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We analyse random errors (variances) in cross-correlations of ambient seismic noise in the frequency domain, which differ from previous time domain methods. Extending previous theoretical results on ensemble averaged cross-spectrum, we estimate confidence interval of stacked cross-spectrum of finite amount of data at each frequency using non-overlapping windows with fixed length. The extended theory also connects amplitude and phase variances with the variance of each complex spectrum value. Analysis of synthetic stationary ambient noise is used to estimate the confidence interval of stacked cross-spectrum obtained with different length of noise data corresponding to different number of evenly spaced windows of the same duration. This method allows estimating Signal/Noise Ratio (SNR) of noise cross-correlation in the frequency domain, without specifying filter bandwidth or signal/noise windows that are needed for time domain SNR estimations. Based on synthetic ambient noise data, we also compare the probability distributions, causal part amplitude and SNR of stacked cross-spectrum function using one-bit normalization or pre-whitening with those obtained without these pre-processing steps. Natural continuous noise records contain both ambient noise and small earthquakes that are inseparable from the noise with the existing pre-processing steps. Using probability distributions of random cross-spectrum values based on the theoretical results provides an effective way to exclude such small earthquakes, and additional data segments (outliers) contaminated by signals of different statistics (e.g. rain, cultural noise), from continuous noise waveforms. This technique is applied to constrain values and uncertainties of amplitude and phase velocity of stacked noise cross-spectrum at different frequencies, using data from southern California at both regional scale (∼35 km) and dense linear array (∼20 m) across the plate-boundary faults. A block bootstrap resampling method is used to account for temporal correlation of noise cross-spectrum at low frequencies (0.05-0.2 Hz) near the ocean microseismic peaks.

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Waxy crude oil exhibits complex shear-and-thermal-history-dependent non-Newtonian behaviors. In the past 10 years, driven by the petroleum industry, crude oil rheology has been an active field. Studies on crude oil rheology have been passing a way from simply relying on rheological measurements, through quantitative experimental simulation of shear and thermal history effects in pipelining, to recent development of correlation between flow properties and shear and thermal history. Currently, the study is toward quantitative inquiry of relations between the rheological behaviors and micro-structures of wax crystals as well as oil compositions. Advances achieved by the author' team are summarized, including simulation of the thermal and shear history effects, correlations and computation of flow properties, fractal characterization of morphology and structure of wax crystals, relations of rheological behaviors to fractal dimension and oil compositions, and the most successful example of the application of rheology in crude oil pipelining. Future studies are prospected.