A new waveform inversion workflow: Application to near-surface velocity estimation in Saudi Arabia

Waveform inversion workflow

Our waveform inversion workflow consists of three successive steps:

       1) First arrival traveltime tomography.
       2) Wave-equation traveltime inversion.
       3) Early arrival acoustic waveform inversion.

The first step relies on ray theory to estimate an initial low frequency velocity model to explain the first arrival picks. In the second step, we use the output of the conventional traveltime tomography as input to wave-equation traveltime inversion (Luo and Schuster, 1991). This result is then used as input for the third step of full waveform inversion. Since both the traveltime and waveform inversion are derived from the same wave-equation, they can both be described in a common framework where the objective function can be written as

$${f\bf\left(d_{obs},D(m)\right) \approx 0, } \\$$ (1)

where ${ f }$ is a function of ${\bf d_{obs}}$ and ${\bf D(m)}$ , the observed data and forward modeled synthetic data from the velocity model ${\bf m}$ respectively. Observed data can be either in frequency domain or in time domain, depending on the actual form of ${\bf f}$ . For example if we take ${\bf f}$ as the L2 norm of ${\bf\left(d_{obs}-D(m)\right)}$ , we obtain the objective function of conventional waveform inversion (Tarantola, 1984; Pratt et al., 1998); if we take ${\bf f}$ as the L2 norm of the time lag difference of the cross-correlation of ${\bf D(m)}$ and ${\bf d_{obs}}$ , we obtain an objective function for wave-equation traveltime inversion. (Luo and Schuster, 1991). This second formulation is more robust than the first one in the presence of large velocity contrasts or to inaccuracies in the initial model. However, wave-equation traveltime inversion provides lower model resolution compared to conventional full waveform inversion. near-surface low velocity layer and resulting shingling data lead to inaccurate velocity estimates using ray-based methods. The workflow adopted in this paper tries to compensate for these issues by adding an intermediate wave-equation traveltime inversion to the conventional workflow.

A new waveform inversion workflow: Application to near-surface velocity estimation in Saudi Arabia