Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Independent and mediating organizational commitment effects of trust in leadership on employees' job satisfaction and : a study within social and health care sector

The purpose of this study was to examine whether trust in supervisor and trust in senior management enhance employees' job satisfaction and organizational commitment, and whether trust mediates the relationship between perceived justice and these outcomes. Trust in supervisor was expected to mediate the effects of distributive justice and interactional justice, and trust in senior management was expected to mediate the effects of procedural justice. Theoretical background of the study is based on the framework for trust in leadership developed by Dirks and Ferrin (2002). According to the framework, perceived fairness of leaders' actions helps employees to draw inferences about the basis of the relationship and about leaders' characters. This allows trust formation. Reciprocation of care and concern in the relationship and confidence in leaders' characters are likely to enhance employees' job satisfaction and organizational commitment. This study was conducted with cross-sectional data (A/ = 960) of employees from social and health care sector. Hypotheses were studied using correlation analysis and several hierarchical regression analyses. Significances of the mediations were assessed using the Sobel test. Results partially supported the hypotheses. Trust in leadership was positively related to job satisfaction and organizational commitment. Trust in senior management mediated the relationship between procedural justice and the outcomes. Some support was also found for the mediating effect of trust in supervisor in the relationship between distributive justice and organizational commitment. Due to high correlation between trust in supervisor anil interactional justice, it wasn't possible to study the mediating e fleet of trust in supervisor in the relationship between interactional justice and the outcomes. Against expectations, results indicated that trust in senior management had a mediating effect in the relationship between distributive justice and organizational commitment, and in the relationship between interactional justice and organizational commitment. Results also indicated that trust in supervisor had a mediating effect in the relationship between procedural justice and organizational commitment.