To overcome the weaknesses of conventional prestack amplitude variation with angle inversion based on various linear or quasi-linear approximations, we have conducted a nonlinear inversion method using the exact Zoeppritz matrix (EZAI). However, the inversion using the exact Zoeppritz matrix was highly nonlinear and often unstable, if not properly treated. To tackle these issues, we have used an iteratively regularizing Levenberg-Marquardt scheme (IRLM), which regularizes the inversion problem within an algorithm that minimizes the misfit between the observed and the modeled data at the same time by incorporating the Tikhonov regularization method. As a result, the new EZAI method solved using the IRLM scheme is feasible for seismic data sets with large incidence angles, even up to or beyond the critical angle as well as strong parameter contrasts. Single and multilayered synthetic examples were used to test these features. These tests also showed that EZAI is robust on noisy gathers for parameter extraction and has weak dependence on the initial model. For the influence of inaccurate amplitudes, dominant frequencies, and phase angles, we found that EZAI is less sensitive to the variation in amplitude and phase shifts than to the dominant frequencies. Specifically, the inversion results of EZAI for P- and S-wave velocities and density were reliable if the inaccurate range for the amplitude was within 20% or the angle of the phase shift was no more than 20°. The superiority of EZAI makes it a very promising method for the estimation of subsurface elastic parameters.

Normal-moveout (NMO) correction is one of the most important routines in seismic processing. NMO is usually implemented by a sample-by-sample procedure; unfortunately, such implementation not only decreases the frequency content but also distorts the amplitude of seismic waveforms resulting from the well-known stretch. The degree of stretch increases with increasing offset. To minimize severe stretch associated with far offset, we use a dynamic time warping (DTW) algorithm to achieve an automatic dynamic matching NMO nonstretch correction, which does not handle crossing events and convoluted events such as thin layers. Our algorithm minimizes the stretch through an automatic static temporal correction of seismic wavelets. The local static time shifts are obtained using a DTW algorithm, which is a nonlinear optimization method. To mitigate the influence of noise, we evaluated a multitrace window strategy to improve the signal-to-noise ratio of seismic data by obtaining a more precise moveout correction at far-offset traces. To illustrate the effectiveness of our algorithm, we first applied our method to synthetic data and then to field seismic data. Both tests illustrate that our algorithm minimizes the stretch associated with far offsets, and the method preserves the amplitude fidelity.

For seismic data interpretation, horizon picking based on seismic events in stacked or migrated seismic sections is essential for obtaining informatio

S-velocity and density are very important parameters to distinguish lithology and estimate other petrophysical properties. A reliable estimate of S-velocity and density is very difficult to obtain, even from long-offset gather data. Joint inversion of PP and PS data provides a promising strategy for stabilizing and improving the results of inversion in estimating elastic parameters and density. For 2D or 3D inversion, the trace-by-trace strategy is still the most widely used method although it often suffers from unclearness because of its high efficiency owing to parallel computing. This paper describes a two-stage inversion method for nonlinear PP and PS joint inversion based on the exact Zoeppritz equations. There are several advantages for our proposed methods as follows: (1) Thanks to the exact Zoeppritz equation, our joint inversion method is applicable for wide angle AVA inversion; (2) The use of both P- and S- wave information can further enhance the stability and accuracy of parameter estimation, especially for the S-velocity and density. (3) The two-stage inversion procedure proposed in this paper can achieve good compromise between efficiency and precision. On the one hand, the trace-by-trace strategy used in the first stage can be processed in parallel so that it has high computational efficiency; On the other hand, to deal with the indistinctness and undesired disturbances of the inversion results obtained from the first stage, we apply the second stage-TV regularization stage. By enforcing the spatial and temporal constraints, the TV regularization stage deblurs the inversion results and leads to parameters estimation with greater precision. Noticeably, the computation consumption of the TV regularization stage can be ignored compared to the first stage because it is solved using the fast Split-Bregman iterations. Numerical examples using well log and Marmousi II model show that the proposed joint inversion is a reliable method capable of accurately estimating the density parameter as well as P-wave velocity and S-wave velocity, even when the seismic data is noisy with signal-to-noise ratio (SNR) of 5.