Study Of The Application Of Cross Gradients In Joint Seismic And Non-seismic Data Inversion

In the exploration of geophysics, the application of joint inversion is more and more extensive. The combination of different data, such as seismic traveltime data,seismic waveform data, electromagnetic data, gravity, radar data, etc., provides more structural information for our analysis of subsurface media. Multiple parameters help determine more accurate location of mineral deposits, traps or reservoirs. At the same time, the multi-parameter inversion provides the different properties of the underground structure, reducing the non-uniqueness of the seismic interpretation.There are two kinds of joint inversion which have been developed. One is based on the physical relationship formula between the different characterization parameters of the material, and the other is based on the structural consistency of the material.We introduce the development and application of these two kinds of joint inversion respectively, and then pay attention to the cross-gradient constraint, which is structural constraint in the joint inversion. In this paper, we employ seismic data and non-seismic data, by applying cross-gradient operator to achieve joint inversion for multiple parameters.Full waveform inversion is becoming more and more important in seismic exploration, and high-resolution complex underground structures can be retrieved by wavefonn inversion. The acoustic full waveform inversion can invert the P-wave velocity, but cannot describe the elastic characteristics such as shear wave conversion, and thus, it is not conducive to provide more detailed reservoir information. The elastic full waveform inversion can provide the compressional wave velocity, shear wave velocity, attenuation, density and other elastic parameters,thus the application of elastic wave waveform inversion can provide us with more detailed and more accurate underground structure distribution. Because of the complex structure of the weathering layer and the low velocity layer in the near surface, it is difficult to perform deep imaging. Therefore, it is very important to remove the influence of the near surface structure or obtain the accurate near-surface structure by inversion before performing the deep imaging. In addition, the near-surface structure is loose and the seismic wave attenuation is obvious. The traditional full waveform inversion does not consider the influence of the attenuation parameters in seismic wave propagation. Therefore, the inverted velocity model is deviated from the real structure. We simulate the forward modelling of the waveform for near-surface structure, through comparison we can observe that the low Q value affects the amplitudes, phases, and traveltimes of waveforms significantly, and thus, we can apply the waveform received on surface to perform inversion for attenuation, which is characterized by Q factor. For near-surface area,the early arrivals primarily contain P-wave information, the surface waves primarily contain S-wave information, and thus, we propose to combine the early arrivals and the surface waves together to perform joint inversion for QP and Qs by applying cross-gradient constraint. In real case, the velocity of the medium cannot be accurately obtained, and the attenuation parameters and the seismic wave velocity are coupled by the wave equation during the propagation, thus the joint inversion of velocity and attenuation is especially crucial. We propose to employ early arrivals and surface waves to invert the P-wave velocity, shear wave velocity, QP and Qs simultaneously by applying four-parameter cross-gradient operator to constrain the structures. 2D elastic full waveform inversion costs too much computational time.We perform one-dimensional forward modelling but invert 2D structures by applying a two-dimensional Tikhonov regularization term to form the two-dimensional Jacobian matrix. By the structural constraint of cross gradients, we obtain the velocity and attenuation models. The computational efficiency of this pseudo-two-dimensional joint inversion method is significantly improved compared with the true two-dimensional elastic full waveform inversion. However, the pseudo-2D inversion can solve the layered structure with small variations or anomalies, but cannot deal with complex structures such as fault structures with velocity or attenuation changing severely. Through the synthetic tests and the real data tests, we can apply this method to obtain reliable velocity models and attenuation models.Seismic traveltime data have been employed to invert for the distribution of the subsurface velocity. However, the data received on the surface are difficult to image low velocity structures or hidden layers, and the inverted velocity model is too smooth with limited details. Airborne electromagnetic data are used to image the distribution of subsurface resistivity. The acquisition for EM data is convenient and quantitative, and thus, EM data can image detailed structures. Also, the electromagnetic inversion can image the high resistivity and low resistivity regions,but with low vertical resolution. The two distinct data are consistent with the depth of the near-surface detection, and thus, in order to provide more efficient information for geophysical interpretation, we combine the airborne electromagnetic data with the seismic traveltimes to simultaneously invert the resistivity and velocity.Because of the high computational cost of the three-dimensional electromagnetic inversion, we propose a method to perform joint inversion. This technique includes one-dimensional frequency-domain airborne electromagnetic forward modelling,three-dimensional seismic traveltime calculation, and 3D joint inversion with cross-gradient constraints between electrical resistivity and seismic slowness. By applying the three-dimensional Tikhonov regularization term, the 1D frequency-airborne electromagnetic forward modelling forms a three-dimensional Jacobian matrix.Through several synthetic tests, we demonstrate that the joint inversion can reconstruct a more accurate near-surface velocity model than one from inverting a single dataset. We apply this technique to real data. We calculate the static corrections and perform stacks for the seismic data. Reflection stacking section shows significant improvements with static corrections associated with the velocity model from joint inversion. Joint seismic and electromagnetic inversion helps determine better velocity model to calculate statics for seismic processing.