ALBERT

Description: Elastic reverse time migration (RTM) can yield accurate subsurface information (e.g. PP and PS reflectivity) by imaging the multicomponent seismic data. However, the existing RTM methods are still insufficient to provide satisfactory results because of the finite recording aperture, limited bandwidth and imperfect illumination. Besides, the P - and S -wave separation and the polarity reversal correction are indispensable in conventional elastic RTM. Here, we propose an iterative elastic least-squares RTM (LSRTM) method, in which the imaging accuracy is improved gradually with iteration. We first use the Born approximation to formulate the elastic de-migration operator, and employ the Lagrange multiplier method to derive the adjoint equations and gradients with respect to reflectivity. Then, an efficient inversion workflow (only four forward computations needed in each iteration) is introduced to update the reflectivity. Synthetic and field data examples reveal that the proposed LSRTM method can obtain higher-quality images than the conventional elastic RTM. We also analyse the influence of model parametrizations and misfit functions in elastic LSRTM. We observe that Lamé parameters, velocity and impedance parametrizations have similar and plausible migration results when the structures of different models are correlated. For an uncorrelated subsurface model, velocity and impedance parametrizations produce fewer artefacts caused by parameter crosstalk than the Lamé coefficient parametrization. Correlation- and convolution-type misfit functions are effective when amplitude errors are involved and the source wavelet is unknown, respectively. Finally, we discuss the dependence of elastic LSRTM on migration velocities and its antinoise ability. Imaging results determine that the new elastic LSRTM method performs well as long as the low-frequency components of migration velocities are correct. The quality of images of elastic LSRTM degrades with increasing noise.

Description: Surface-related multiples have been utilized in the reverse-time migration (RTM) procedures, and additional illumination for subsurface can be provided. Meanwhile, many cross-talks are generated from undesired interactions between forward- and backward-propagated seismic waves. In this paper, subsequent to analysing and categorizing these cross-talks, we propose RTM of first-order multiples to avoid most undesired interactions in RTM of all-order multiples, where only primaries are forward-propagated and crosscorrelated with the backward-propagated first-order multiples. With primaries and multiples separated during regular seismic data processing as the input data, first-order multiples can be obtained by a two-step scheme: (1) the dual-prediction of higher-order multiples; and (2) the adaptive subtraction of predicted higher-order multiples from all-order multiples within local offset-time windows. In numerical experiments, two synthetic and a marine field data sets are used, where different cross-talks generated by RTM of all-order multiples can be identified and the proposed RTM of first-order multiples can provide a very interpretable image with a few cross-talks.

Description: New National School Lunch Program (NSLP) guidelines aim to reduce sodium and saturated fats, limit calories, and eliminate trans-fat and whole milk. This paper provides a novel approach to understanding how the healthfulness of NSLP participants’ entrée selections varies across socioeconomic and demographic groups. Unlike previous studies that rely on dietary recalls, we use a mixed logit model to examine students’ entrée choices in a school cafeteria. We estimate the likelihood that an entrée is selected from the available lunch choices as a function of the entrée’s nutrients (fat, carbohydrate, protein, and sodium) and entrée’s taste profile characteristics (e.g., Mexican, Pizza-like), as well as the student’s socio-economic and demographic characteristics. Using these estimates, we examine how changing the nutritional content of an offering impacts the probability of selecting each of the offerings. Free lunch recipients are more likely to choose entrées higher in fat but lower in sodium than other students. Full-price lunch recipients are the most responsive to changes in nutritional content of the offerings and are most likely to respond to changes in the nutritional content of the offered entrées by substituting a lunch brought from home for the school-purchased lunch. Replacing less healthy menu items with popular but healthier items reduces the selection of total calories, calories from fat, and sodium by approximately 4%, 18%, and 8%, respectively, over the study period. The new guidelines should be effective at improving the nutrition of school-age children, and potentially reducing childhood obesity, provided NSLP participation does not decline appreciably.

Description: Markov chain Monte-Carlo (McMC) sampling generates correlated random samples such that their distribution would converge to the true distribution only as the number of samples tends to infinity. In practice, McMC is found to be slow to converge, convergence is not guaranteed to be achieved in finite time, and detection of convergence requires the use of subjective criteria. Although McMC has been used for decades as the algorithm of choice for inference in complex probability distributions, there is a need to seek alternative approaches, particularly in high dimensional problems. Walker & Curtis ( 2014 ) developed a method for Bayesian inversion of 2-D spatial data using an exact sampling alternative to McMC which always draws independent samples of the target distribution. Their method thus obviates the need for convergence and removes the concomitant bias exhibited by finite sample sets. Their algorithm is nevertheless computationally intensive and requires large memory. We propose a more efficient method for Bayesian inversion of categorical variables, such as geological facies that requires no sampling at all. The method is based on a 2-D Hidden Markov Model (2D-HMM) over a grid of cells where observations represent localized data constraining each cell. The data in our example application are seismic attributes such as P - and S -wave impedances and rock density; our categorical variables are the hidden states and represent the geological rock types in each cell—facies of distinct subsets of lithology and fluid combinations such as shale, brine-sand and gas-sand. The observations at each location are assumed to be generated from a random function of the hidden state (facies) at that location, and to be distributed according to a certain probability distribution that is independent of hidden states at other locations – an assumption referred to as ‘localized likelihoods’. The hidden state (facies) at a location cannot be determined solely by the observation at that location as it also depends on prior information concerning the spatial distribution of other hidden states elsewhere. The prior information is included in the inversion in the form of a training image which represents a conceptual depiction of local geologies that might be expected, but other forms of prior information can be used in the method as desired. The method provides direct estimates of posterior marginal probability distributions over each variable, so these do not need to be estimated from samples such as in McMC. Nevertheless, in the case that samples are desired, these can be generated. On a 2-D test example the method is shown to outperform previous methods significantly, at a fraction of the computational cost. In many foreseeable applications there are therefore no serious impediments to extending the method to 3-D cases.

Description: The possibility of applying one explicit finite-difference (FD) scheme to all interior grid points (points not lying on a grid border) no matter what their positions are with respect to the material interface is one of the key factors of the computational efficiency of the FD modelling. Smooth or discontinuous heterogeneity of the medium is accounted for only by values of the effective grid moduli and densities. Accuracy of modelling thus very much depends on how these effective grid parameters are evaluated. We present an orthorhombic representation of a heterogeneous medium for the FD modelling. We numerically demonstrate its superior accuracy. Compared to the harmonic-averaging representation the orthorhombic representation is more accurate mainly in the case of strong surface waves that are especially important in local surface sedimentary basins. The orthorhombic representation is applicable to modelling seismic wave propagation and earthquake motion in isotropic models with material interfaces and smooth heterogeneities using velocity–stress, displacement–stress and displacement FD schemes on staggered, partly staggered, Lebedev and collocated grids.

Description: We present two independent, automated methods for estimating the absolute horizontal misorientation of seismic sensors. We apply both methods to 44 free-fall ocean-bottom seismometers (OBSs) of the RHUM-RUM experiment ( http://www.rhum-rum.net/ ). The techniques measure the 3-D directions of particle motion of (1) P -waves and (2) Rayleigh waves of earthquake recordings. For P -waves, we used a principal component analysis to determine the directions of particle motions (polarizations) in multiple frequency passbands. We correct for polarization deviations due to seismic anisotropy and dipping discontinuities using a simple fit equation, which yields significantly more accurate OBS orientations. For Rayleigh waves, we evaluated the degree of elliptical polarization in the vertical plane in the time and frequency domain. The results obtained for the RHUM-RUM OBS stations differed, on average, by 3.1° and 3.7° between the methods, using circular mean and median statistics, which is within the methods’ estimate uncertainties. Using P -waves, we obtained orientation estimates for 31 ocean-bottom seismometers with an average uncertainty (95 per cent confidence interval) of 11° per station. For 7 of these OBS, data coverage was sufficient to correct polarization measurements for underlying seismic anisotropy and dipping discontinuities, improving their average orientation uncertainty from 11° to 6° per station. Using Rayleigh waves, we obtained misorientation estimates for 40 OBS, with an average uncertainty of 16° per station. The good agreement of results obtained using the two methods indicates that they should also be useful for detecting misorientations of terrestrial seismic stations.