphic and geomorphological stratigraphic relationship between different sampling units (Rhodes et al.,2003;Zinke et al.,2017,2019).As described in Zinke et al.(2019),this method is divided into two steps and the MCMC (Markov Chain Monte Carlo) method was used in the workflow of radiocarbon calibration program OxCal_v4.4 (Ramsey,2001,2017;Rhodes et al.,2003).The first step of the Bayesian Age Model is to adjust the age probability distribution according to the relative stratigraphic sequence,and assume that the samples with higher strata are younger than those with lower strata.The second step of the Bayesian Age Model accounts for morphostratigraphic relationships among the terraces and channels,that higher terraces are sequentially older than lower ones.On the basis of the results of the first step,adjust and trim all ages probability distribution to get the modled age(Fig.4c).

4.Advance in evaluating the fitting of between the displacement and dating results

4.1.Strath terrace formation and strike-slip faulting

Geological slip rate determination is usually constrained by two input parameters,the slip along the fault and the corresponding slip accumulation time.The fault slip rate determination also depends on how well the age and displacement correlate with each other.The misinterpretation of corresponding age,however,will bring large uncertainties as with the above-mentioned different fault slip rates obtained at the same sites by different researchers(Cowgill,2007;Gold et al.,2009;Mériaux et al.,2004,2005;Peltzer et al.,1989;Van Der Woerd et al.,1998,2002;Zhang et al.,2007,2008).

In the ideal situation,such as the area where the river cuts down rapidly,the abandoned age of the upper and lower terraces is relatively close.The slip rate of the strike-slip fault can be limited to a small range.In many regions,however,the ages of the upper and lower terraces are so different that the bounds they place in the slip rate are too large to be useful.If there is a large difference between the abandoned years of the upper and lower terraces,the evolution process of the river terraces should be reconstructed according to the specific topographical parameters of the study site and the relationship between the river terraces and the strike-slip faults(Cowgill,2007;Yao et al.,2019;Zhang et al.,2007,2008).The applicable terraces model should be selected,and the abandoned ages of the terraces closer to the initial time of the accumulated displacements of the terraces should be adopted,to give an approximate value of the fault slip rate.Different researchers use different terrace reconstruction models for the same fault to get different slip rates(Cowgill,2007;Lasserre et al.,2002;Mériaux et al.,2004,2005;Xu et al.,2005;Yao et al.,2019;Zhang et al.,2007).However,due to the different erosion degree of the river flow on the terrace scarps in different areas,the lower terrace model usually gives the upper limit of the slip rate,while the upper terrace model gives the lower limit.In the weak erosion case,the ages of upper terraces should be more closely approximate the ages of the risers than those of the lower terraces(Fig.5).Therefore,the appropriate terrace reconstruction should be selected according to the actual situation.

4.2.Effects of lateral erosion

For geological bodies of one thousand years or even one hundred years,with the decrease of timescale,the uncertainty will gradually increase under the influence of lateral erosion.The method of obtaining fault slip rate from Holocene terraces requires careful analysis of the uncertainty caused by lateral erosion.

In the calculation of the Holocene slip rate of fault,the accuracy of the accumulated displacement amount and its corresponding age will have a significant impact on the calculation of slip rate,and a smaller age error will cause a larger slip rate deviation(Ren et al.,2013).In the calculation of the slip rate of strike-slip faults,the mismatch between the measured age of the geological body and the actual accumulated displacement time will cause uncertainty in the calculation of the slip rate,mainly because of whether the accumulated displacement time is consistent with the measured age of the geological body and the erosion during the formation of the geological body displacement.

In the process of terrace evolution,the method to obtain the corresponding slip rate by using the displacement and its upper and lower ages of the corresponding terrace needs to determine the starting time of the fault displacement(Cowgill,2007;Gold et al.,2009;Zhang et al.,2007,2008).The results are more accurate on the timescale close to ten thousand years or even longer.However,for geological bodies on the scale of one thousand years or even one hundred years,with the decrease of timescale,the slip rate obtained will gradually increase under the influence of lateral displacement.In order to eliminate the influence of lateral erosion,Ren et al.(2013)proposed to use the different methods to calculate the slip rate of strike-slip faults,that is,to use the difference between the accumulated displacement amount of high and low terraces and the age difference of corresponding terraces to calculate the slip rate of faults.This method can reduce the influence of lateral erosion on the slip rate of strike-slip faults to a certain extent,the reliability of the obtained slip rate is improved.Ren et al.(2013) applied this method to calculate the slip rate of Altyn Tagh fault and Kunlunshan fault,and obtained the slip rate of 4.7-8.8 mm/yr,which solves the problem of large amount of dislocation caused by lateral erosion in young geological bodies.

5.Advances in paleoslip analysis

5.1.Comprehensive analysis of multi level data

The simplest method to calculate the slip rate is from the time of a single displacement.However,due to the influence of special topography and human factors,the slip rate of a single point may have great uncertainty,sometimes it can not represent the whole fault,so multiple results need to be mutually corrected (Herbert et al.,2014;Liu et al.,2018,2019;Resor et al.,2018).The errors in offsets and dating results are independently obtained from offset measurements and dating processes,respectively.Consequently,some unreasonable errors might also be involved in the slip rate without analysis of the slip history.

Fig.5.Schematic diagrams showing the evolution of Strath terrace and strike-slip faulting (Cowgill,2007;Van Der Woerd et al.,2002;Zhang et al.,2007).

Using the offset and age data of multiple-levels geomorphic markers and comprehensively considering the rationality of slip history,a more reasonable fault slip rate can be obtained.The Monte Carlo simulation method mainly uses offset-time data to quantitatively identify the slip history and distribution (Gold and Cowgill,2011;Gold et al.,2017;Liu et al.,2018,2020).This method introduces an error rectangular window in the analysis of fault slip rate,which can quantify the error of single age and displacement measurement,that is,taking the maximum and minimum offset-age observed in geology and chronology as the boundary,The envelope of offset-time point is formed,and the rectangle surrounded by this envelope is the synthesis of all possible slip histories.Because the fault landform has experienced the same slip history and the motion sense of the fault do not reverse,the uncertainty of slip rate can be reduced by integrating the relationship between multiple offset-age envelopes.If these geological bodies have experienced the same slip history,the displacement of the old geological body must be greater than or equal to that of the young geological body,that is,the slip history cannot have a negative slope.The advantage of Monte Carlo method is that it can combine multiple offset-time data and comprehensively consider the displacement and age errors to reduce the uncertainty of average slip rate calculation.We also reanalyzed the slip rate of the specified Haiyuan fault using offset and dating results for multiple terrace levels from Li et al.(2009) and obtained smaller uncertainties of 4.5±0.3 mm/yr(Table 1,Fig.6).Compared with individual age and offset measurements,we think that using the Monte Carlo analysis method to integrate the offsets and ages of multiple terrace levels could greatly reduce the uncertainties in the fault slip rate.The uncertainties of individual displacement-time points can be large;however,the range of permitted slip histories is reduced by combining overlapping displacement-time measurements (Gold et al.,2017).

Table 1 Age and offset constraints along the Haiyuan fault.

6.Discussion and conclusion

6.1.The evaluation of different stages of slip rate results of strike-slip faults

With the improvement of the slip rate constraint method of a strikeslip fault,the results are very variable in different research stages.Lasserre et al.(1999) determined the strike-slip rate of the Lenglongling fault of 12±4 mm/yr by dating the abandoned age of offset moraines,which are 3-5 times faster than geodetic studies.In recent years,Yao et al.(2019)re-evaluated the terrace displacement at the site of Lasserre et al.(1999)using a new high-resolution DEM(digital elevation model)combined with exposure-age dating,OSL and radiocarbon,and obtained a lower slip rate of 5.0-8.9 mm/yr.The difference of slip rate in different research stages reflects the progress of technical methods and the high-resolution LiDAR data can provide finer fault information for displacement measurement.The previous higher slip rate is considered to be inclined to systematically use lower terrace reconstruction to explain the faulting age,which leads to a wrong understanding of geomorphic surface formation.Since the high slip rates along the Altyn Tagh have been reevaluated as less than～10 mm/yr(Cowgill,2007;Mériaux et al.,2004,2005;Zhang et al.,2007).

6.2.Advances in the slip rate constraint methods of strike-slip faults

The accurate average rate of fault slip is very important for the seismic dynamics and the risk assessment.It is not easy to constrain a reliable slip rate of strike-slip fault.In the past decade,the development of LiDAR technology and other high-resolution remote-sensing technologies realized the application of high-resolution terrain data to determine the displacement of large-scale active strike-slip faults.The meter to submeter scale detection and measurement of offset landform promote the improvement of strike-slip fault slip rate (Lin et al.,2020).For the multi-level offset landforms at the same research location,the Bayesian Age Model approach can provide optimum age control for the preserved offset markers.In addition to improving the resolution of age and displacement,we should pay attention to the fitting of the two parameters,and analyze and discuss according to the specific situation.Furthermore,the Monte Carlo method synthesizes the error of displacement and time,which reduces the uncertainty of slip rateobtained by previous single point data,and is more in line with the geological history process.It is suggested that the research site of multi-level offset geomorphic surface,or a small straight fault segment with the same slip history should be selected to obtain a comprehensive slip rate.

Fig.6.Reanalysis of the average slip rate of the Haiyuan fault from (Li et al.,2009).(a) Average slip rate estimation on the Haiyuan fault;(b) D-t envelopes of the Haiyuan fault.(c) 1000 slip history paths from the synthetic dataset.(d) Paleoslip of the Haiyuan fault from the Monte Carlo model.

Acknowledgements

This work is sponsored by the National Nonprofit Fundamental Research Grant of China(IGCEA1803,IGCEA1901)and the National Key R&D Program of China (2017YFC1500401).The authors thank Ryan Gold and Olaf Zielke for sharing their Matlab codes for displacement measurement and slip rate determination.