Seismic acoustic impedance inversion plays an important role in subsurface quantitative interpretation. Due to the band-limited property of the seismic record and the discretization of the continuous elastic parameters with a limited sampling interval, the inverse problem suffers from serious ill-posedness. Various regularization methods are introduced into the seismic inversion to make the inversion results comply with the prespecified characteristics. However, conventional seismic inversion methods can only reflect fixed distribution characteristics and do not take into account discretization challenges. We have adopted a new poststack seismic impedance inversion method with upsampling and adaptive regularization. The adaptive regularization is constructed with two trained dictionaries from the true model and upsampled model-based inversion result to capture the features of high- and low-resolution details, and a sparsity-based statistical model is proposed to build the relationship between their sparse representations. The high-resolution components can be recovered based on the prediction model and low-resolution sparse representations, and the parameters of the statistical prediction model can be obtained effectively with conventional optimization algorithms. The synthetic and field data tests show that the model-based inversion is dependent on the sample interval, and our method can reveal more thin layers and enhance the extension of the strata compared with conventional inversion methods. Moreover, the inverted impedance variance of our method matches well with the borehole observations. The tests demonstrate that the interpolated model-based inversion result combined with the sparsity-based prediction model can effectively improve the resolution and accuracy of the inversion results.

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