INTRODUCTION ................................................... IV CHAPTER 1. Some Problems of Integral Geometry ................... 1 1. Problem of Determining a Function from Integrals over Ellipsoids of Revolution ..................................... 2 2. Generalization to Analytic Curves ........................... 10 5. Problem of Determining a Function inside a Circle from Integrals along a Family of Curves Invariant to Rotation about the Center of the Circle .............................. 13 4. On the Problem of Determining a Function from Its Mean Values over Circles ......................................... 19 CHAPTER 2. Linearized Inverse Dynamic Problem for the Telegraph Equation ............................................. 22 1. Statement of the Inverse Problem and Its Linearization ...... 22 2. Linearized One-Dimensional Inverse Problem in Two- Dimenslonal Space ........................................... 24 3. Two Formulations of the Linearized Inverse Problem In Three-Dimensional Space ..................................... 28 4. Derivation of a Nonlinear Differential Equation for the Inverse Problem ............................................. 31 CHAPTER 3. Linearized Inverse Kinematic Problem for the Wave Equation ....................................................... 33 1. Formulation of the Problem and Its Linearization ............ 33 2. An Application of the Linearized Version of the Inverse Kinematic Problem to Geophysics ............................. 36 CHAPTER 4. Inverse Heat Conduction Problems with Continuously Active Sources .................................... 39 1. Inverse Heat Conduction Problems for a Half-Plane ........... 39 2. n-Dimensional Inverse Heat Conduction Problems .............. 45 3. Application of the Problems to Geophysics ................... 49 CHAPTER 5. Inverse Problems for Second-Order Elliptic Equations ...................................................... 51 1. Inverse Problem for Equation (1) in a Half-Plane ............ 52 2. Inverse Problem for Equation (1) in a Half-Space ............ 54 BIBLIOGRAPHY ................................................... 57