**Ray tracing equations in transversely isotropic media**

*Cosmin Macesanu and Faruq Akbar, SEIMAX Technologies, LP*

We discuss a simple, compact approach to deriving ray tracing equations in transversely isotropic media. The general equations derived here are given in terms of the ray slowness vector and the direction of the axis of symmetry of the medium, which can change orientation depending on location. The standard Thomsen parameters are used instead of stress-energy tensor-components, thus allowing for easy connection with experimentally relevant quantities. The TTI results can easily be simplified to the VTI and HTI cases (corresponding to particular orientations of the symmetry axis). Both weak and strong anisotropy are considered. The accuracy of our formula is verified by comparing travel times with 2-way wave equation numerical results.

**Separation of specular reflection and diffraction images in Kirchhoff depth migration**

*Faruq E Akbar and Jun Ma, SEIMAX Technologies, LP*

Seismic diffractions may occur from faults, fractures, rough surfaces, and buried channels. In depth migrated volumes these relatively weak arrivals, as discussed by Hilterman, (1975) are often masked by stronger specular reflections. We propose a new method to separate specular reflections from diffractions in Kirchhoff depth migration using local angle information from ray tracing and dip picking from the stacked depth image. We derive a formula for the Fresnel zone that is a function of local ray angles to differentiate between seismic diffractions and specular reflections. Our method provides a cost effective alternative to currently used methods for separation of specular reflections from diffractions.

**First-arrival waveform inversion using low-frequency regenerated data **

*Ken Xu and Cosmin Macesanu, SEIMAX Technologies, LP*

We propose a new approach to solve cycle skipping issues in full-waveform inversion (FWI) by regenerating low-frequency first arrivals. By using the regenerated first arrivals for the initial FWI, we can provide an improved starting velocity model for the subsequent FWI run with the original band-limited data. Furthermore, the quality-control (QC) work of the first-break times can be done easily by comparing the regenerated first arrivals with the original ones. The method is robust since the regenerated first arrivals are just the synthetic data with full-frequency bandwidth and correct time shifts. Without complicated theory, only one conventional time-domain FWI algorithm is needed for building the starting model, and final high-resolution velocity reconstruction.

**Partial fast Fourier transform (PFFT) to improve the computer efficiency of hybrid-domain FWI**

*Ken Xu (SEIMAX Technologies, LP) and George A. McMechan (UT Dallas)*

To improve the signal to noise ratio (S/N) and the robustness of the inversion in hybrid-domain FWI, generally a large number of frequencies are treated as a single frequency group before cycle skipping occurs. However, with this approach, discrete Fourier transforms (DFT) become more costly. We propose a new Fourier transform method, Partial Fast Fourier Transform (PFFT) to improve the computational efficiency of the frequency extraction with the time-domain wavefield propagation, but without the enormous requirements for disk storage and input/output (I/O) that the Fast Fourier Transform (FFT) method requires.