FRESNEL ZONE INVERSION FOR LATERAL HETEROGENEITIES IN THE EARTH

We propose a different kind of seismic inversion from travel-time or waveform inversion for lateral heterogeneities in the earth: Fresnel zone inversion. Amplitude and phase delay of data in several frequency ranges are inverted for model space around ray paths with a width corresponding to the considered frequency so that primary effect of finiteness of wavelength be included. For vertically heterogeneous media, Frechet derivatives for inversion are obtained very efficiently using the paraxial ray approximation, with nearly similar amounts of computation compared to travel-time inversion. As an example, Frechet derivatives are computed for a teleseismic observation system for a three-dimensional structure in the lithosphere beneath an array of seismic stations. Even if the used frequency is around 2 Hz, the width of Frechet derivatives cannot be neglected, particularly near the bottom of the lithosphere. Sensitivity of model parameters to observations is, moreover, different in our approach from conventional travel-time inversion: it is zero along ray paths but large slightly away from them. Some model calculations show that travel-time inversion, particularly with models divided into very fine meshes or blocks, might give misleading results. An example of inversion for a simple Camembert model, in the event that travel-time inversion gives no reliable results, shows how this technique works with much smaller data sets and computation than waveform inversions.