Multi-scale data joint inversion of minerals and porosity in altered igneous reservoirs—A case study in the South China Sea

There are abundant igneous gas reservoirs in the South China Sea with significant value of research,and lithology classification,mineral analysis and porosity inversion are important links in reservoir evaluation.However,affected by the diverse lithology,complicated mineral and widespread alteration,conventional logging lithology classification and mineral inversion become considerably difficult.At the same time,owing to the limitation of the wireline log response equation,the quantity and accuracy of minerals can hardly meet the exploration requirements of igneous formations.To overcome those issues,this study takes the South China Sea as an example,and combines multi-scale data such as micro rock slices,petrophysical experiments,wireline log and element cutting log to establish a set of joint inversion methods for minerals and porosity of altered igneous rocks.Specifically,we define the lithology and mineral characteristics through core slices and mineral data,and establish an igneous multi-mineral volumetric model.Then we determine element cutting log correction method based on core element data,and combine wireline log and corrected element cutting log to perform the lithology classification and joint inversion of minerals and porosity.However,it is always difficult to determine the elemental eigenvalues of different minerals in inversion.This paper uses multiple linear regression methods to solve this problem.Finally,an integrated inversion technique for altered igneous formations was developed.The results show that the corrected element cutting log are in good agreement with the core element data,and the mineral and porosity results obtained from the joint inversion based on the wireline log and corrected element cutting log are also in good agreement with the core data from X-ray diffraction.The results demonstrate that the inversion technique is applicable and this study provides a new direction for the mineral inversion research of altered igneous formations.

Crustal and uppermost mantle structure of the northeastern Qinghai-Xizang Plateau from joint inversion of surface wave dispersions and receiver functions with P velocity constraints

Lithospheric structure beneath the northeastern Qinghai-Xizang Plateau is of vital significance for studying the geodynamic processes of crustal thickening and expansion of the Qinghai-Xizang Plateau. We conducted a joint inversion of receiver functions and surface wave dispersions with P-wave velocity constraints using data from the Chin Array Ⅱ temporary stations deployed across the Qinghai-Xizang Plateau. Prior to joint inversion, we applied the H-κ-c method(Li JT et al., 2019) to the receiver function data in order to correct for the back-azimuthal variations in the arrival times of Ps phases and crustal multiples caused by crustal anisotropy and dipping interfaces. High-resolution images of vS, crustal thickness, and vP/vSstructures in the Qinghai-Xizang Plateau were simultaneously derived from the joint inversion. The seismic images reveal that crustal thickness decreases outward from the Qinghai-Xizang Plateau. The stable interiors of the Ordos and Alxa blocks exhibited higher velocities and lower crustal vP/vSratios. While, lower velocities and higher vP/vSratios were observed beneath the Qilian Orogen and Songpan-Ganzi terrane(SPGZ), which are geologically active and mechanically weak, especially in the mid-lower crust.Delamination or thermal erosion of the lithosphere triggered by hot asthenospheric flow contributes to the observed uppermost mantle low-velocity zones(LVZs) in the SPGZ. The crustal thickness, vS, and vP/vSratios suggest that whole lithospheric shortening is a plausible mechanism for crustal thickening in the Qinghai-Xizang Plateau, supporting the idea of coupled lithospheric-scale deformation in this region.

An empirical method for joint inversion of wave and wind parameters based on SAR and wave spectrometer data

Synthetic aperture radar(SAR)and wave spectrometers,crucial in microwave remote sensing,play an essential role in monitoring sea surface wind and wave conditions.However,they face inherent limitations in observing sea surface phenomena.SAR systems,for instance,are hindered by an azimuth cut-off phenomenon in sea surface wind field observation.Wave spectrometers,while unaffected by the azimuth cutoff phenomenon,struggle with low azimuth resolution,impacting the capture of detailed wave and wind field data.This study utilizes SAR and surface wave investigation and monitoring(SWIM)data to initially extract key feature parameters,which are then prioritized using the extreme gradient boosting(XGBoost)algorithm.The research further addresses feature collinearity through a combined analysis of feature importance and correlation,leading to the development of an inversion model for wave and wind parameters based on XGBoost.A comparative analysis of this model with ERA5 reanalysis and buoy data for of significant wave height,mean wave period,wind direction,and wind speed reveals root mean square errors of 0.212 m,0.525 s,27.446°,and 1.092 m/s,compared to 0.314 m,0.888 s,27.698°,and 1.315 m/s from buoy data,respectively.These results demonstrate the model’s effective retrieval of wave and wind parameters.Finally,the model,incorporating altimeter and scatterometer data,is evaluated against SAR/SWIM single and dual payload inversion methods across different wind speeds.This comparison highlights the model’s superior inversion accuracy over other methods.

High-resolution seismic inversion method based on joint data-driven in the time-frequency domain

Seismic inversion can be divided into time-domain inversion and frequency-domain inversion based on different transform domains.Time-domain inversion has stronger stability and noise resistance compared to frequencydomain inversion.Frequency domain inversion has stronger ability to identify small-scale bodies and higher inversion resolution.Therefore,the research on the joint inversion method in the time-frequency domain is of great significance for improving the inversion resolution,stability,and noise resistance.The introduction of prior information constraints can effectively reduce ambiguity in the inversion process.However,the existing modeldriven time-frequency joint inversion assumes a specific prior distribution of the reservoir.These methods do not consider the original features of the data and are difficult to describe the relationship between time-domain features and frequency-domain features.Therefore,this paper proposes a high-resolution seismic inversion method based on joint data-driven in the time-frequency domain.The method is based on the impedance and reflectivity samples from logging,using joint dictionary learning to obtain adaptive feature information of the reservoir,and using sparse coefficients to capture the intrinsic relationship between impedance and reflectivity.The optimization result of the inversion is achieved through the regularization term of the joint dictionary sparse representation.We have finally achieved an inversion method that combines constraints on time-domain features and frequency features.By testing the model data and field data,the method has higher resolution in the inversion results and good noise resistance.

Joint PP and PS AVO inversion based on Bayes theorem

Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.

Generalized linear joint PP-PS inversion based on two constraints

Conventional joint PP-PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS;therefore,the inversion precision and stability cannot satisfy current exploration requirements.We propose a joint PP-PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion.A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data,the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion,low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness,and a fast algorithm is used to solve the objective function while minimizing the computational load.The proposed method has superior antinoising properties and well reproduces real data.

Joint inversion of gravity and magnetic data for a two-layer model

Based on the synchronous joint gravity and magnetic inversion of single interface by Pilkington and the need of revealing Cenozoic and crystalline basement thickness in the new round of oil-gas exploration, we propose a joint gravity and magnetic inversion methodfor two-layer models by concentrating on the relationship between the change of thicknessI and position of the middle layer and anomaly and discuss the effects of the key parameters. Model tests and application to field data show the validity of this method.

AVO approximation for PS-wave and its application in PP/PS joint inversion

Multi-component exploration has many advantages over ordinary P-wave exploration. PP/PS joint AVO analysis and inversion are useful and powerful methods to discriminate between reservoir and non-productive lithology. In this paper, we derive a new PS-wave reflection coefficient approximation equation which is more accurate at larger incidence angles. The equation is simplified for small incidence angles, which makes AVO analysis clearer and easier for angles less than 30 degrees. Based on this approximation, a PP/PS joint inversion is introduced. A real data example shows that oil sands, brine sands and shales can be differentiated based on the P- to S-wave velocity ratio from the PP/PS joint inversion. Fluid factors and Poisson＇s ratio also indicate an anomaly in the target zone at the oil well location.

Nonlinear joint PP-PS AVO inversion based on improved Bayesian inference and LSSVM

Multiwave seismic technology promotes the application of joint PP–PS amplitude versus offset (AVO) inversion;however conventional joint PP–PS AVO inversioan is linear based on approximations of the Zoeppritz equations for multiple iterations. Therefore the inversion results of P-wave, S-wave velocity and density exhibit low precision in the faroffset;thus, the joint PP–PS AVO inversion is nonlinear. Herein, we propose a nonlinear joint inversion method based on exact Zoeppritz equations that combines improved Bayesian inference and a least squares support vector machine (LSSVM) to solve the nonlinear inversion problem. The initial parameters of Bayesian inference are optimized via particle swarm optimization (PSO). In improved Bayesian inference, the optimal parameter of the LSSVM is obtained by maximizing the posterior probability of the hyperparameters, thus improving the learning and generalization abilities of LSSVM. Then, an optimal nonlinear LSSVM model that defi nes the relationship between seismic refl ection amplitude and elastic parameters is established to improve the precision of the joint PP–PS AVO inversion. Further, the nonlinear problem of joint inversion can be solved through a single training of the nonlinear inversion model. The results of the synthetic data suggest that the precision of the estimated parameters is higher than that obtained via Bayesian linear inversion with PP-wave data and via approximations of the Zoeppritz equations. In addition, results using synthetic data with added noise show that the proposed method has superior anti-noising properties. Real-world application shows the feasibility and superiority of the proposed method, as compared with Bayesian linear inversion.

Stepwise joint inversion of surface wave dispersion,Rayleigh wave ZH ratio,and receiver function data for 1D crustal shear wave velocity structure

Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio （i.e., ellipticity）, and receiver function data to better resolve 1D crustal shear wave velocity （Vs） structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensi- tivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast （e.g., due to the existence of crustal interfaces） and Vp/Vs ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the Vs model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute vs model and then incorporate receiver function data in the joint inver- sion to obtain a finer Vs model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal Vs structures and with little initial model dependency.

Rupture process of the 2011 Tohoku earthquake from the joint inversion of teleseismic and GPS data

Teleseismic and GPS data were jointly inverted for the rupture process of the 2011 Tohoku earthquake. The inversion results show that it is a bilateral rupture event with an average rupture velocity less than 2.0 km/s along the fault strike direction. The source rupture process consists of three sub-events, the first oc- curred near the hypocenter and the rest two ruptured along the up-dip direction and broke the sea bed, causing a maximum slip of about 30 m. The large-scale sea bed breakage may account for the tremendous tsunami disaster which resulted in most of the death and missing in this mega earthquake.

2D joint inversion of CSAMT and magnetic data based on cross-gradient theory

A two-dimensional forward and backward algorithm for the controlled-source audio-frequency magnetotelluric （CSAMT） method is developed to invert data in the entire region （near, transition, and far） and deal with the effects of artificial sources. First, a regularization factor is introduced in the 2D magnetic inversion, and the magnetic susceptibility is updated in logarithmic form so that the inversion magnetic susceptibility is always positive. Second, the joint inversion of the CSAMT and magnetic methods is completed with the introduction of the cross gradient. By searching for the weight of the cross-gradient term in the objective function, the mutual influence between two different physical properties at different locations are avoided. Model tests show that the joint inversion based on cross-gradient theory offers better results than the single-method inversion. The 2D forward and inverse algorithm for CSAMT with source can effectively deal with artificial sources and ensures the reliability of the final joint inversion algorithm.

Source model of the 11th July 2004 Zhongba earthquake revealed from the joint inversion of InSAR and seismological data

We use interferometric synthetic aperture radar （InSAR） and broadband seismic waveform data to estimate a source model of the 11th July, 2004 M W 6.2 Zhongba earthquake, Tibet of China. This event occurred within the seismically active zone of southwestern Tibetan Plateau where the east-west extension of the upper crust is observed. Because of limitations in one pair of InSAR data available, there are trade-offs among centroid depth, rupture area and amount of slip. Available seismic data tightly constrain the focal mechanism and centroid depth of the earthquake but not the horizontal location. Together, two complementary data sets can be used to identify the actual fault plane, better constrain the slip model and event location. We first use regional seismic waveform to estimate point source mechanism, then InSAR data is used to obtain better location. Finally, a joint inversion of teleseismic P-waves and InSAR data is performed to obtain a distributed model. Our preferred point source mechanism indicates a seismic moment of ～2.2×10 18 N·m （～M W 6.2）, a fault plane solution of 171° （342 ° ）/42 ° （48 ° ）/-83 ° （-97 ° ）, corresponding to strike/dip/rake, and a depth of 11 km. The fault plane with strike of 171 ？ and dip of 42° is identified as the ruptured fault with the aid of InSAR data. The preferred source model features compact area of slips between depth of 5–11 km and 10 km along strike with maximum slip amplitude of about 1.5 m.

Elastic modulus extraction based on generalized pre-stack PP–PS wave joint linear inversion

Joint PP–PS inversion offers better accuracy and resolution than conventional P-wave inversion. P-and S-wave elastic moduli determined through data inversions are key parameters for reservoir evaluation and fluid characterization. In this paper, starting with the exact Zoeppritz equation that relates P-and S-wave moduli, a coefficient that describes the reflections of P-and converted waves is established. This method effectively avoids error introduced by approximations or indirect calculations, thus improving the accuracy of the inversion results. Considering that the inversion problem is ill-posed and that the forward operator is nonlinear, prior constraints on the model parameters and modified low-frequency constraints are also introduced to the objective function to make the problem more tractable. This modified objective function is solved over many iterations to continuously optimize the background values of the velocity ratio, which increases the stability of the inversion process. Tests of various models show that the method effectively improves the accuracy and stability of extracting P and S-wave moduli from underdetermined data. This method can be applied to provide inferences for reservoir exploration and fluid extraction.

The distribution of deep source rocks in the GS Sag:joint MT-gravity modeling and constrained inversion

The coal-bearing strata of the deep Upper Paleozoic in the GS Sag have high hydrocarbon potential. Because of the absence of seismic data, we use electromagnetic （MT） and gravity data jointly to delineate the distribution of deep targets based on well logging and geological data. First, a preliminary geological model is established by using three-dimensional （3D） MT inversion results. Second, using the formation density and gravity anomalies, the preliminary geological model is modified by interactive inversion of the gravity data. Then, we conduct MT-constrained inversion based on the modified model to obtain an optimal geological model until the deviations at all stations are minimized. Finally, the geological model and a seismic profile in the middle of the sag is analysed. We determine that the deep reflections of the seismic profile correspond to the Upper Paleozoic that reaches thickness up to 800 m. The processing of field data suggests that the joint MT-gravity modeling and constrained inversion can reduce the multiple solutions for single geophysical data and thus improve the recognition of deep formations. The MT-constrained inversion is consistent with the geological features in the seismic section. This suggests that the joint MT and gravity modeling and constrained inversion can be used to delineate deep targets in similar basins.

Joint inversion of gravity and seismic data along a profile across the seismogenic fault of 2010 Yushu Ms7. 1 earthquake

Yushu Ms7.1 earthquake occurred on the Ganzi-Yushu fault zone, across which we carried out a joint relative-gravity and seismic-reflection survey, and then performed a gravity inversion constrained by the seismic-reflection result. Based on the data of complete Bouguer gravity anomaly and seismic reflection, we obtained a layered interface structure in deep crust down to Moho. Our study showed that the inversion could reveal the interfaces of strata along the survey profile and the directions of regional faults in two-dimension. From the characteristics of the observed topography of the Moho basement, we tentatively confirmed that the uplift of eastern edge of Qinghai-Tibet plateau was caused by the subduetion of the Indian plate.

3D inversion modeling of joint gravity and magnetic data based on a sinusoidal correlation constraint

Joint inversion based on a correlation constraint utilizes a linear correlation function as a structural constraint.The linear correlation function contains a denominator,which may result in a singularity as the objective function is optimized,leading to an unstable inversion calculation.To improve the robustness of this calculation,this paper proposes a new method in which a sinusoidal correlation function is employed as the structural constraint for joint inversion instead of the conventional linear correlation function.This structural constraint does not contain a denominator,thereby preventing a singularity.Compared with the joint inversion method based on a cross-gradient constraint,the joint inversion method based on a sinusoidal correlation constraint exhibits good performance.An application to actual data demonstrates that this method can process real data.

Prestack AVA joint inversion of PP and PS waves using the vectorized reflectivity method

Most current prestack AVA joint inversion methods are based on the exact Zoeppritz equation and its various approximations. However, these equations only reflect the relation between reflection coefficients, incidence angles, and elastic parameters on either side of the interface, which means that wave-propagation effects, such as spherical spreading, attenuation, transmission loss, multiples, and event mismatching of P-and S-waves, are not considered and cannot accurately describe the true propagation characteristics of seismic waves. Conventional AVA inversion methods require that these wave-propagation effects have been fully corrected or attenuated before inversion but these requirements can hardly be satisfied in practice. Using a one-dimensional(1 D) earth model, the reflectivity method can simulate the full wavefield response of seismic waves. Therefore, we propose a nonlinear multicomponent prestack AVA joint inversion method based on the vectorized reflectivity method, which uses a fast nondominated sorting genetic algorithm(NSGA II) to optimize the nonlinear multiobjective function to estimate multiple parameters, such as P-wave velocity, S-wave velocity, and density. This approach is robust because it can simultaneously cope with more than one objective function without introducing weight coefficients. Model tests prove the effectiveness of the proposed inversion method. Based on the inversion results, we find that the nonlinear prestack AVA joint inversion using the reflectivity method yields more accurate inversion results than the inversion by using the exact Zoeppritz equation when the wave-propagation effects of transmission loss and internal multiples are not completely corrected.

3D v_P and v_S models of southeastern margin of the Tibetan plateau from joint inversion of body-wave arrival times and surface-wave dispersion data

A new 3D velocity model of the crust and upper mantle in the southeastern （SE） margin of the Tibetan plateau was obtained by joint inversion of body- and sur- face-wave data. For the body-wave data, we used 7190 events recorded by 102 stations in the SE margin of the Tibetan plateau. The surface-wave data consist of Rayleigh wave phase velocity dispersion curves obtained from ambient noise cross-correlation analysis recorded by a dense array in the SE margin of the Tibetan plateau. The joint inversion clearly improves the Vs model because it is constrained by both data types. The results show that at around 10 km depth there are two low-velocity anomalies embedded within three high-velocity bodies along the Longmenshan fault system. These high-velocity bodies correspond well with the Precambrian massifs, and the two located to the northeast of 2013 Ms 7.0 Lushan earthquake are associated with high fault slip areas during the 2008 Wenchuan earthquake. The aftershock gap between 2013 Lushan earthquake and 2008 Wenchuan earthquake is associated with low-velocity anomalies, which also acts as a barrier zone for ruptures of two earthquakes. Generally large earthquakes （M 〉 5） in the region occurring from 2008 to 2015 are located around the high-velocity zones, indicating that they may act as asperities for these large earthquakes. Joint inversion results also clearly show that there exist low-velocity or weak zones in the mid-lower crust, which are not evenly distributed beneath the SE margin of Tibetan plateau.

Coseismic deformation of the 2021 M_(W)7.4 Maduo earthquake from joint inversion of InSAR, GPS, and teleseismic data

The M_(W)7.4 Maduo earthquake occurred on 22 May 2021 at 02:04 CST with a large-expansion surface rupture.This earthquake was located in the Bayan Har block at the eastern Tibetan Plateau,where eight earthquakes of M_(S)>7.0 have occurred in the past 25 years.Here,we combined interferometric synthetic aperture radar,GPS,and teleseismic data to study the coseismic slip distribution,fault geometry,and dynamic source rupture process of the Maduo earthquake.We found that the overall coseismic deformation field of the Maduo earthquake is distributed in the NWW-SEE direction along 285°.There was slight bending at the western end and two branches at the eastern end.The maximum slip is located near the eastern bending area on the northern branch of the fault system.The rupture nucleated on the Jiangcuo fault and propagated approximately 160 km along-strike in both the NWW and SEE directions.The characteristic source rupture process of the Maduo earthquake is similar to that of the 2010 M_(W)6.8 Yushu earthquake,indicating that similar earthquakes with large-expansion surface ruptures and small shallow slip deficits can occur on both the internal fault and boundary fault of the Bayan Har block.