ALBERT

Description: The Kalman filter has been applied extensively in the area of kinematic geodetic positioning. The reliability of the linear filtering results, however, is reduced when the kinematic model noise is not accurately modeled in filtering or the measurement noises at any measurement epoch are not normally distributed. A new adaptively robust filtering is proposed based on the robust M (maximum-likelihood-type) estimation. It consists in weighting the influence of the updated parameters in accordance with the magnitude of discrepancy between the updated parameters and the robust estimates obtained from the kinematic measurements and in weighting individual measurements at each discrete epoch. The new procedure is different from functional model-error compensation; it changes the covariance matrix or equivalently changes the weight matrix of the predicted parameters to cover the model errors. A general estimator for an adaptively robust filter is developed, which includes the estimators of the classical Kalman filter, adaptive Kalman filter, robust filter, sequential least-squares adjustment and robust sequential adjustment. The procedure can not only resist the influence of outlying kinematic model errors, but also controls the effects of measurement outliers. In addition to the robustness, the feasibility of implementing the new filter is achieved by using the equivalent weights of the measurements and the predicted state parameters. A numerical example is given to demonstrate the ideas involved.

Description: Ambient noise tomography is applied to the significant data resources now available across Tibet and surrounding regions to produce Rayleigh wave phase speed maps at periods between 6 and 50 s. Data resources include the permanent Federation of Digital Seismographic Networks, five temporary U.S. Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL) experiments in and around Tibet, and Chinese provincial networks surrounding Tibet from 2003 to 2009, totaling ∼600 stations and ∼150,000 interstation paths. With such a heterogeneous data set, data quality control is of utmost importance. We apply conservative data quality control criteria to accept between ∼5000 and ∼45,000 measurements as a function of period, which produce a lateral resolution between 100 and 200 km across most of the Tibetan Plateau and adjacent regions to the east. Misfits to the accepted measurements among PASSCAL stations and among Chinese stations are similar, with a standard deviation of ∼1.7 s, which indicates that the final dispersion measurements from Chinese and PASSCAL stations are of similar quality. Phase velocities across the Tibetan Plateau are lower, on average, than those in the surrounding nonbasin regions. Phase velocities in northern Tibet are lower than those in southern Tibet, perhaps implying different spatial and temporal variations in the way the high elevations of the plateau are created and maintained. At short periods (〈20 s), very low phase velocities are imaged in the major basins, including the Tarim, Qaidam, Junggar, and Sichuan basins, and in the Ordos Block. At intermediate and long periods (〉20 s), very high velocities are imaged in the Tarim Basin, the Ordos Block, and the Sichuan Basin. These phase velocity dispersion maps provide information needed to construct a 3-D shear velocity model of the crust across the Tibetan Plateau and surrounding regions.

Description: Surface wave tomography routinely uses empirically scaled density model in the inversion of dispersion curves for shear wave speeds of the crust and uppermost mantle. An improperly selected empirical scaling relationship between density and shear wave speed can lead to unrealistic density models beneath certain tectonic formations such as sedimentary basins. Taking the Sichuan basin east to the Tibetan plateau as an example, we investigate the differences between density profiles calculated from four scaling methods and their effects on Rayleigh wave phase velocities. Analytical equations for 1-D layered models and adjoint tomography for 3-D models are used to examine the trade-off between density and S -wave velocity structures at different depth ranges. We demonstrate that shallow density structure can significantly influence phase velocities at short periods, and thereby affect the shear wave speed inversion from phase velocity data. In particular, a deviation of 25 per cent in the initial density model can introduce an error up to 5 per cent in the inverted shear velocity at middle and lower crustal depths. Therefore one must pay enough attention in choosing a proper velocity–density scaling relationship in constructing initial density model in Rayleigh wave inversion for crustal shear velocity structure.

Description: We collect two months of ambient noise data recorded by 35 broad-band seismic stations in a 9 x 11 km area (1–3 km station interval) near Karamay, China, and do cross-correlation of noise data between all station pairs. Array beamforming analysis of the ambient noise data shows that ambient noise sources are unevenly distributed and the most energetic ambient noise mainly comes from azimuths of 40°–70°. As a consequence of the strong directional noise sources, surface wave components of the cross-correlations at 1–5 Hz show clearly azimuthal dependence, and direct dispersion measurements from cross-correlations are strongly biased by the dominant noise energy. This bias renders that the dispersion measurements from cross-correlations do not accurately reflect the interstation velocities of surface waves propagating directly from one station to the other, that is, the cross-correlation functions do not retrieve empirical Green's functions accurately. To correct the bias caused by unevenly distributed noise sources, we adopt an iterative inversion procedure. The iterative inversion procedure, based on plane-wave modeling, includes three steps: (1) surface wave tomography, (2) estimation of ambient noise energy and biases and (3) phase velocities correction. First, we use synthesized data to test the efficiency and stability of the iterative procedure for both homogeneous and heterogeneous media. The testing results show that: (1) the amplitudes of phase velocity bias caused by directional noise sources are significant, reaching ~2 and ~10 per cent for homogeneous and heterogeneous media, respectively; (2) phase velocity bias can be corrected by the iterative inversion procedure and the convergence of inversion depends on the starting phase velocity map and the complexity of the media. By applying the iterative approach to the real data in Karamay, we further show that phase velocity maps converge after 10 iterations and the phase velocity maps obtained using corrected interstation dispersion measurements are more consistent with results from geology surveys than those based on uncorrected data. As ambient noise in high-frequency band (〉1 Hz) is mostly related to human activities or climate events, both of which have strong directivity, the iterative approach demonstrated here helps improve the accuracy and resolution of ANT in imaging shallow earth structures.

Description: Surface waves contain fundamental mode and higher modes, which could interfere with each other. If different modes are not properly separated, the inverted Earth structures using surface waves could be biased. In this study, we apply linear radon transform (LRT) to synthetic seismograms and real seismograms from the USArray to demonstrate the effectiveness of LRT in separating fundamental-mode Love waves from higher modes. Analysis on synthetic seismograms shows that two-station measurements on reconstructed data obtained after mode separation can completely retrieve the fundamental-mode Love-wave phase velocities. Results on USArray data show that higher mode contamination effects reach up to ~10 per cent for two-station measurements of Love waves, while two-station measurements on mode-separated data obtained by LRT are very close to the predicted values from a global dispersion model of GDM52, demonstrating that the contamination of overtones on fundamental-mode Love-wave phase velocity measurements is effectively mitigated by the LRT method and accurate fundamental-mode Love-wave phase velocities can be measured.