SummaryThe present review describes the current status of synthetic five and six-membered cyclic peroxides such as 1,2-dioxolanes, 1,2,4-trioxolanes (ozonides), 1,2-dioxanes, 1,2-dioxenes, 1,2,4-trioxanes, and 1,2,4,5-tetraoxanes. The literature from 2000 onwards is surveyed to provide an update on synthesis of cyclic peroxides. The indicated period of time is, on the whole, characterized by the development of new efficient and scale-up methods for the preparation of these cyclic compounds. It was shown that cyclic peroxides remain unchanged throughout the course of a wide range of fundamental organic reactions. Due to these properties, the molecular structures can be greatly modified to give peroxide ring-retaining products. The chemistry of cyclic peroxides has attracted considerable attention, because these compounds are used in medicine for the design of antimalarial, antihelminthic, and antitumor agents.

A facile, experimentally simple, and selective method was developed for the synthesis of bridged 1,2,4,5-tetraoxanes based on the reaction of hydrogen peroxide with beta-diketones catalyzed by strong acids (H(2)SO(4), HClO(4), HBF(4), or BF(3)). The yields of the target products vary from 44% to 77%. 1,2,4,5-Tetraoxanes can easily be separated from other reaction products by column chromatography. A high concentration of a strong acid is a key factor determining the selectivity of formation and the yield of 1,2,4,5-tetraoxanes. Unlike many compounds containing the O-O bond, which undergo rearrangements in acidic media, the resulting cyclic peroxides are quite stable under these conditions.

The transition metal (Cu, Fe, Mn, Co) catalyzed peroxidation of beta-dicarbonyl compounds at the alpha position by tert-butyl hydroperoxide was discovered. A selective, experimentally convenient, and gram-scale method was developed for the synthesis of alpha-peroxidated derivatives of beta-diketones, beta-keto esters, and diethyl malonate. Virtually stoichiometric (2-3/1) molar ratios of tert-butyl hydroperoxide and a dicarbonyl compound were used in the reactions with beta-diketones and beta-keto esters. The target compounds were synthesized in the highest yields from beta-keto esters (45-90%) and in somewhat lower yields from beta-diketones (46-75%) and malonates (37-67%).

Estimating subsurface seismic properties is an important topic in civil engineering, oil and gas exploration, and global seismology. We have developed an application of 2D elastic waveform inversion with an active-source on-shore data set, as is typically acquired in exploration seismology on land. The maximum offset is limited to 12 km, and the lowest available frequency is 5 Hz. In such a context, surface waves are generally treated as noise and are removed as a part of data processing. In contrast to the conventional approach, our workflow starts by inverting surface waves to constrain shallow parts of the shear wavespeed model. To mitigate cycle skipping, frequency- and offset-continuation approaches are used. To accurately take into account free-surface effects (and irregular topography), a spectral-element-based wave propagation solver is used for forward modeling. To reduce amplitude influences, a normalized crosscorrelation (NC) objective function is used in conjunction with systematic updates of the source wavelet during the inversion process. As the inversion proceeds, body waves are gradually incorporated in the process. At the final stage, surface and body waves are inverted together using the entire offset range over the band between 5 and 15 Hz. The inverted models include high-resolution features in the first 500 m of compressional and shear wavespeeds, with some model updates down to 4.0 km in the first parameter. The inversion results confirmed by well-log information, indicate a better fit of compressional to shear wavespeeds ratios compared with the initial model. The final data fit is also noticeably improved compared to the initial one. Although our results confirm previous studies demonstrating that an NC norm combined with a source time function correction can partly stabilize purely elastic inversions of viscoelastic data, we believe that including an attenuation depth model in the forward simulation gives better results.

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Full-waveform inversion (FWI) is a powerful method for estimating the earth’s material properties. We demonstrate that surface-wave-driven FWI is well-suited to recovering near-surface structures and effective at providing S-wave speed starting models for use in conventional body-wave FWI. Using a synthetic example based on the SEG Advanced Modeling phase II foothills model, we started with an envelope-based objective function to invert for shallow large-scale heterogeneities. Then we used a waveform-difference objective function to obtain a higher-resolution model. To accurately model surface waves in the presence of complex tomography, we used a spectral-element wave-propagation solver. Envelope misfit functions are found to be effective at minimizing cycle-skipping issues in surface-wave inversions, and surface waves themselves are found to be useful for constraining complex near-surface features.

Accurate and efficient forward modeling methods are important for simulation of seismic wave propagation in 3D realistic Earth models and crucial for high-resolution full waveform inversion. In the presence of attenuation, wavefield simulation could be inaccurate or unstable over time if not well treated, indicating the importance of the implementation of a strong stability preserving time discretization scheme. In this study, to solve the anelastic wave equation, we choose the optimal strong stability preserving Runge-Kutta (SSPRK) method for the temporal discretization and apply the fourth-order MacCormack scheme for the spatial discretization. We approximate the rheological behaviors of the Earth by using the generalized Maxwell body model and use an optimization procedure to calculate the anelastic coefficients determined by the Q(ω) law. This optimization constrains positivity of the anelastic coefficients and ensures the decay of total energy with time, resulting in a stable viscoelastic system even in the presence of strong attenuation. Moreover, we perform theoretical and numerical analyses of the SSPRK method, including the stability criteria and the numerical dispersion. Compared with the traditional fourth-order Runge-Kutta method, the SSPRK has a larger stability condition number and can better suppress numerical dispersion. We use the complex-frequency-shifted perfectly matched layer for the absorbing boundary conditions based on the auxiliary difference equation and employ the traction image method for the free-surface boundary condition on curvilinear grids representing the surface topography. Finally, we perform several numerical experiments to demonstrate the accuracy of our anelastic modeling in the presence of surface topography. Key Points:• We develop a new optimal strong stability preserving Runge-Kutta (SSPRK) method for solving the anelastic wave equation • We perform theoretical and numerical analyses of the SSPRK method • We demonstrate the accuracy and efficiency of the SSPRK method in anelastic wavefield modeling in the presence of surface topographySupporting Information:• Supporting Information S1 ). Modeling three-dimensional wave propagation in anelastic models with surface topography by the optimal strong stability preserving Runge-Kutta method. Withers et al., 2015) for a weak frequency dependence of Q is sometimes of interest. We follow a conventional way to calculate the anelastic coefficients determined by the Q(ω) law (Emmerich & Korn, 1987;Käser et al., 2007;Kristek & Moczo, 2003), but we constrain the coefficients to be positive (Blanc et al., 2016;Yang et al., 2016). This positivity ensures the decay of total energy over time as proved in the supporting information (SI) section A. Assuming the attenuation factors at a reference frequency f r for P and S waves is Q P and Q S , the frequency range of interest in the classical approach to calculate the anelastic coefficients is defined as [f min , f max ] = [f r /f amp , f r × f amp ],

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