가우스-뉴턴법을 이용한 탄성파 단일 트레이스 역산 알고리즘 개발 및 적용

Abstract

In this study, a seismic single trace inversion algorithm was developed to build a subsurface velocity model using waveform inversion. The existing single trace inversion algorithm is conducted based on the convolution theory. In contrast, the proposed algorithm assumes that the subsurface velocity model is one-dimensional, and utilizes the Gauss-Newton method to build a velocity model. To develop the algorithm, a numerical modeling algorithm based on the staggered grid finite difference method was applied, and the virtual source term was defined to calculate the Hessian matrix. In addition, the seismic source estimation technique was used.

The validity of the proposed algorithm was verified through numerical tests using the Marmousi2 model. First, the numerical test using post-stack data was conducted. In this test, an inverted velocity model was built using the proposed algorithm, and the algorithm was compared with the post-stack inversion algorithms of the Hampson-Russell software. As a result, the proposed algorithm seems to yield better results than the existing algorithms. Next, a numerical test was conducted to investigate the effect of offset. For such purpose, numerical modeling data obtained by a single channel were used. As a result, a reliable result within 10m offset was confirmed. Finally, the algorithm was applied to the field dataset obtained from Busan Port to build a velocity model, and the proposed algorithm was found to be applicable to field data.