Full waveform inversion using envelope-based global correlation norm

To increase the feasibility of full waveform inversion on real data, we suggest a new objective function, which is defined as the global correlation of the envelopes of modelled and observed data. The envelope-based global correlation norm has the advantage of the envelope inversion that generates artificial low-frequency information, which provides the possibility to recover long-wavelength structure in an early stage. In addition, the envelope-based global correlation norm maintains the advantage of the global correlation norm, which reduces the sensitivity of the misfit to amplitude errors so that the performance of inversion on real data can be enhancedwhen the exact sourcewavelet is not available and more complex physics are ignored. Through the synthetic example for 2-D SEG/EAGE overthrust model with inaccurate source wavelet, we compare the performance of four different approaches, which are the least-squares waveform inversion, least-squares envelope inversion, global correlation norm and envelopebased global correlation norm. Finally, we apply the envelope-based global correlation norm on the 3-D Ocean Bottom Cable (OBC) data from the North Sea. The envelope-based global correlation norm captures the strong reflections from the high-velocity caprock and generates artificial low-frequency reflection energy that helps us recover long-wavelength structure of the model domain in the early stages. From this long-wavelength model, the conventional global correlation norm is sequentially applied to invert for higher-resolution features of the model.