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High-efficiency forward modeling methods play a fundamental role in full waveform inversion (FWI). In this paper, the developed nearly analytic discrete (DNAD) method is proposed to accelerate frequency-domain forward modeling processes. We first derive the discretization of frequency-domain wave equations via numerical schemes based on the nearly analytic discrete (NAD) method to obtain a linear system. The coefficients of numerical stencils are optimized to make the linear system easier to solve and to minimize computing time. Wavefield simulation and numerical dispersion analysis are performed to compare the numerical behavior of DNAD method with that of the conventional NAD method. The results demonstrate the superiority of our proposed method. Finally, the DNAD method is implemented in frequency-domain FWI, and high-resolution inverse results are obtained. [ABSTRACT FROM AUTHOR]

To further improve the efficiency of solving the Helmholtz equation in heterogeneous media with large wavenumber, the Krylov subspace methods incorporated with a class of inexact rotated block triangular preconditioners are presented to solve a block two-by-two linear system derived from the discrete Helmholtz equation. We further develop the eigenvalue properties of the preconditioned matrices to discuss the convergence of the corresponding preconditioned iteration methods. The superiority of such preconditioned iteration methods is prominent according to the numerical results when comparing with other classical iteration methods. We also investigate how the wavenumber influences the performance of the corresponding methods and it is shown that the iteration number of our proposed methods linearly increase with the wavenumber, roughly. Furthermore, the computational wave-fields which conform the real physical law are exhibited to show the correctness of our proposed numerical modeling algorithm. [ABSTRACT FROM AUTHOR]

Based on water quality surveys over 2 years (July to December, in 2014 and 2015) in a typical arid river in northern China the Xingtai segment of the Fuyang River basin — the variation of nitrogen (N) and phosphorus (P) was analyzed. The extent of water eutrophication of this segment was also assessed using a universal index formula for eutrophic evaluation and a logarithmic power function. The results showed that the average concentration of total N (TN) was 27.2 mg/L (NH 3 -N, 63.5%), total P (TP) was 2.0 mg/L (solution reactive phosphorus, 68.8%). Temporal and spatial variations of N and P in this segment were observed. Concentrations of N and P in the arid season were higher than those in the rainy season. Spatially, the N and P concentrations followed the same trend; i.e. , higher in the city segment than in the suburbs, and decreasing along the river. The water eutrophication in the studied segment reached extremely high levels at all times (eutrophication index ≥ 76.3). Spatially, its trend was clearly linked with N and P. Water shortage, pollution accumulation and a weak self-purification function are the main reasons for the prominent eutrophication in this segment. [ABSTRACT FROM AUTHOR]