Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Interacting controls on innate sources of CO2 efflux from a calcareous arid zone soil under experimental acidification and wetting

More than half of global soil carbon is stored as carbonates, primarily in arid and semi-arid zones. Climate change models predict more frequent and severe rainfall events in some parts of the globe, many of which are dominated by calcareous soils. Such events trigger substantial increases in soil CO2 efflux. We hypothesised that the primary source of CO2 emissions from calcareous, arid zone soil during a single wetting event is abiotic and that soil acidification and wetting have a positive, potentially interacting, effect. We manipulated soil pH, soil moisture, and controlled soil respiration by gamma irradiating half of an 11 day incubation experiment. All manipulated experimental treatments had a rapid and enormous effect on CO2 emission. Respiration contributed ca. 5% of total CO2 efflux; the major source (carbonate buffering) varied depending on the extent of acidification and wetting. Maximum CO2 efflux occurred when pH was lowest and at intermediate matric potential. CO2 efflux was lowest at native pH when soil was air dry. Our data suggest that there may be an underestimate of soil-atmosphere carbon fluxes in arid ecosystems with calcareous soils. There is also a clear potential that these soils may become net carbon sources depending on changes in rainfall patterns, rainfall acidity, and future land management. Our findings have major implications for carbon cycling in arid zone soil and further study of carbon dynamics in these terrestrial systems at a landscape level will be required if we are to improve global climate and carbon cycling models.