Wave Equation Reflection Traveltime Inversion Using Gauss–Newton Optimization

Wave equation reflection traveltime inversion (RTI) takes advantage of the convexity of traveltime objective function to robustly build the background velocity structure for seismic migration and waveform inversion. However, the current wave-equation-based RTI suffers from slow convergence and low resolution because the widely used gradient-based optimization can not account for the blurring effects caused by the finite observation. To accelerate the convergence and improve the accuracy, we propose a Gauss–Newton RTI (GN-RTI) method by incorporating the Hessian information. We derive the reflection traveltime Fréchet derivative and Hessian matrix based on the Born scattering theory. The explicitly constructed Hessian matrix and point spread functions show that the parameter coupling effects of different spatial locations in RTI vary significantly in the model space. Based on the understandings of these coupling effects, a matrix-free approach is applied to solve the Gauss–Newton equation of RTI using the conjugate-gradient method in a nested inner loop. Synthetic and real data examples show that the proposed GN-RTI method can effectively retrieve the background velocity structures for seismic imaging and subsequent waveform inversion.