ALBERT

Beschreibung: 〈span〉〈div〉Summary〈/div〉Seismic free oscillations, or normal modes, provide a convenient tool to calculate low-frequency seismograms in heterogeneous Earth models. A procedure called ‘full mode coupling’ allows the seismic response of the Earth to be computed. However, in order to be theoretically exact, such calculations must involve an infinite set of modes. In practice, only a finite subset of modes can be used, introducing an error into the seismograms. By systematically increasing the number of modes beyond the highest frequency of interest in the seismograms, we investigate the convergence of full-coupling calculations. As a rule-of-thumb, it is necessary to couple modes 1–2 mHz above the highest frequency of interest, although results depend upon the details of the Earth model. This is significantly higher than has previously been assumed. Observations of free oscillations also provide important constraints on the heterogeneous structure of the Earth. Historically, this inference problem has been addressed by the measurement and interpretation of splitting functions. These can be seen as secondary data extracted from low frequency seismograms. The measurement step necessitates the calculation of synthetic seismograms, but current implementations rely on approximations referred to as self- or group-coupling and do not use fully accurate seismograms. We therefore also investigate whether a systematic error might be present in currently published splitting functions. We find no evidence for any systematic bias, but published uncertainties must be doubled to properly account for the errors due to theoretical omissions and regularization in the measurement process. Correspondingly, uncertainties in results derived from splitting functions must also be increased. As is well known, density has only a weak signal in low-frequency seismograms. Our results suggest this signal is of similar scale to the true uncertainties associated with currently published splitting functions. Thus, it seems that great care must be taken in any attempt to robustly infer details of Earth's density structure using current splitting functions.〈/span〉

Beschreibung: 〈span〉〈div〉Summary〈/div〉In this paper, we propose a new wavelet-based 3-D inversion method for frequency-domain airborne electromagnetic (FDAEM) data. Instead of inverting the model in the space domain using a smoothing constraint, this new method recovers the model in the wavelet domain based on a sparsity constraint. In the wavelet domain, the model is represented by two types of coefficients, which contain both large- and fine-scale informations of the model, meaning the wavelet-domain inversion has inherent multiresolution. In order to accomplish a sparsity constraint, we minimize an L〈sub〉1〈/sub〉-norm measure in the wavelet domain that mostly gives a sparse solution. The final inversion system is solved by an iteratively reweighted least-squares method. We investigate different orders of Daubechies wavelets to accomplish our inversion algorithm, and test them on synthetic frequency-domain AEM data set. The results show that higher order wavelets having larger vanishing moments and regularity can deliver a more stable inversion process and give better local resolution, while the lower order wavelets are simpler and less smooth, and thus capable of recovering sharp discontinuities if the model is simple. At last, we test this new inversion algorithm on a frequency-domain helicopter EM (HEM) field data set acquired in Byneset, Norway. Wavelet-based 3-D inversion of HEM data is compared to L〈sub〉2〈/sub〉-norm-based 3-D inversion's result to further investigate the features of the new method.〈/span〉

Beschreibung: 〈span〉〈div〉Summary〈/div〉A monitoring method to grasp the spatio-temporal change in the interplate coupling in a subduction zone based on the spatial gradients of surface displacement rate fields is proposed. I estimated the spatio-temporal change in the interplate coupling along the plate boundary in northeastern (NE) Japan by applying the proposed method to the surface displacement rates based on global positioning system observations. The gradient of the surface velocities is calculated in each swath configured along the direction normal to the Japan Trench for time windows such as 0.5, 1, 2, 3 and 5 yr being shifted by one week during the period of 1997–2016. The gradient of the horizontal velocities is negative and has a large magnitude when the interplate coupling at the shallow part (less than approximately 50 km in depth) beneath the profile is strong, and the sign of the gradient of the vertical velocity is sensitive to the existence of the coupling at the deep part (greater than approximately 50 km in depth). The trench-parallel variation of the spatial gradients of a displacement rate field clearly corresponds to the trench-parallel variation of the amplitude of the interplate coupling on the plate interface, as well as the rupture areas of previous interplate earthquakes. Temporal changes in the trench-parallel variation of the spatial gradient of the displacement rate correspond to the strengthening or weakening of the interplate coupling. We can monitor the temporal change in the interplate coupling state by calculating the spatial gradients of the surface displacement rate field to some extent without performing inversion analyses with applying certain constraint conditions that sometimes cause over- and/or underestimation at areas of limited spatial resolution far from the observation network. The results of the calculation confirm known interplate events in the NE Japan subduction zone, such as the post-seismic slip of the 2003 M8.0 Tokachi-oki and 2005 M7.2 Miyagi-oki earthquakes and the recovery of the interplate coupling around the rupture area of the 1994 M7.6 Sanriku-Haruka-oki earthquake. The results also indicate the semi-periodic occurrence of slow slip events and the expansion of the area of slow slip events before the 2011 Tohoku-oki earthquake (M9.0) approaching the hypocentre of the Tohoku-oki earthquake.〈/span〉

Beschreibung: 〈span〉〈div〉Summary〈/div〉We image the internal structure of the San Jacinto fault zone (SJFZ) in the trifurcation area southeast of Anza, California, with seismic records from dense linear and rectangular arrays. The examined data include recordings from more than 20 000 local earthquakes and nine teleseismic events. Automatic detection algorithms and visual inspection are used to identify 〈span〉P〈/span〉 and 〈span〉S〈/span〉 body waves, along with 〈span〉P〈/span〉- and 〈span〉S〈/span〉-types fault zone trapped waves (FZTW). The location at depth of the main branch of the SJFZ, the Clark fault, is identified from systematic waveform changes across lines of sensors within the dense rectangular array. Delay times of 〈span〉P〈/span〉 arrivals from teleseismic and local events indicate damage asymmetry across the fault, with higher damage to the NE, producing a local reversal of the velocity contrast in the shallow crust with respect to the large-scale structure. A portion of the damage zone between the main fault and a second mapped surface trace to the NE generates 〈span〉P〈/span〉- and 〈span〉S〈/span〉-types FZTW. Inversions of high-quality 〈span〉S〈/span〉-type FZTW indicate that the most likely parameters of the trapping structure are width of ∼70 m, 〈span〉S〈/span〉-wave velocity reduction of 60 per cent, 〈span〉Q〈/span〉 value of 60 and depth of ∼2 km. The local reversal of the shallow velocity contrast across the fault with respect to large-scale structure is consistent with preferred propagation of earthquake ruptures in the area to the NW.〈/span〉

Beschreibung: 〈span〉〈div〉Summary〈/div〉The computational cost of quasi-〈span〉P〈/span〉 wave extrapolation depends on the complexity of the medium, and specifically the anisotropy. Our effective-model method splits the anisotropic dispersion relation into an isotropic background and a correction factor to handle this dependency. The correction term depends on the slope (measured using the gradient) of current wavefields and the anisotropy. As a result, the computational cost is independent of the nature of anisotropy, which makes the extrapolation efficient. A dynamic implementation of this approach decomposes the original pseudo-differential operator into a Laplacian, handled using the low-rank approximation of the spectral operator, plus an angular dependent correction factor applied in the space domain to correct for anisotropy. We analyse the role played by the correction factor and propose a new spherical decomposition of the dispersion relation. The proposed method provides accurate wavefields in phase and more balanced amplitudes than a previous spherical decomposition. Also, it is free of 〈span〉SV〈/span〉-wave artefacts. Applications to a simple homogeneous transverse isotropic medium with a vertical symmetry axis (VTI) and a modified Hess VTI model demonstrate the effectiveness of the approach. The Reverse Time Migration applied to a modified BP VTI model reveals that the anisotropic migration using the proposed modelling engine performs better than an isotropic migration.〈/span〉