Summary
One of the main limitations of full waveform inversion (FWI) is the need for a good starting model in order to avoid cycle-skipping and convergence to a local minimum of the cost function. Image-based methods such as tomography are therefore used in typical industrial workflows to create the initial model for FWI. In this work we propose an alternative model building workflow based on Laplace-Fourier FWI. This technique widens the frequency bandwidth of the seismic data by localizing seismic events in time. To assess its applicability in a real depth imaging project, we apply it on a carbonate field from offshore West Africa. The results confirm that the new FWI workflow can provide a model comparable to the classic one, starting from a model derived by reflection tomography. The minimal data pre-processing requirements of Laplace-Fourier FWI combined with its ability to start from a simple initial model offers the potential for a significant reduction in the turnaround time of imaging projects.
Introduction
Full waveform inversion (FWI) is a powerful tool capable of improving the resolution of the subsurface earth models used in the seismic imaging process (Bamberger et al., 1982; Tarantola, 1984; Pratt, 1999). It is well known that FWI requires a good starting model to avoid the risk of the inversion converging to a local minimum due to cycle skipping (Mora, 1989). This requirement is relaxed when the seismic traces contain useful low frequency components, but the limited low-end of the spectrum of common seismic data in turn limits standard FWI model updates to the intermediate and short wavelength range. Industrial workflows therefore typically use an image-based method such as tomography (Pratt and Goulty, 1991, Operto et al., 2004) or wave equation migration velocity analysis (Symes and Carazzone, 1991; Sava and Biondi, 2004; Biondi and Almomin, 2013) upstream of FWI. However, these methods require time consuming data pre-processing to ensure clean image gathers, and at least one full-frequency migration; three-dimensional wave equation migration velocity analysis is potentially significantly more computationally intensive and time-consuming than FWI itself.
An alternative is to estimate initial model parameters by inverting the data in the Laplace-Fourier domain as proposed by Shin and Cha (2009). The embedded Laplace transform extends the spectrum of the wavefield by convolution with the transform of the exponential damping operator. This creates low-frequency components beyond the limits of the recorded data allowing the inversion to access robustly the long-wavelengths of the model (Calandra et al., 2011). In this paper we show how the Laplace-Fourier low frequency components can be used to build a background velocity model suitable for initiating conventional FWI of the data in the recorded bandwidth. This will be demonstrated by application to a shallow marine dataset.
