Seismic Attenuation Anisotropy in the Southernmost Part of the Taupo Volcanic Zone, North Island, New Zealand

<p>We investigate the mechanisms of seismic anisotropy and attenuation (1/Q) beneath the southernmost part of the Taupo Volcanic Zone (TVZ) by computing variations in S-wave attenuation factors with the direction of wave polarization. We rotate pairs of horizontal components in steps of 22.5◦ from 0◦ to 67.5◦ and into the radial and transverse directions to search for the optimal separation of the attenuation curves and thereby determine an anisotropy symmetry system. The frequency dependence of Q for the rotated S-waves is estimated by means of the non-parametric generalized inversion technique (GIT) of Castro et al. (1990) using shallow earthquakes (< 40 km depth) recorded by GeoNet within 100 km of Mt. Ruapehu. To analyze the effects on computed attenuation properties of source locations, we divide our dataset into two groups: a “TVZ” group containing earthquakes within the TVZ in a distance range of 5–55 km and a “non-TVZ” group containing earthquakes outside the TVZ in a distance range of 5–50 km. To measure Q, we compute the spectral amplitude decay with distance in terms of empirical functions at 20 separate frequencies in the frequency bands 2–10 Hz and 2– 12 Hz for the TVZ and non-TVZ datasets respectively. We construct homogeneous and two-layer Q models for the TVZ dataset based on characteristic features of the attenuation function, while for outside TVZ we only analyse a homogeneous Q model. The homogeneous Q models obtained for the two datasets indicate that S-waves are more attenuated within the TVZ than outside. The homogeneous Q model for the TVZ dataset reveals that the S-wave is anisotropic at high frequencies ( f > 6 Hz) along N–S/E– W directions with the relation QSE ( f ) = (6.15±1.22) f (1.73±0.12) and QSN ( f ) = (4.14± 1.26) f (2.06±0.14), while the non-TVZ dataset shows a weak frequency dependence of attenuation anisotropy at low frequencies in NE–SW/SE–NW directions giving the power law function QSNE ( f ) = (50.93±1.18) f (0.20±0.10) and QSSE ( f ) = (22.60±1.10) f (0.53±0.06). Here, the uncertainty estimates are 95% confidence intervals. To investigate the variation of attenuation anisotropy with depth within the TVZ, we first calculate Q along propagation paths (< 25 km, which corresponds to a maximum turning point depth of 9 km ) and then using paths of 25–55 km length. Small attenuation anisotropy with low attenuation in the N–S direction for the upper crust of TVZ may be related to heterogenous structure as reported by previous studies. Attenuation anisotropy in the northwest direction yielding lower attenuation inferred for the deeper crust suggests the presence of connected melt aligned with the extension direction of TVZ .</p>

Seismic Attenuation Anisotropy in the Southernmost Part of the Taupo Volcanic Zone, North Island, New Zealand

<p>We investigate the mechanisms of seismic anisotropy and attenuation (1/Q) beneath the southernmost part of the Taupo Volcanic Zone (TVZ) by computing variations in S-wave attenuation factors with the direction of wave polarization. We rotate pairs of horizontal components in steps of 22.5◦ from 0◦ to 67.5◦ and into the radial and transverse directions to search for the optimal separation of the attenuation curves and thereby determine an anisotropy symmetry system. The frequency dependence of Q for the rotated S-waves is estimated by means of the non-parametric generalized inversion technique (GIT) of Castro et al. (1990) using shallow earthquakes (< 40 km depth) recorded by GeoNet within 100 km of Mt. Ruapehu. To analyze the effects on computed attenuation properties of source locations, we divide our dataset into two groups: a “TVZ” group containing earthquakes within the TVZ in a distance range of 5–55 km and a “non-TVZ” group containing earthquakes outside the TVZ in a distance range of 5–50 km. To measure Q, we compute the spectral amplitude decay with distance in terms of empirical functions at 20 separate frequencies in the frequency bands 2–10 Hz and 2– 12 Hz for the TVZ and non-TVZ datasets respectively. We construct homogeneous and two-layer Q models for the TVZ dataset based on characteristic features of the attenuation function, while for outside TVZ we only analyse a homogeneous Q model. The homogeneous Q models obtained for the two datasets indicate that S-waves are more attenuated within the TVZ than outside. The homogeneous Q model for the TVZ dataset reveals that the S-wave is anisotropic at high frequencies ( f > 6 Hz) along N–S/E– W directions with the relation QSE ( f ) = (6.15±1.22) f (1.73±0.12) and QSN ( f ) = (4.14± 1.26) f (2.06±0.14), while the non-TVZ dataset shows a weak frequency dependence of attenuation anisotropy at low frequencies in NE–SW/SE–NW directions giving the power law function QSNE ( f ) = (50.93±1.18) f (0.20±0.10) and QSSE ( f ) = (22.60±1.10) f (0.53±0.06). Here, the uncertainty estimates are 95% confidence intervals. To investigate the variation of attenuation anisotropy with depth within the TVZ, we first calculate Q along propagation paths (< 25 km, which corresponds to a maximum turning point depth of 9 km ) and then using paths of 25–55 km length. Small attenuation anisotropy with low attenuation in the N–S direction for the upper crust of TVZ may be related to heterogenous structure as reported by previous studies. Attenuation anisotropy in the northwest direction yielding lower attenuation inferred for the deeper crust suggests the presence of connected melt aligned with the extension direction of TVZ .</p>

Homotopy theory of Moore flows (II)

This paper proves that the q-model structures of Moore flows and of multipointed d-spaces are Quillen equivalent. The main step is the proof that the counit and unit maps of the Quillen adjunction are isomorphisms on the q-cofibrant objects (all objects are q-fibrant). As an application, we provide a new proof of the fact that the categorization functor from multipointed d-spaces to flows has a total left derived functor which induces a category equivalence between the homotopy categories. The new proof sheds light on the internal structure of the categorization functor which is neither a left adjoint nor a right adjoint. It is even possible to write an inverse up to homotopy of this functor using Moore flows.

Comparing the transport-limited and ξ−q models for sediment transport

We present a comparison between two of the most widely used reduced-complexity models for the representation of sediment transport and deposition processes, namely the transport limited (or TL) model and the under-capacity (or ξ−q) model more recently developed by Davy and Lague (2009). Using both models, we investigate the behavior of a sedimentary continental system fed by a fixed sedimentary flux from a nearby active orogen though which sediments transit to a fixed base level representing a large river, a lake or an ocean. Our comparison shows that the two models share the same steady-state solution, for which we derive a simple 1D analytical solution that reproduces the major features of such sedimentary systems: a steep fan that connects to a shallower alluvial plain. The resulting fan geometry obeys basic observational constraints on fan size and slope with respect to the upstream drainage area, A0. The solution is strongly dependent on the size of the system, L, in comparison to a distance L0 that is determined by the size of A0 and gives rise to two fundamentally different types of sedimentary systems: constrained system where L<L0 and open systems where L>L0. We derive simple expressions that show the dependence of the system response time on the system characteristics, such as its length, the size of the upstream catchment area, the amplitude of the incoming sedimentary flux and the respective rate parameters (diffusivity or erodibility) for each of the two models. We show that the ξ−q model predicts longer response times, which we relate to its greater efficiency at propagating signals through its entire length. We demonstrate that, although the manner in which signals propagates through the sedimentary system differs greatly between the two models, they both predict that perturbations that last longer than the response time of the system can be recorded in the stratigraphy of the sedimentary system and in particular of the fan. Interestingly, the ξ−q model predicts that all perturbations in incoming sedimentary flux will be transmitted through the system whereas the TL model predicts that rapid perturbations cannot. We finally discuss why and under which conditions these differences are important and propose observational ways to determine which of the two models is most appropriate to represent natural systems.

A New Technique for ARMA-System Identification Based on QR-Decomposition of Third Order Cumulants Matrix

In this paper a new technique to estimate the coefficients of a general Autoregressive Moving Average (ARMA) (p, q) model is proposed. The ARMA system is excited by an un-observable independently identically distributed (i.i.d) non-Gaussian process. The proposed ARMA coefficients estimation method uses the QR-Decomposition (QRD) of a special matrix built with entries of third order cumulants (TOC) of the available output data only. The observed output may be corrupted with additive colored or white Gaussian noise of unknown power spectral density. The proposed technique was compared with several good methods such as the residual time series (RTS) and the Q-slice algorithm (QSA) methods. Simulations for several examples were tested. The results for these examples confirm the good performance of the proposed technique with respect to existing well-known methods.