Amplitude Compensation for One-Way Wave Propagators in Inhomogeneous Media and its Application to Seismic Imaging

TheWKBJ solution for the one-waywave equations inmediawith smoothly varying velocity variation with depth,c(z),is reformulated from the principle of energy flux conservation for acoustic media.The formulation is then extended to general heterogeneous media with local angle domain methods by introducing the concepts of Transparent Boundary Condition(TBC)and Transparent Propagator(TP).The influence of the WKBJ correction on image amplitudes in seismic imaging,such as depth migration in exploration seismology,is investigated in both smoothly varying c(z)and general heterogeneous media.We also compare the effect of the propagator amplitude compensation with the effect of the acquisition aperture correction on the image amplitude.Numerical results in a smoothly varying c(z)medium demonstrate that theWKBJ correction significantly improves the one-way wave propagator amplitudes,which,after compensation,agree very well with those from the full wave equation method.Images for a point scatterer in a smoothly varying c(z)medium show that the WKBJ correction has some improvement on the image amplitude,though it is not very significant.The results in a general heterogeneous medium(2D SEG/EAGE salt model)show similar phenomena.When the acquisition aperture correction is applied,the image improves significantly in both the smoothly varying c(z)medium and the 2D SEG/EAGE saltmodel.The comparisons indicate that although theWKBJ compensation for propagator amplitude may be important for forward modeling(especially for wide-angle waves),its effect on the image amplitude in seismic imaging is much less noticeable compared with the acquisition aperture correction for migration with limited acquisition aperture in general heterogeneous media.

Local synchronization and amplitude of the fluctuation of spontaneous brain activity in attention-deficit/hyperactivity disorder:a resting-state fMRI study

Regional homogeneity（ReHo）and the amplitude of low-frequency fluctuation（ALFF）are two approaches to depicting different regional characteristics of resting-state functional magnetic resonance imaging（RS-fMRI）data.Whether they can complementarily reveal brain regional functional abnormalities in attention-deficit/hyperactivity disorder（ADHD）remains unknown.In this study,we applied ReHo and ALFF to 23 medication-na ve boys diagnosed with ADHD and 25 age-matched healthy male controls using whole-brain voxel-wise analysis.Correlation analyses were conducted in the ADHD group to investigate the relationship between the regional spontaneous brain activity measured by the two approaches and the clinical symptoms of ADHD.We found that the ReHo method showed widely-distributed differences between the two groups in the fronto-cingulo-occipitocerebellar circuitry,while the ALFF method showed a difference only in the right occipital area.When a larger smoothing kernel and a more lenient threshold were used for ALFF,more overlapped regions were found between ALFF and ReHo,and ALFF even found some new regions with group differences.The ADHD symptom scores were correlated with the ReHo values in the right cerebellum,dorsal anterior cingulate cortex and left lingual gyrus in the ADHD group,while no correlation was detected between ALFF and ADHD symptoms.In conclusion,ReHo may be more sensitive to regional abnormalities,at least in boys with ADHD,than ALFF.And ALFF may be complementary to ReHo in measuring local spontaneous activity.Combination of the two may yield a more comprehensive pathophy-siological framework for ADHD.