Ha, J., Shin, S., Shin, C.S. and Chung, W., 2015. Time domain full waveform inversion of seismic data for the East Sea, Korea, using a pseudo-Hessian method with source estimation. Journal of Seismic Exploration, 24: 419-437. Waveform inversion is used to estimate subsurface velocity information using seismic datasets. To overcome the computational burden, the use of back-propagation algorithm and the pseudo-Hessian matrix are proposed. Many researchers using these algorithms have shown successful results with synthetic and field data tests. In particular, the computational efficiency of waveform inversion is improved by using a pseudo-Hessian with regularization using a virtual source vector. However, these theoretical concepts have been mainly applied to waveform inversion in the frequency or Laplace domains. We propose full waveform inversion using an estimated source wavelet with the pseudo-Hessian matrix and back-propagation in the time domain. We derive the virtual source vector for the first order hyperbolic equation based on 2D staggered-grid modeling. The updated gradient direction is obtained from both the virtual source and back-propagation wavefield vectors. To improve the availability for field data sets, we also perform the source estimation using deconvolution of the observed data based on the least-squares method. In a synthetic test with a modified Marmousi2 model, the inverted velocity model obtained by the proposed waveform inversion algorithm using estimated wavelets shows similarity to the true velocity. The estimated source wavelet shows good agreement with the true source wavelet. We also test the proposed waveform inversion with field data from the East Sea, Korea. The calculated traces with the estimated source wavelet and the inverted velocity model show direct and reflection events similar to those in the real seismic traces. This confirms that the proposed algorithm can be applied to field data.