Probabilistic seismic inversion based on physics-guided deep mixture density network

Deterministic inversion based on deep learning has been widely utilized in model parameters estimation.Constrained by logging data,seismic data,wavelet and modeling operator,deterministic inversion based on deep learning can establish nonlinear relationships between seismic data and model parameters.However,seismic data lacks low-frequency and contains noise,which increases the non-uniqueness of the solutions.The conventional inversion method based on deep learning can only establish the deterministic relationship between seismic data and parameters,and cannot quantify the uncertainty of inversion.In order to quickly quantify the uncertainty,a physics-guided deep mixture density network(PG-DMDN)is established by combining the mixture density network(MDN)with the deep neural network(DNN).Compared with Bayesian neural network(BNN)and network dropout,PG-DMDN has lower computing cost and shorter training time.A low-frequency model is introduced in the training process of the network to help the network learn the nonlinear relationship between narrowband seismic data and low-frequency impedance.In addition,the block constraints are added to the PG-DMDN framework to improve the horizontal continuity of the inversion results.To illustrate the benefits of proposed method,the PG-DMDN is compared with existing semi-supervised inversion method.Four synthetic data examples of Marmousi II model are utilized to quantify the influence of forward modeling part,low-frequency model,noise and the pseudo-wells number on inversion results,and prove the feasibility and stability of the proposed method.In addition,the robustness and generality of the proposed method are verified by the field seismic data.

Pre-stack seismic density inversion in marine shale reservoirs in the southern Jiaoshiba area, Sichuan Basin, China

For a typical marine shale reservoir in the Jiaoshiba area, Sichuan Basin of China, P-impedance is sensitive for identifying lithology but not suitable for indicating good shale reservoirs. In comparison, density is an important quantity, which is sensitive for identifying the organic-rich mud shale from non-organic-rich mud shale. Due to the poor data quality and incidence angle range, density cannot be easily inverted by directly solving the ill-posed pre-stack seismic inversion in this area. Meanwhile, the traditional density regularizations implemented by directly using the more robust P-impedance inversion tend to be inaccurate for recovering density for this shale reservoir. In this paper, we combine the P-impedance and the minus uranium to construct the pseudo-P-impedance（PIp） at well locations. The PIp is observed to be sensitive for identifying organic-rich mud shale and has a good correlation with density in this area. We employ the PIp–density relation into the pre-stack inversion framework to estimate density. Three types of regularization are tested on both numerical and field data： These are no regularization, traditional regularization and the proposed approach. It is observed that the proposed method is better for recovering the density of organic-rich mud shale in the Jiaoshiba area.

Gravity inversion using the frequency characteristics of the density distribution

Three-dimensional gravity inversion based on the mass property model is very popular in recent years. The time and efficiency of inversion algorithms is relative to the magnitude of the target mesh. One approach is to search over the entire solution space for a more refined result. However, the inversion will be difficult with the increased parameters in the large search space and the number of computations increases exponentially. ｜n this paper, we propose a novel approach based on the frequency characteristics of the density distribution over the mesh. The purposes of our study are to reduce the parameters of three- dimensional gravity inversion and to lighten the image quality of the inversion result. The results show that the new method can expedite the inversion processing and get a better geological interpretation than tradition methods.

Prestack density inversion using the Fatti equation constrained by the P-and S-wave impedance and density

Simultaneous prestack inversion is based on the modified Fatti equation and uses the ratio of the P- and S-wave velocity as constraints. We use the relation of P-wave impedance and density （PID） and S-wave impedance and density （SID） to replace the constant Vp/Vs constraint, and we propose the improved constrained Fatti equation to overcome the effect of P-wave impedance on density. We compare the sensitivity of both methods using numerical simulations and conclude that the density inversion sensitivity improves when using the proposed method. In addition, the random conjugate-gradient method is used in the inversion because it is fast and produces global solutions. The use of synthetic and field data suggests that the proposed inversion method is effective in conventional and nonconventional lithologies.

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.

Pre-stack inversion for caved carbonate reservoir prediction:A case study from Tarim Basin,China

The major storage space types in the carbonate reservoir in the Ordovician in the TZ45 area are secondary dissolution caves.For the prediction of caved carbonate reservoir,post-stack methods are commonly used in the oilfield at present since pre-stack inversion is always limited by poor seismic data quality and insufficient logging data.In this paper,based on amplitude preserved seismic data processing and rock-physics analysis,pre-stack inversion is employed to predict the caved carbonate reservoir in TZ45 area by seriously controlling the quality of inversion procedures.These procedures mainly include angle-gather conversion,partial stack,wavelet estimation,low-frequency model building and inversion residual analysis.The amplitude-preserved data processing method can achieve high quality data based on the principle that they are very consistent with the synthetics.Besides,the foundation of pre-stack inversion and reservoir prediction criterion can be established by the connection between reservoir property and seismic reflection through rock-physics analysis.Finally,the inversion result is consistent with drilling wells in most cases.It is concluded that integrated with amplitude-preserved processing and rock-physics,pre-stack inversion can be effectively applied in the caved carbonate reservoir prediction.

Characteristics of subsurface density variations before the 4.20 Lushan M_s7.0 earthquake in the Longmenshan area: inversion results

The 4.20 Lushan Ms7.0 earthquake occurred on the southwest segment of the Longmenshan fault on 20 April 2013. Some meaningful information on the prepa- ration and occurrence of this earthquake was found based on the dynamic variation of gravity （DVG）. To examine the great progress of the Lushan earthquake, we obtained the density variation （DENV） derived from the DVG using the compact gravity inversion method in this article. The inversion results reveal three main findings： （1） the DENV in the crust in the Jinshajiang fault area changed from positive in 2010-2011 to negative in 2011-2012. （2） The DENV in the Xianshuihe fault area decreased continuously from 2010 to 2012. （3） The DENV of the uppermost mantle of South China decreased in 2010-2011 and increased in 2011-2012. We propose that the flow/expansion of the middle-lower crust beneath the Bayan Har block and Moho subsidence on the southwest margin of the Chuan-Dian block may have been the major causes of the Lushan earthquake.

Three-dimensional crustal density distribution beneath North China by sequential inversion of local earthquake traveltimes and gravity anomaly

A three-dimensional crustal density model beneath North China is determined using P-wave traveltimes and gravity datum by sequential inversion method in this paper. To improve the uniqueness of the solution, we used a linear relationship between velocity and density to achieve mutual conversions and constraints between velocity difference and density difference. Algebraic reconstruction technique （ART） was used in density inversion, which highly improved the calculation speed comparing with common least squares method. The inversion results indicate that the crustal density beneath North China is extremely inhomogeneous with its distribution coherent with regional tectonics. The lower crust of Taihang mountain tectonic zone shows an obvious low density characteristic. We proposed that it may be an indicator of upwelling of mantle materials or partial melting of lowermost crust.

3D density inversion of gravity gradiometry data with a multilevel hybrid parallel algorithm

The density inversion of gravity gradiometry data has attracted considerable attention;however,in large datasets,the multiplicity and low depth resolution as well as efficiency are constrained by time and computer memory requirements.To solve these problems,we improve the reweighting focusing inversion and probability tomography inversion with joint multiple tensors and prior information constraints,and assess the inversion results,computing efficiency,and dataset size.A Message Passing Interface(MPI)-Open Multi-Processing(OpenMP)-Computed Unified Device Architecture(CUDA)multilevel hybrid parallel inversion,named Hybrinv for short,is proposed.Using model and real data from the Vinton Dome,we confirm that Hybrinv can be used to compute the density distribution.For data size of 100×100×20,the hybrid parallel algorithm is fast and based on the run time and scalability we infer that it can be used to process the large-scale data.

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.

Impedance inversion of pre-stack seismic data in the depth domain

The extensive application of pre-stack depth migration has produced huge volumes of seismic data,which allows for the possibility of developing seismic inversions of reservoir properties from seismic data in the depth domain.It is difficult to estimate seismic wavelets directly from seismic data due to the nonstationarity of the data in the depth domain.We conduct a velocity transformation of seismic data to make the seismic data stationary and then apply the ridge regression method to estimate a constant seismic wavelet.The estimated constant seismic wavelet is constructed as a set of space-variant seismic wavelets dominated by velocities at different spatial locations.Incorporating the weighted superposition principle,a synthetic seismogram is generated by directly employing the space-variant seismic wavelets in the depth domain.An inversion workflow based on the model-driven method is developed in the depth domain by incorporating the nonlinear conjugate gradient algorithm,which avoids additional data conversions between the time and depth domains.The impedance inversions of the synthetic and field seismic data in the depth domain show good results,which demonstrates that seismic inversion in the depth domain is feasible.The approach provides an alternative for forward numerical analyses and elastic property inversions of depth-domain seismic data.It is advantageous for further studies concerning the stability,accuracy,and efficiency of seismic inversions in the depth domain.

Inversion of 3D density interface with PSO-BP method

BP( Back Propagation) neural network and PSO( Particle Swarm Optimization) are two main heuristic optimization methods,and are usually used as nonlinear inversion methods in geophysics. The authors applied BP neural network and BP neural network optimized with PSO into the inversion of 3D density interface respectively,and a comparison was drawn to demonstrate the inversion results. To start with,a synthetic density interface model was created and we used the proceeding inversion methods to test their effectiveness. And then two methods were applied into the inversion of the depth of Moho interface. According to the results,it is clear to find that the application effect of PSO-BP is better than that of BP network. The BP network structures used in both synthetic and field data are consistent in order to obtain preferable inversion results. The applications in synthetic and field tests demonstrate that PSO-BP is a fast and effective method in the inversion of 3D density interface and the optimization effect is evident compared with BP neural network merely,and thus,this method has practical value.

Fast pre-stack multi-channel inversion constrained by seismic reflection features

Classical multi-channel technology can significantly reduce the pre-stack seismic inversion uncertainty, especially for complex geology such as high dipping structures. However, due to the consideration of complex structure or reflection features, the existing multi-channel inversion methods have to adopt the highly time-consuming strategy of arranging seismic data trace-by-trace, limiting its wide application in pre-stack inversion. A fast pre-stack multi-channel inversion constrained by seismic reflection features has been proposed to address this issue. The key to our method is to re-characterize the reflection features to directly constrain the pre-stack inversion through a Hadamard product operator without rearranging the seismic data. The seismic reflection features can reflect the distribution of the stratum reflection interface, and we obtained them from the post-stack profile by searching the shortest local Euclidean distance between adjacent seismic traces. Instead of directly constructing a large-size reflection features constraint operator advocated by the conventional methods, through decomposing the reflection features along the vertical and horizontal direction at a particular sampling point, we have constructed a computationally well-behaved constraint operator represented by the vertical and horizontal partial derivatives. Based on the Alternating Direction Method of Multipliers (ADMM) optimization, we have derived a fast algorithm for solving the objective function, including Hadamard product operators. Compared with the conventional reflection features constrained inversion, the proposed method is more efficient and accurate, proved on the Overthrust model and a field data set.

Pre-stack AVO inversion with adaptive edge preserving smooth filter regularization based on Aki-Richard approximation

With the development of exploration of oil and gas resources,the requirements for seismic inversion results are getting more accurate.In particular,it is hoped that the distribution patterns of oil and gas reservoirs can be finely characterized,and the seismic inversion results can clearly characterize the location of stratigraphic boundaries and meet the needs of accurate geological description.Specifically,for pre-stack AVO inversion,it is required to be able to distinguish smaller geological targets in the depth or time domain,and clearly depict the vertical boundaries of the geological objects.In response to the above requirements,we introduce the preprocessing regularization of the adaptive edge-preserving smooth filter into the pre-stack AVO elastic parameter inversion to clearly invert the position of layer boundary and improve the accuracy of the inversion results.

Application Study on Rigidity Correlation Method for Density Inversion of Rockfill

Based on the theoretical model of rigidity correlation method, the study on application was carried out with Chinese Liyuan face rockfill dam as example. The linear relation equations between the rockfill rigidity and density measured by pit method were established, and the regression performance and accuracy of rigidity correlation method were analyzed by calculating the inversion values of density. The results show that the regression equations of rigidity correlation method are high significant so as to work out the rockfill density precisely;rigidity correlation method is used for density inversion of rockfill with minor error and namely high accuracy, which is proper with satisfactory results.

Concealed porphyry delineation based on nonlinear three-dimensional densitydifference inversion: An example in the Beiya mine area, Western Yunnan, China

Intermediate acid-complex rock masses with low-density characteristics are the most important prospecting sign in the Beiya area, of western Yunnan province, and provide a physical basis for good gravity exploration. It is usually difficult to obtaining solutions in connection with actual geological situations due to the ambiguity of the conventional gravity-processing results and lack of deep constraints. Thus, the three-dimensional (3D) inversion technology is considered as the main channel for reducing the number of solutions and improving the vertical resolution at the current stage. The current study starts from a model test and performs nonlinear 3D density-difference inversion called “model likelihood exploration”, which performs 3D inversion imaging and inversion of the known model while considering the topographic effects. The inversion results are highly consistent with those of the known models. Simultaneously, we consider the Beiya gold mine in Yunnan as an example. The nonlinear 3D densitydifference inversion technology, which is restricted by geological information, is explored to obtain the 3D density body structure below 5 km in the mine area, and the 3D structure of the deep and concealed rock masses are obtained using the density constraints of the intermediate-acid-complex rock masses. The results are well consistent with the surface geological masses and drilling-controlled deep geological masses. The model test and examples both show that the 3D density-difference nonlinear inversion technology can reduce inversion ambiguity, improve resolution, optimize the inversion results, and realize “transparency” in deeply concealed rock masses in ore-concentrated areas,which is useful in guiding the deep ore prospecting.

Key parameter optimization and analysis of stochastic seismic inversion

Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density function （PDF） of subsurface models. The Markov chain Monte Carlo （MCMC） method is used to sample the posterior PDF and the subsurface model characteristics can be inferred by analyzing a set of the posterior PDF samples. In this paper, we first introduce the stochastic seismic inversion theory, discuss and analyze the four key parameters： seismic data signal-to-noise ratio （S/N）, variogram, the posterior PDF sample number, and well density, and propose the optimum selection of these parameters. The analysis results show that seismic data S/N adjusts the compromise between the influence of the seismic data and geostatistics on the inversion results, the variogram controls the smoothness of the inversion results, the posterior PDF sample number determines the reliability of the statistical characteristics derived from the samples, and well density influences the inversion uncertainty. Finally, the comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more reliable information of the subsurface character.

Full tensor gravity gradiometry data inversion:Performance analysis of parallel computing algorithms

We apply reweighted inversion focusing to full tensor gravity gradiometry data using message-passing interface （MPI） and compute unified device architecture （CUDA） parallel computing algorithms, and then combine MPI with CUDA to formulate a hybrid algorithm. Parallel computing performance metrics are introduced to analyze and compare the performance of the algorithms. We summarize the rules for the performance evaluation of parallel algorithms. We use model and real data from the Vinton salt dome to test the algorithms. We find good match between model efficiency and feasibility of parallel computing gravity gradiometry data. and real density data, and verify the high algorithms in the inversion of full tensor

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

Inversion of river-bottom sediment parameters using mechanically sampled specimens and subbottom profiling data

The study of river dynamics requires knowledge of physical parameters, such as porosity, permeability, and wave propagation velocity, of river-bottom sediments. To do so, sediment properties are determined on mechanically sampled specimens and from subbottom profiling. However, mechanical sampling introduces disturbances that affect test results, with the exception of grain-size distribution. In this study, we perform inversion of acoustic data using the grain-size distribution of mechanically sampled specimens and the relation between porosity and permeability from the Kozeny-Carman equation as prior information. The wave reflection coefficient of the water-silt interface is extracted from the raw subbottom profile. Based on the effective density fluid model, we combine the Kozeny-Carman equation and the wave reflection coefficient. We use experimental data from two Yellow River reservoirs to obtain the wave velocity and density of multiple sections and their spatial variations, and find that the inversion and testing results are in good agreement.