Amplitude preserving AMO from true amplitude DMO and inverse DMO
Starting from the definition of Azimuth Moveout ( AM O) as the cascade of D M O and inverse D M O at different offsets and azimuths, we derive an amplitude-preserving function for the AM O operator. This amplitude function is based on the FK definition of D M O and the definition of its true inverse. Similar to Liner’s formalism of a true inverse for Hale’s D M O, we derive an asymptotically true inverse for Black/Zhang’s D M O and Bleinstein’s Born D M O. A numerical test is given that compares amplitude preservation using kinematically equivalent D M O operators cascaded with their true inverses. We define amplitude-preserved processing as the preservation of the offset-dependent reflectivity after AM O transformation, where the reflectivity is considered to be proportional to the peak amplitude of each event. We found that an AM O operator defined using Zhang’s D M O cascaded with its true inverse best reconstructs data amplitudes after transformation to a new offset and azimuth. The new amplitude function represents an amplitudepreserving azimuth moveout.
Squeezing dip moveout for depth-variable velocity
In dip moveout (DMO) processing, velocity variations with depth can be handled approximately by squeezing a constant-velocity DMO operator to narrow its impulse response. This squeezed DMO approximation provides a computationally efficient and reasonably accurate method of DMO correction for depth-variable velocity. DMO is squeezed by two modifications to constant-velocity DMO. One modification is a squeezing function of time that depends only on simple time averages of velocity that are likely to be known before DMO is applied. This squeeze function ensures that squeezed DMO accurately handles moderately steep reflections, and can be incorporated with simple time stretching before and after DMO, without any changes to existing constant-velocity DMO methods. The second modification is a constant squeezing factor, which may be used to tune squeezed DMO to better handle steep reflections. This factor requires only trivial changes to constant-velocity DMO methods. Tests with both synthetic and recorded seismic data suggest that squeezed DMO is an effective method for handling velocity variations with depth. These tests also show that the differences between constant-velocity DMO and squeezed DMO can be significant.
Inequality trends in health and future health risk among English children and young people, 1999–2009
Objective To investigate trends in health inequality among children and young people between 1999 and 2009, using outcomes consistent with the current NHS reforms. Design/data Secondary analysis of participants aged 0–24 in the Health Surveys for England (HSE) undertaken in 1999, 2004, 2006 and 2009. Main outcome measures Changes in the absolute and relative risks of four health outcomes by deprivation tertiles, based on occupation of the head of household ▸ self/parent-reported general health, ▸ presence of a long-standing illness (LSI), ▸ obesity ▸ smoking. Results No indicator showed a reduction in relative or absolute inequality between 1999 and 2009. For children (0–12 years), the relative risk comparing the most and least deprived tertiles increased significantly for poor general health (1999:1.6 (95% CI 1.2 to 2.2); 2009:3.9 (2.4 to 6.2), while the absolute difference in LSI prevalence(%) increased from 1.3 (−2.9 to 5.5) to 7.4 (3.6 to 11.4). Among young people (13–24 years), the absolute difference in LSI prevalence increased from −5.9 (−10.9 to −1.1) to 3.1 (−4.1 to 10.7). Absolute inequality in having tried smoking among children aged 8–15(%) increased significantly in the first half of the decade before decreasing in the second half (1999:3.3 (−1.1 to 7.7); 2004:14.1 (9.6 to 18.8); 2009:4.1 (0.1 to 8.8)). However, the increase in absolute inequality for smoking prevalence among young adults (16–24 years) was maintained throughout the decade (1999:−7.0 (−15.6 to 1.3); 2004:11.6 (3.7 to 20.0); 2009:8.2 (−0.3 to 16.9)). Conclusions The national programme between 1999 and 2009 was not successful in reducing inequality in four key indicators of health status and future health risk among children and young people. Some inequality measures for general health, LSI prevalence and smoking increased over this time.