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.

Fast 3D joint inversion of gravity and magnetic data based on cross gradient constraint

The gravity and magnetic data can be adopted to interpret the internal structure of the Earth.To improve the calculation efficiency during the inversion process and the accuracy and reliability of the reconstructed physical property models,the triple strategy is adopted in this paper to develop a fast cross-gradient joint inversion for gravity and magnetic data.The cross-gradient constraint contains solving the gradients of the physical property models and performing the cross-product calculation of their gradients.The sparse matrices are first obtained by calculating the gradients of the physical property models derived from the first-order finite difference.Then,the triple method is applied to optimize the storages and the calculations related to the gradients of the physical property models.Therefore,the storage compression amount of the calculations related to the gradients of the physical property models and the cross-gradient constraint are reduced to one-fold of the number of grid cells at least,and the compression ratio increases with the increase of the number of grid cells.The test results from the synthetic data and field data prove that the structural coupling is achieved by using the fast cross-gradient joint inversion method to effectively reduce the multiplicity of solutions and improve the computing efficiency.

Joint inversion of Rayleigh group and phase velocities for S-wave velocity structure of the 2021 M_(S)6.0 Luxian earthquake source area,China

On September 16,2021,a MS6.0 earthquake struck Luxian County,one of the shale gas blocks in the Southeastern Sichuan Basin,China.To understand the seismogenic environment and its mechanism,we inverted a fine three-dimensional S-wave velocity model from ambient noise tomography using data from a newly deployed dense seismic array around the epicenter,by extracting and jointly inverting the Rayleigh phase and group velocities in the period of 1.6–7.2 s.The results showed that the velocity model varied significantly beneath different geological units.The Yujiasi syncline is characterized by low velocity at depths of~3.0–4.0 km,corresponding to the stable sedimentary layer in the Sichuan Basin.The eastern and western branches of the Huayingshan fault belt generally exhibit high velocities in the NE-SW direction,with a few local low-velocity zones.The Luxian MS6.0 earthquake epicenter is located at the boundary between the high-and low-velocity zones,and the earthquake sequences expand eastward from the epicenter at depths of 3.0–5.0 km.Integrated with the velocity variations around the epicenter,distribution of aftershock sequences,and focal mechanism solution,it is speculated that the seismogenic mechanism of the main shock might be interpreted as the reactivation of pre-existing faults by hydraulic fracturing.

Joint inversion of gravity and vertical gradient data based on modified structural similarity index for the structural and petrophysical consistency constraint

Joint inversion is one of the most effective methods for reducing non-uniqueness for geophysical inversion.The current joint inversion methods can be divided into the structural consistency constraint and petrophysical consistency constraint methods,which are mutually independent.Currently,there is a need for joint inversion methods that can comprehensively consider the structural consistency constraints and petrophysical consistency constraints.This paper develops the structural similarity index(SSIM)as a new structural and petrophysical consistency constraint for the joint inversion of gravity and vertical gradient data.The SSIM constraint is in the form of a fraction,which may have analytical singularities.Therefore,converting the fractional form to the subtractive form can solve the problem of analytic singularity and finally form a modified structural consistency index of the joint inversion,which enhances the stability of the SSIM constraint applied to the joint inversion.Compared to the reconstructed results from the cross-gradient inversion,the proposed method presents good performance and stability.The SSIM algorithm is a new joint inversion method for petrophysical and structural constraints.It can promote the consistency of the recovered models from the distribution and the structure of the physical property values.Then,applications to synthetic data illustrate that the algorithm proposed in this paper can well process the synthetic data and acquire good reconstructed results.

Curupira V1.0: Joint Inversion of VES and TEM for Environmental and Mass Movements Studies

An innovative inversion code, named “Curupira v1.0”, has been developed using Matlab to determine the vertical distribution of resistivity beneath the subsoil. The program integrates Vertical Electrical Sounding (VES), successful in shallow subsurface exploration and Time Domain Electromagnetic (TEM) techniques, better suited for deeper exploration, both of which are widely employed in geophysical exploration. These methodologies involve calculating subsurface resistivity through appropriate inversion processes. To address the ill-posed nature of inverse problems in geophysics, a joint inversion scheme combining VES and TEM data has been incorporated into Curupira v1.0. The software has been tested on both synthetic and real-world data, the latter of which was acquired from the Parana sedimentary basin which we summarise here. The results indicate that the joint inversion of VES and TEM techniques offers improved recovery of simulated models and demonstrates significant potential for hydrogeological studies.

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.

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.

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.

Effective elastic thickness of the lithosphere from joint inversion in western China and its implications

The western China lies in the convergence zone between Eurasian and Indian plates.It is an ideal place to study the lithosphere dynamics and tectonic evolutions on the continental Earth.The lithospheric strength is a key factor in controlling the lithosphere dynamics and deformations.The effective elastic thickness(T_(e))of the lithosphere can be used to address the lithospheric strength.Previous researchers only used one of the admittance or coherence methods to investigate the T_(e) in the western China.Moreover,most of them ignored the internal loads of the lithosphere during the T_(e) calculation,which can produce large biases in the T_(e) estimations.To provide more reliable T_(e) estimations,we used a new joint inversion method that integrated both admittance and coherence techniques to compute the T_(e) in this study,with the WGM2012 gravity data,the ETOPO1 topographic data,and the Moho depths from the CRUST1.0 model.The internal loads are considered and investigated using the load ratio(F).Our results show that the joint inversion method can yield reliable T_(e) and F values.Based on the analysis of T_(e) and F distributions,we suggest(1)the northern Tibetan Plateau could be the front edge of the plate collision of Eurasian and Indian plates;(2)the southern and part of central Tibetan Plateau have a strong lithospheric mantle related to the rigid underthrusting Indian plate;(3)the southeastern Tibetan Plateau may be experiencing the delamination of lithosphere and upwelling of asthenosphere.

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.

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.

3D joint inversion of controlled-source audio-frequency magnetotelluric and magnetotelluric data

Different geophysical exploration methods have significant differences in terms of exploration depth,especially in frequency domain electromagnetic(EM)exploration.According to the definition of skin depth,this difference will increase with the effective detection frequency of the method.As a result,when performing three-dimensional inversion on single type of EM data,it is not possible to effectively distinguish the subsurface geoelectric structure at the full scale.Therefore,it is necessary to perform joint inversion on different type of EM data.In this paper we combine the magnetotelluric method(MT)with the controlled-source audio-magnetotelluric method(CSAMT)to study the frequency-domain three-dimensional(3D)joint inversions,and we use the unstructured finite-element method to do the forward modeling for them,so that the numerical simulation accuracies of different electromagnetic methods can be satisfied.By combining the two sets of data,we can obtain the sensitivity of the electrical structure at different depths,and depict the full-scale subsurface geoelectric structures.In actual mineral exploration,the 3D joint inversion is more useful for identifying subsurface veins in the shallow part and blind mines in the deep part.It can delineate the morphological distribution of ore bodies more completely and provide reliable EM interpretations to guide the mining of minerals.

S-wave velocity structure in Tangshan earthquake region and its adjacent areas from joint inversion of receiver functions and surface wave dispersion

Using the seismic records of 83 temporary and 17 permanent broadband seismic stations deployed in Tangshan earthquake region and its adjacent areas(39°N–41.5°N,115.5°E–119.5°E),we conducted a nonlinear joint inversion of receiver functions and surface wave dispersion.We obtained some detailed information about the Tangshan earthquake region and its adjacent areas,including sedimentary thickness,Moho depth,and crustal and upper mantle S-wave velocity.Meanwhile,we also obtained the vP/vS structure along two sections across the Tangshan region.The results show that:(1)the Moho depth ranges from 30 km to 38 km,and it becomes shallower from Yanshan uplift area to North China basin;(2)the thickness of sedimentary layer ranges from 0 km to 3 km,and it thickens from Yanshan uplift region to North China basin;(3)the S-wave velocity structure shows that the velocity distribution of the upper crust has obvious correlation with the surface geological structure,while the velocity characteristics of the middle and lower crust are opposite to that of the upper crust.Compared with the upper crust,the heterogeneity of the middle and lower crust is more obvious;(4)the discontinuity of Moho on the two sides of Tangshan fault suggests that Tangshan fault cut the whole crust,and the low vS and high vP/vS beneath the Tangshan earthquake region may reflect the invasion of mantle thermal material through Tangshan fault.

Source rupture model of the 2018 M_(W)6.7 Iburi,Hokkaido earthquake from joint inversion of strong motion and InSAR observations

The 2018 M_(W)6.7 Iburi earthquake shocked the eastern Iburi region to the west of the Hidaka Collision Zone in Hokkaido,which is a destructive inland earthquake.We resolved the kinematic rupture process of the event by combining strong motions(SM)and synthetic aperture radar(SAR)images in a joint inversion.The results reveal that the duration of the whole rupture is about 17s,yielding a total seismic moment of 1.4×10^(19)N·m(M_(W)=6.7).The main slip area is located at a depth of approximately 24 km with a peak slip of~0.8m above the hypocenter.The comparison with the regional velocity model shows the earthquake was initiated in the upper mantle,while the majority of slips are located in the lower crust,which is an“aseismic”domain in the typical sandwich model.The location of the major slip area is consistent with a high-conductivity volume.We proposed a mechanism of low frictional property(<0.3)produced by high pore pressure to explain the abnormal high dip angle and centroid depth located in the ductile lower-crust.Aftershocks are distributed in areas where the Coulomb frictional stress increases due to co-seismic displacement with a mechanism conjugating to the mainshock.

Tomographic determination of 3－D crustal structure──Joint inversion of explosion and earthquake data

In this paper, the theory and method, obtaining the tomographic determination of three-dimensional velocity structure of the crust by use of the joint inversion of explosion and earthquake data, are given. The velocity distribution of the crust is regarded as a continuous function of the spatial coordinates without parametrization of the velocity model ahead, so that the inversion solution would not be influenced by different parametrization procedures.The expressions of integration kernels, which relates the two kinds of data sets, are also given. The authors have processed the observed data in Tangshan earthquake region by the method proposed in this paper, and obtained the tomographic results of the middle and upper crust structures in this region. The comparison of these results with the result obtained only by the explosion data, has also been made.

The 2023 M_(w)6.8 Adassil Earthquake(Chichaoua,Morocco)on a steep reverse fault in the deep crust and its geodynamic implications

The Mw 6.8 Adassil earthquake that occurred in the High Atlas on September 8,2023,was a catastrophic event that provided a rare opportunity to study the mechanics of deep crustal seismicity.This research aimed to decipher the rupture characteristics of the Adassil earthquake by analyzing teleseismic waveform data in conjunction with interferometric synthetic aperture radar(InSAR)observations from both ascending and descending orbits.Our analysis revealed a reverse fault mechanism with a centroid depth of approximately 28 km,exceeding the typical range for crustal earthquakes.This result suggests the presence of cooler temperatures in the lower crust,which facilitates the accumulation of tectonic stress.The earthquake exhibited a steep reverse mechanism,dipping at 70°,accompanied by minor strike-slip motion.Within the geotectonic framework of the High Atlas,known for its volcanic legacy and resulting thermal irregularities,we investigated the potential contributions of these factors to the initiation of the Adassil earthquake.Deep seismicity within the lower crust,away from plate boundaries,calls for extensive research to elucidate its implications for regional seismic hazard assessment.Our findings highlight the critical importance of studying and preparing for significant seismic events in similar geological settings,which would provide valuable insights into regional seismic hazard assessments and geodynamic paradigms.

An inversion of site response and Lg attenuation using Lg waveform

Based on spectral ratio method, a joint inversion method was used to obtain parameters of Lg wave attenuation and site response. The inversion method allows simple and direct （two-parameter） determination of Lg wave attenuation and site response from sparse spectral data, which are not affected by radiation pattern factor and different response of same instrument after geometrical spreading. The method was used successfully for estimating site response of stations of Zhejiang Seismic Network and measuring Lg wave attenuation. The study is based on 20 earthquakes occurred in northeast of Taiwan with magnitude Ms5.0-6.7 and 960 seismic wave records from 16 stations in Zhejiang area from 2002 to 2005. The parameters of site response and Lg attenuation were calculated with a frequency interval of 0.2 Hz in the range of 0.5 Hz to 10 Hz. Lg wave attenuation coefficient corresponding to U-D, E-W and N-S components are γ（f）=0.00175f^0.43485, γ（f）=0.00145f^0.48467 and γ（f）=0.0021f^0.41241, respectively. It is found that the site response is component-independent. It is also found that the site response of QIY station is significant above the frequency of 1.5 Hz, and that the site response of NIB station is low for most frequency

Focal mechanism inversion of the 2018 M_(W)7.1 Anchorage earthquake based on high-rate GPS observation

The M_(W)7.1 Anchorage earthquake is the most destructive earthquake since the 1964 M_(W)9.2 great Alaska earthquake in the United States.In this study,high-rate GPS data and near-field broadband seismograms are used in separate and joint inversions by the generalized Cut-and-Paste(gCAP)method to estimate the focal mechanism.In order to investigate the influence of crustal velocity structure on the focal mechanism inversion results,two velocity models(Crustl.0 and Alaska Earthquake Center(AEC))are used for detailed comparison and analysis.The results show that:(1)The two nodal planes of the optimal double-couple solution are nearly north-south striking,with dip angles of about 30°and 60°respectively,and the centroid focal depth is 54-55 km,which is an intraplate normal fault event.(2)The inversion results for the two types of data and the two velocity models are consistent with some previous studies,which indicates that the results are stable and reliable.The more accurate velocity structure model is helpful for focal mechanism inversion of the complex earthquake.(3)The inclusion of high-rate GPS data in joint inversion provides a more effective constraint on centroid depth.