Robust scaling strategy for frequency-domain acoustic full waveform inversion

Abstract

The purpose of seismic full waveform inversion (FWI) is to identify subsurface physical properties that yield waveforms similar to those of recorded data. Because subsurface physical properties are important to characterize reservoirs in oil and gas exploration, FWI has attracted the attention of geophysicists and applied mathematicians. Nevertheless, FWI is still not practical and has some problems to be resolved for real data application. One of the problems encountered when we apply FWI to real field data is noise. Because real field data contain various types of noise with non-uniform distributions, the inverse problem for real seismic data involves many uncertainties. There have been attempts to increase the robustness of FWI for noisy data by introducing new objective functions. However, most objective functions have not provided robust inversion results for the incoherent random noise, such as ambient ground motions. To minimize the influence of random noise in frequency-domain acoustic FWI, We propose a frequency-depth scaling strategy that combines the spectral scaling strategy using the denoise function and the depth scaling strategy using the constraint of the Levenberg-Marquardt method. The inversion results for synthetic data containing low-frequency random noise for the modified Marmousi-2 model show that the denoise function is approximately proportional to the signal-to-noise ratio and effectively filters out the noisy single-frequency gradient directions. In addition, the flexible damping factor acts like a depth filter, controlling the energy concentration in the gradient. In the early iterations, the energy of the gradient is concentrated in the shallow parts, whereas in the later iterations, the energy concentration moves to the deeper parts. The denoise function and the damping factor are determined with little human intervention and without any prior information about the subsurface structure during the inversion and improve the inversion results for data containing random noise.