Estimating SHmax azimuth with P sources and vertical geophones: Use P-P reflection amplitudes or use SV-P reflection times?

We compared two methods for extracting the azimuth of maximum horizontal stress (SHmax) from 3D land-based seismic data generated by a P source and recorded with vertical geophones. In the first method, we used the direct-SV mode that is produced by all land-based P sources. P sources generate SV illumination that radiates in all azimuth directions from a source station and creates SV-P reflections that are recorded by vertical geophones. Unless stratigraphy has steep dip, SV-P raypaths recorded by vertical geophones are the reverse of P-SV raypaths recorded by horizontal geophones. Thus, SV-P data provide the same S-wave sensitivity to stress fields as popular P-SV data do. In the second method, we retrieved P-P reflections and then performed an amplitude-versus-incident-angle (AVA) analysis of the amplitude-gradient behavior of P-P reflection wavelets. We did this analysis in narrow azimuth corridors to determine the gradient of reflection-wavelet amplitudes as a function of azimuth. This P-P AVA amplitude-gradient method has been of great interest in the reflection seismology community since it was introduced in the late 1990s. Each of these methods, AVA analysis of the gradient of P-P reflection amplitudes and azimuth-dependent arrival times of SV-P reflections can be used to determine the azimuth of SHmax stress. We compare the results of the two methods with ground truth measurements of SHmax azimuth at a CO2 sequestration site in the Michigan Basin. SHmax azimuths were determined from P-P and SV-P data at three major boundaries at depths of approximately 3500 ft (1067 m), 5500 ft (1676 m), and 7500 ft (2286 m). Two estimates of SHmax azimuth (one using SV-P data and one using P-P data) were made at each stacking bin inside a 24 mi2 (62 km2) image space. The result was approximately 98,000 estimates of SHmax azimuth across each of these three boundaries for each of these two prediction strategies. Histogram displays of PP AVA gradient estimates had peaks at correct azimuths of SHmax at all three depths, but the spread of the distributions widened with depth and split into two peaks at the deepest boundary. In contrast, each histogram of SHmax azimuth predicted by azimuth-dependent SV-P traveltimes had a single, definitive peak that was positioned at the correct SHmax azimuth at all three boundary depths.

Directional Selection on Tree Seedling Traits Driven by Experimental Drought Differs Between Mesic and Dry Populations

We evaluated population differences and drought-induced phenotypic selection on four seedling traits of the Australian forest tree Eucalyptus pauciflora using a glasshouse dry-down experiment. We compared dry and mesic populations and tested for directional selection on lamina length (reflecting leaf size), leaf shape, the node of ontogenetic transition to the petiolate leaf (reflecting the loss of vegetative juvenility), and lignotuber size (reflecting a recovery trait). On average, the dry population had smaller and broader leaves, greater retention of the juvenile leaf state and larger lignotubers than the mesic population, but the populations did not differ in seedling survival. While there was statistical support for directional selection acting on the focal traits in one or other population, and for differences between populations in selection gradient estimates for two traits, only one trait—lamina length—exhibited a pattern of directional selection consistent with the observed population differences being a result of past adaptation to reduce seedling susceptibility to acute drought. The observed directional selection for lamina length in the mesic population suggests that future increases in drought risk in the wild will shift the mean of the mesic population toward that of the dry population. Further, we provide evidence suggesting an early age trade-off between drought damage and recovery traits, with phenotypes which develop larger lignotubers early being more susceptible to drought death. Such trade-offs could have contributed to the absence of population mean differences in survival, despite marked differentiation in seedling traits.

Gradient estimates for an orthotropic nonlinear diffusion equation

We consider a quasilinear degenerate parabolic equation driven by the orthotropic p-Laplacian. We prove that local weak solutions are locally Lipschitz continuous in the spatial variable, uniformly in time.

Gradient estimates for Monge–Ampère type equations on compact almost Hermitian manifolds with boundary

We investigate Monge–Ampère type fully nonlinear equations on compact almost Hermitian manifolds with boundary and show a priori gradient estimates for a smooth solution of these equations.