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Full-waveform inversion (FWI) is known as a seismic data processing methodthat achieves high-resolution imaging. In the inversion part of the method thatbrings high resolution in finding a convergence point in the model space, alocal numerical optimization algorithm minimizes the objective function basedon the norm using the least-square form. Since the norm is sensitive tooutliers and noise, the method may often lead to inaccurate imaging results.Thus, a new regulation form with a more practical relaxation form is proposedto solve the overfitting drawback caused by the use of the norm,, namely theK-support norm, which has the form of more reasonable and tighter constraints.In contrast to the least-square method that minimizes the norm, our K-supportconstraints combine the and the norms. Then, a quadratic penalty method isadopted to linearize the non-linear problem to lighten the computational load.This paper introduces the concept of the K-support norm and integrates thisscheme with the quadratic penalty problem to improve the convergence androbustness against background noise. In the numerical example, two syntheticmodels are tested to clarify the effectiveness of the K-support norm bycomparison to the conventional norm with noisy data set. Experimental resultsindicate that the modified FWI based on the new regularization form effectivelyimproves inversion accuracy and stability, which significantly enhances thelateral resolution of depth inversion even with data with a low signal-to-noiseratio (SNR).

Improved full-waveform inversion for seismic data in the presence of noise based on the K-support norm