Stochastic models which separate fractal dimension and Hurst effect

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal dimension, a measure of roughness, and Hurst coefficient, a measure of long-memory dependence. This letter introduces simple stochastic models which allow for any combination of fractal dimension and Hurst exponent. We synthesize images from these models, with arbitrary fractal properties and power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure

Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling regime, focusing on the long time properties. By a saddle point analysis of the mode-coupling equations, we derive exact results for the correlation function in the long time limit - a limit which is hard to study using simulations. The correlation function at wavevector k in dimension d is found to behave asymptotically at time t as C(k,t)\simeq 1/k^{d+4-2z} (Btk^z)^{\gamma/z} e^{-(Btk^z)^{1/z}}, with \gamma=(d-1)/2, A a determined constant and B a scale factor.Comment: RevTex, 4 pages, 1 figur

Petrophysical properties across scales and compositions

The scales at which observations from geophysical imaging are made are orders of magnitude larger than those made in field-based studies of fossil subduction and collision zones. Even more so, the determination of petrophysical properties of rocks is typically based on millimeter to centimeter-scale samples, and the so-obtained information is then used to inform large-scale geophysical imaging studies. Information on how such properties can be up-scaled to geophysically relevant scales is rare, underlining the need to combine petrophysical properties with structural data, obtained from relevant field analogues. We provide results from three field analogues; (1) Tenda massif, Corsica, (2) Monte Mucrone, Sesia Zone, western Alps, and (3) Holsnøy, Lindås nappe, Scandinavian Caledonides. The bulk rock compositions cover a gradient from felsic (1-2) to mafic (3), as would be expected in the upper and lower continental crust, respectively. Petrophysical properties (P and S wave velocities and their ratios and anisotropies) were determined by direct measurement (ultrasonic pulse transmission technique) and calculated (based on texture data from neutron diffraction measurements). The data set is then used for numerical modeling (finite element method) of meter to kilometer-scale structural associations as mapped in the field (3). The obtained results show that high-pressure metamorphism of mafic rocks results in significant increase in both P and S wave velocities, that in principle would generate a sufficient impedance contrast to be imaged by seismic methods. While structures observed in the field are typically below the scale of geophysical imaging techniques, our considerations of bulk petrophysical properties indicate that significant anisotropy may still be detectable on the kilometer scale. On the other hand, the increase of P and S wave velocities of felsic rocks during high pressure metamorphism is much smaller, however, as such compositions have a higher potential to form rocks with high mica contents, they display a large variability in seismic anisotropy, hinting at the potential to link relatively low seismic velocities, combined with high anisotropy to fluid intake during metamorphism

Imaging the lithosphere beneath NE Tibet: Teleseismic P and S body wave tomography incorporating surface wave starting models

The northeastern margin of the Tibetan Plateau, which includes the Qiangtang and Songpan-Ganzi terranes as well as the Kunlun Shan and the Qaidam Basin, continues to deform in response to the ongoing India–Eurasia collision. To test competing hypotheses concerning the mechanisms for this deformation, we assembled a high-quality data set of approximately 14 000 P- and 4000 S-wave arrival times from earthquakes at teleseismic distances from the International Deep Profiling of Tibet and the Himalaya, Phase IV broad-band seismometer deployments. We analyse these arrival times to determine tomographic images of P- and S-wave velocities in the upper mantle beneath this part of the plateau. To account for the effects of major heterogeneity in crustal and uppermost mantle wave velocities in Tibet, we use recent surface wave models to construct a starting model for our teleseismic body wave inversion. We compare the results from our model with those from simpler starting models, and find that while the reduction in residuals and results for deep structure are similar between models, the results for shallow structure are different. Checkerboard tests indicate that features of ~125km length scale are reliably imaged throughout the study region. Using synthetic tests, we show that the best recovery is below ~300km, and that broad variations in shallow structure can also be recovered. We also find that significant smearing can occur, especially at the edges of the model. We observe a shallow dipping seismically fast structure at depths of ~140–240km, which dies out gradually between 33°N and 35°N. Based on the lateral continuity of this structure (from the surface waves) we interpret it as Indian lithosphere. Alternatively, the entire area could be thickened by pure shear, or the northern part could be an underthrust Lhasa Terrane lithospheric slab with only the southern part from India. We see a deep fast wave velocity anomaly (below 300?km), that is consistent with receiver function observations of a thickened transition zone and could be a fragment of oceanic lithosphere. In NE Tibet, it appears to be disconnected from faster wave velocities above (i.e. it is not downwelling or subducting here). Our models corroborate results of previous work which imaged a relatively slow wave velocity region below the Kunlun Shan and northern Songpan-Ganzi Terrane, which is difficult to reconcile with the hypothesis of southward-directed continental subduction at the northern margin. Wave velocities in the shallow mantle beneath the Qaidam Basin are faster than normal, and more so in the east than the west.This work was supported by a Natural Environment Research Council studentship (grant NE/H52449X/1)This version of record of this article can be found in Geophysical Journal International (March, 2014) 196 (3): 1724-1741. doi: 10.1093/gji/ggt47

The crust in the pamir: Insights from receiver functions

The Cenozoic convergence between India and Asia has created Earth's thickest crust in the Pamir‐Tibet Plateau by extreme crustal shortening. Here we study the crustal structure of the Pamir and western Tian Shan, the adjacent margins of the Tajik, Tarim, and Ferghana Basins, and the Hindu Kush, using data collected by temporary seismic experiments. We derive, compare, and combine independent observations from P and S receiver functions. The obtained Moho depth varies from ~40 km below the basins to a double‐normal thickness of 65–75 km underneath the Pamir and Hindu Kush. A Moho doublet—with the deeper interface down to a depth of ~90 km—coincides with the arc of intermediate‐depth seismicity underneath the Pamir, where Asian continental lower crust delaminates and rolls back. The crust beneath most of the Central and South Pamir has a low Vp/Vs ratio (<1.70), suggesting a dominantly felsic composition, probably a result of delamination/foundering of the mafic rocks of the lower crust. Beneath the Cenozoic gneiss domes of the Central and South Pamir, which represent extensional core complexes, the Vp/Vs ratios are moderate to high (~1.75), consistent with the previously observed, midcrustal low‐velocity zones, implying the presence of crustal partial melts. Even higher crustal average Vp/Vs ratios up to 1.90 are found in the sedimentary basins and along the Main Pamir Thrust. The ratios along the latter—the active thrust front of the Pamir—may reflect fluid accumulations within a strongly fractured fault system

Superficial simplicity of the 2010 El Mayor–Cucapah earthquake of Baja California in Mexico

The geometry of faults is usually thought to be more complicated at the surface than at depth and to control the initiation, propagation and arrest of seismic ruptures. The fault system that runs from southern California into Mexico is a simple strike-slip boundary: the west side of California and Mexico moves northwards with respect to the east. However, the M_w 7.2 2010 El Mayor–Cucapah earthquake on this fault system produced a pattern of seismic waves that indicates a far more complex source than slip on a planar strike-slip fault. Here we use geodetic, remote-sensing and seismological data to reconstruct the fault geometry and history of slip during this earthquake. We find that the earthquake produced a straight 120-km-long fault trace that cut through the Cucapah mountain range and across the Colorado River delta. However, at depth, the fault is made up of two different segments connected by a small extensional fault. Both segments strike N130° E, but dip in opposite directions. The earthquake was initiated on the connecting extensional fault and 15 s later ruptured the two main segments with dominantly strike-slip motion. We show that complexities in the fault geometry at depth explain well the complex pattern of radiated seismic waves. We conclude that the location and detailed characteristics of the earthquake could not have been anticipated on the basis of observations of surface geology alone

Endochondral bone formation in toothless (osteopetrotic) rats: failures of chondrocyte patterning and type X collagen expression

The pacemaker of endochondral bone growth is cell division and hypertrophy of chondrocytes. The developmental stages of chondrocytes, characterized by the expression of collagen types II and X, are arranged in arrays across the growth zone. Mutations in collagen II and X genes as well as the absence of their gene products lead to different, altered patterns of chondrocyte stages which remain aligned across the growth plate (GP). Here we analyze GP of rats bearing the mutation toothless (tl) which, apart from bone defects, develop a progressive, severe chondrodystrophy during postnatal weeks 3 to 6. Mutant GP exhibited disorganized, non-aligned chondrocytes and mineralized metaphyseal bone but without cartilage mineralization or cartilaginous extensions into the metaphysis. Expression of mRNA coding for collagen types II (Col II) and X (Col X) was examined in the tibial GP by in situ hybridization. Mutant rats at 2 weeks exhibited Col II RNA expression and some hypertrophied chondrocytes (HC) but no Col X RNA was detected. By 3rd week, HC had largely disappeared from the central part of the mutant GP and Col II RNA expression was present but weak and in 2 separate bands. Peripherally the GP contained HC but without Col X RNA expression. This abnormal pattern was exacerbated by the fourth week. Bone mineralized but cartilage in the GP did not. These data suggest that the tl mutation involves a regulatory function for chondrocyte maturation, including Col X RNA synthesis and mineralization, and that the GP abnormalities are related to the Col X deficiency. The differences in patterning in the tl rat GP compared to direct Col X mutations may be explained by compensatory effects

Deep lithospheric structures along the southern central Chile Margin from wide-angle P-wave modellilng

Crustal- and upper-mantle structures of the subduction zone in south central Chile, between 42 degrees S and 46 degrees S, are determined from seismic wide-angle reflection and refraction data, using the seismic ray tracing method to calculate minimum parameter models. Three profiles along differently aged segments of the subducting Nazca Plate were analysed in order to study subduction zone structure dependencies related to the age, that is, thermal state, of the incoming plate. The age of the oceanic crust at the trench ranges from 3 Ma on the southernmost profile, immediately north of the Chile triple junction, to 6.5 Ma old about 100 km to the north, and to 14.5 Ma old another 200 km further north, off the Island of Chiloe. Remarkable similarities appear in the structures of both the incoming as well as the overriding plate. The oceanic Nazca Plate is around 5 km thick, with a slightly increasing thickness northward, reflecting temperature changes at the time of crustal generation. The trench basin is about 2 km thick except in the south where the Chile Ridge is close to the deformation front and only a small, 800-m-thick trench infill could develop. In south central Chile, typically three quarters (1.5 km) of the trench sediments subduct below the decollement in the subduction channel. To the north and south of the study area, only about one quarter to one third of the sediments subducts, the rest is accreted above. Similarities in the overriding plate are the width of the active accretionary prism, 35-50 km, and a strong lateral crustal velocity gradient zone about 75-80 km landward from the deformation front, where landward upper-crustal velocities of over 5.0-5.4 km s&lt;SU-1&lt;/SU decrease seaward to around 4.5 km s&lt;SU-1&lt;/SU within about 10 km, which possibly represents a palaeo-backstop. This zone is also accompanied by strong intraplate seismicity. Differences in the subduction zone structures exist in the outer rise region, where the northern profile exhibits a clear bulge of uplifted oceanic lithosphere prior to subduction whereas the younger structures have a less developed outer rise. This plate bending is accompanied by strongly reduced rock velocities on the northern profile due to fracturing and possible hydration of the crust and upper mantle. The southern profiles do not exhibit such a strong alteration of the lithosphere, although this effect may be counteracted by plate cooling effects, which are reflected in increasing rock velocities away from the spreading centre. Overall there appears little influence of incoming plate age on the subduction zone structure which may explain why the M-w = 9.5 great Chile earthquake from 1960 ruptured through all these differing age segments. The rupture area, however, appears to coincide with a relatively thick subduction channel