oa Fresnel Zone Wavepath Tomography - Theory

In this paper, a developing wavepath based on diffraction tomography in the space-time domain is presented. This wavepath is named Fresnel zone wavepath, derived from the imaginary part of Rhytov approximation. This wavepath is calculated using travel times from source to any point, receiver to any point and source to receiver. The Fresnel zone wavepath is a frequency dependent function. While the frequency is higher, the Fresnel zone wavepath oscillates more frequently than when the frequency is lower. In the high frequency, Fresnel zone wavepath becomes similar to the ray path. In the application of Fresnel zone wavepath to inversion tomography, a ray tracing procedure is not needed. A case of sparse data showed that the inversion result using Fresnel wavepath is better than one using the ray path. We also propose several techniques to enhance the inversion based on Fresnel zone wavepath. These include first Fresnel zone restriction, hybrid inversion and polychromatic wavepath. From the model studies, we show that the above mentioned techniques provide better inversion result.