Closed-loop porosity inversion method with well-seismic joint constraints based on wavelet transform

Porosity is one of the key physical properties of reservoir rocks, directly influencing their capacity to store and transmit oil and gas. Traditional porosity inversion methods are often constrained by the resolution of seismic data, lateral continuity, and secondary inversion errors, which hinder their ability to characterize reservoir properties in complex geological settings. Therefore, a closed-loop porosity inversion method with well-seismic joint constraints based on wavelet transform is proposed to predict porosity directly from post-stack seismic data. This method amplifies the training samples using kernel density estimation, thereby alleviating network instability and overfitting caused by insufficient training data. Subsequently, the seismic data is divided into low-, medium-, and high-frequency information using the wavelet transform, and the local spatial features of different scales are extracted using convolution kernels of different sizes. At the same time, the temporal features of full-frequency post-stack seismic data are extracted using gated recurrent units. Then, a forward network is constructed to replace the implicit convolution model between the post-stack seismic data and porosity, thereby establishing a closed-loop mapping from the post-stack seismic data to full-frequency porosity and back to the post-stack seismic data. Finally, the test results on the thin-layer alternating geological model and actual data show that the method proposed improves the lateral continuity of the inversion results while maintaining the vertical resolution.