  Full-waveform inversion (FWI) is known as a seismic data processing method
that achieves high-resolution imaging. In the inversion part of the method that
brings high resolution in finding a convergence point in the model space, a
local numerical optimization algorithm minimizes the objective function based
on the norm using the least-square form. Since the norm is sensitive to
outliers and noise, the method may often lead to inaccurate imaging results.
Thus, a new regulation form with a more practical relaxation form is proposed
to solve the overfitting drawback caused by the use of the norm,, namely the
K-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-support
constraints combine the and the norms. Then, a quadratic penalty method is
adopted to linearize the non-linear problem to lighten the computational load.
This paper introduces the concept of the K-support norm and integrates this
scheme with the quadratic penalty problem to improve the convergence and
robustness against background noise. In the numerical example, two synthetic
models are tested to clarify the effectiveness of the K-support norm by
comparison to the conventional norm with noisy data set. Experimental results
indicate that the modified FWI based on the new regularization form effectively
improves inversion accuracy and stability, which significantly enhances the
lateral resolution of depth inversion even with data with a low signal-to-noise
ratio (SNR).
