Analysis of Scarp Profiles: Evaluation of Errors in Morphologic Dating

Morphologic analysis of scarp degradation can be used quantitatively to determine relative ages of different scarps formed in cohesionless materials, under the same climatic conditions. Scarps of tectonic origin as well as wavecut or rivercut terraces can be treated as topographic impulses that are attenuated by surface erosional processes. This morphological evolution can be modelled as the convolution of the initial shape with erosion (or degradation) function whose width increases with time. Such modeling applies well to scarps less than 10m high, formed in unconsolidated fanglomerates. To a good approximation, the degradation function is Gaussian with a variance measuring the degree of rounding of the initial shape. This geometric parameter can be called the degradation coefficient. A synthetic experiment shows that the degradation coefficient can be obtained by least squares fitting of profiles levelled perpendicular to the scarp. Gravitational collapse of the free face is accounted for by assuming initial scarp slopes at the angle of repose of the cohesionless materials (30°–35°). Uncertainties in the measured profiles result in an uncertainty in degradation coefficient that can be evaluated graphically. Because the degradation coefficient is sensitive to the regional slope and to three-dimensional processes (gullying, loess accumulation, stream incision, etc.), a reliable and accurate determination of degradation coefficient requires several long profiles across the same scarp. The linear diffusion model of scarp degradation is a Gaussian model in which the degradation coefficient is proportional to numerical age. In that case, absolute dating requires only determination of the propotionality constant, called the mass diffusivity constant. For Holocene scarps a few meters high, in loose alluvium under arid climatic conditions, mass diffusivity constants generally range between 1 and 6 m^2/kyr. Morphologic analysis is a reliable method to compare ages of different scarps in a given area, and it can provide approximate absolute ages of Holocene scarplike landforms

Active Tectonics in Southern Xinjiang, China: Analysis of Terrace Riser and Normal Fault Scarp Degradation Along the Hotan-Qira Fault System

The northern piedmont of the western Kunlun mountains (Xinjiang, China) is marked at its easternmost extremity, south of the Hotan-Qira oases, by a set of normal faults trending N50E for nearly 70 km. Conspicuous on Landsat and SPOT images, these faults follow the southeastern border of a deep flexural basin and may be related to the subsidence of the Tarim platform loaded by the western Kunlun northward overthrust. The Hotan-Qira normal fault system vertically offsets the piedmont slope by 70 m. Highest fault scarps reach 20 m and often display evidence for recent reactivations about 2 m high. Successive stream entrenchments in uplifted footwalls have formed inset terraces. We have leveled topographic profiles across fault scarps and transverse abandoned terrace risers. The state of degradation of each terrace edge has been characterized by a degradation coefficient τ, derived by comparison with analytical erosion models. Edges of highest abandoned terraces yield a degradation coefficient of 33 ± 4 m^2. Profiles of cumulative fault scarps have been analyzed in a similar way using synthetic profiles generated with a simple incremental fault scarp model. The analysis shows that (1) rate of fault slip remained essentially constant since the aggradation of the piedmont surface and (2) the occurrence of inset terraces was synchronous at all studied sites, suggesting a climate-driven terrace formation. Observation of glacial and periglacial geomorphic features along the northern front of the western Kunlun range indicates that the Qira glaciofluvial fan emplaced after the last glacial maximum, during the retreat of the Kunlun glaciers (12–22 ka). The age of the most developed inset terrace in uplifted valleys is inferred to be 10 ± 3 ka, coeval with humid climate pulses of the last deglaciation. The mass diffusivity constant (k=τ/T, being time B.P.) in the Hotan region is determined to be 3.3 ± 1.4 m^2/10^3 years, consistent with other estimates in similar climatic and geologic environments of western China. These results imply a minimum rate for the Tarim subsidence of 3.5 ± 2 mm/yr. If Western Kunlun overthrusts the Tarim platform on a crustal ramp dipping 40°–45° to the south, it would absorb at least 4.5 ± 3 mm/yr of convergence between western Tibet and Tarim

Holocene Hydrological Changes Inferred from Alluvial Stream Entrenchment in North Tian Shan (Northwestern China)

We analyze the possible contribution of climate change or tectonics on fluvial incision from the study of a case example along the northern flank of Tian Shan. The rivers that exit the high range fed large alluvial fans by the end of the last glacial period. They have since deeply entrenched the piedmont by as much as 300 m. We have surveyed several terraces that were cut and abandoned during river entrenchment, providing information on intermediate positions of the riverbed during downcutting. They suggest a gradual decline in river slope during a major phase of incision throughout the Holocene. Tectonic uplift affects only a zone about 5 km wide, corresponding to a growing anticline, and is shown to account for about 10% of total incision. Incision was therefore most probably driven by climate change. From observed fluvial incision, we estimate the water discharge in excess of that needed to carry the sediments supplied by hillslope erosion in the headwaters. We used a model based on a transport‐limited erosion law. The model predicts relaxation process with entrenchment in the upper reach, downstream progradation of the incision‐sedimentation line, and a progressive decrease of river slope during incision consistent with our observations. According to this model, river slope might be used as a proxy for specific discharge and then for volumetric discharge, provided that an assumption is made about river width variations. We conclude that river incision in the study area has resulted from dynamic adjustment of the hydrological system to the settlement of wetter conditions in the early Holocene, when water discharge might have been about three times as high as at present. Then, a rather arid climate with enhanced seasonality has likely prevailed from the mid‐Holocene (~6 ka B.P.) until now

Coseismic surface deformation from air photos: The Kickapoo step over in the 1992 Landers rupture

Coseismic deformation of the ground can be measured from aerial views taken before and after an earthquake. We chose the area of the Kickapoo-Landers step over along the 1992 Landers earthquake zone, using air photos (scale 1:40,000) scanned at 0.4 m resolution. Two photos acquired after the earthquake are used to assess the accuracy and to evaluate various sources of noise. Optical distortions, film deformation, scanning errors, or errors in viewing parameters can yield metric bias at wavelength larger than 1 km. Offset field at shorter wavelength is more reliable and mainly affected by temporal decorrelation of the images induced by changes in radiometry with time. Temporal decorrelation and resulting uncertainty on offsets are estimated locally from the correlation degree between the images. Relative surface displacements are measured independently every about 15 m and with uncertainty typically below 10 cm (RMS). The offset field reveals most of the surface ruptures mapped in the field. The fault slip is accurate to about 7 cm (RMS) and measured independently every 200 m from stacked profiles. Slip distribution compares well with field measurements at the kilometric scale but reveals local discrepancies suggesting that deformation is generally, although not systematically, localized on the major fault zone located in the field. This type of data can provide useful insight into the fault zone's mechanical properties. Our measurements indicate that elastic coseismic strain near the fault zone can be as large as 0.5 × 10^(−3), while anelastic yielding was attained for strain in excess of about 1–2 × 10^(−3)

Deformation due to the 17 August 1999 Izmit, Turkey, earthquake measured from SPOT images

The geometry of the ruptured areas and the coseismic slip distribution data are key to highlighting the behavior of seismic faults. This information is generally retrieved from field investigations and geodetic measurements or synthetic aperture radar (SAR) interferometry. Here we show that SPOT images can also be used to accurately map the fault zone and to determine the slip distribution by subpixel correlation of images acquired before and after an earthquake. The measured slip includes the contribution of possible distributed shear that might not be clearly expressed in surface ruptures and smoothes out possible along-strike variability due to near-surface fault complexities. We apply the technique to the M_s = 7.4, 1999, Izmit earthquake. Our results reveal a <100-m-wide and very linear fault zone that can be traced for 70 km from Gölcük to Akyazi, along which supershear rupture has been inferred. The obtained slip distribution compares well with the field measurements and is consistent with ground deformation measured at some distance from the fault zone using SAR images. Very little deformation was accommodated off the main fault plane. Maximum slip is observed near Sapanca lake at a small fault jog that has probably influenced rupture propagation

Measuring ground displacements from SAR amplitude images: Application to the Landers Earthquake

ERS SAR amplitude images are utilized to map ground displacements from a sub‐pixel correlation method. It yields a ground two‐dimensional displacement field with independent measurements about every 128m in azimuth and 250m in range. The accuracy depends on the characteristics of the images. For the Landers test case, the 1‐σ uncertainty is 0.8m in range and 0.4m in azimuth. We show that this measurement provides a map of major surface fault ruptures accurate to better than 1km and information on coseismic deformation comparable to the 92 GPS measurements available. Although less accurate, this technique is more robust than SAR interferometry and provides complementary information since interferograms are only sensitive to the displacement in range

Introduction to special section: Active Fault-Related Folding: Structural Evolution, Geomorphologic Expression, Paleoseismology, and Seismic Hazards

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Modeling the shortening history of a fault tip fold using structural and geomorphic records of deformation

We present a methodology to derive the growth history of a fault tip fold above a basal detachment. Our approach is based on modeling the stratigraphic and geomorphic records of deformation, as well as the finite structure of the fold constrained from seismic profiles. We parameterize the spatial deformation pattern using a simple formulation of the displacement field derived from sandbox experiments. Assuming a stationary spatial pattern of deformation, we simulate the gradual warping and uplift of stratigraphic and geomorphic markers, which provides an estimate of the cumulative amounts of shortening they have recorded. This approach allows modeling of isolated terraces or growth strata. We apply this method to the study of two fault tip folds in the Tien Shan, the Yakeng and Anjihai anticlines, documenting their deformation history over the past 6–7 Myr. We show that the modern shortening rates can be estimated from the width of the fold topography provided that the sedimentation rate is known, yielding respective rates of 2.15 and 1.12 mm/yr across Yakeng and Anjihai, consistent with the deformation recorded by fluvial and alluvial terraces. This study demonstrates that the shortening rates across both folds accelerated significantly since the onset of folding. It also illustrates the usefulness of a simple geometric folding model and highlights the importance of considering local interactions between tectonic deformation, sedimentation, and erosion

Co-seismic deformation during the M_w 7.3 Aqaba earthquake (1995) from ERS-SAR interferometry

The M_w 7.3 1995 Aqaba earthquake is the largest instrumental earthquake along the Dead Sea Fault. We complement previous seismological studies by analyzing co‐seismic ground displacement from differential interferometry computed from ERS images spanning 3 different areas. They are compared with a synthetic model derived from seismological study. Only far‐field deformation related to the main sub‐event could be revealed because the near‐field area lies within the gulf. The interferometric data imply a 56 km long and 10 km wide fault segment, connecting the Elat Deep to the Aragonese Deep, which strikes N195°E and dips 65° to the west, with 2.1 m left‐lateral slip and a 15.5° rake indicating a slight normal component. The geodetic moment compares well with the seismic momen

In-Flight CCD Distortion Calibration for Pushbroom Satellites Based on Subpixel Correlation

We describe a method that allows for accurate inflight calibration of the interior orientation of any pushbroom camera and that in particular solves the problem of modeling the distortions induced by charge coupled device (CCD) misalignments. The distortion induced on the ground by each CCD is measured using subpixel correlation between the orthorectified image to be calibrated and an orthorectified reference image that is assumed distortion free. Distortions are modeled as camera defects, which are assumed constant over time. Our results show that in-flight interior orientation calibration reduces internal camera biases by one order of magnitude. In particular, we fully characterize and model the Satellite Pour l'Observation de la Terre (SPOT) 4-HRV1 sensor, and we conjecture that distortions mostly result from the mechanical strain produced when the satellite was launched rather than from effects of on-orbit thermal variations or aging. The derived calibration models have been integrated to the software package Coregistration of Optically Sensed Images and Correlation (COSI-Corr), freely available from the Caltech Tectonics Observatory website. Such calibration models are particularly useful in reducing biases in digital elevation models (DEMs) generated from stereo matching and in improving the accuracy of change detection algorithms