  Seismic impedance inversion is one of the most important part of geophysical
exploration. However, due to random noise, the traditional semi-supervised
learning (SSL) methods lack generalization and stability. To solve this
problem, some authors have proposed SSL methods with anti-noise function to
improve noise robustness and inversion accuracy. However, such methods are
often not ideal when faced with strong noise. In addition, Low-frequency
impedance models can mitigate this problem, but creating accurate low-frequency
models is difficult and error-prone when well-log data is sparse and subsurface
structures are complex. To address those issues, we propose a novel deep
learning inversion method called DSIM-USSL (Unsupervised and Semi-supervised
joint Learning for Seismic Inversion based on diffusion model). Specifically,
we are the first to introduce a diffusion model with strong noise tendency and
construct a diffusion seismic inversion model (DSIM). In the reverse diffusion
of DSIM, we design the encoder-decoder which combines CNN for capturing local
features and GRU for global sequence modeling; and we choose U-net to learn the
distribution of random noise, enhancing the generalization and stability of
proposed method. Furthermore, to further improve generalization of the proposed
method, a two-step training approach (USSL) is utilized. First, an unsupervised
trained encoder-decoder is used as the initial network model in place of the
traditional low-frequency wave impedance model that is difficult to accurately
acquire. Then, the SSL is employed to further optimize the encoder-decoder
model. Experimental results on the Marmousi2 model and field data demonstrate
that the DSIM-USSL method achieves higher accuracy in the presence of seismic
data with random noise, and maintains high stability even under strong noise
conditions.
