Simultaneous Inversion Method Research Articles

Pre-stack seismic inversion based on one-dimensional GRU combined with two-dimensional improved ASPP

Abstract Pre-stack seismic inversion is essential to detailed stratigraphic interpretation of seismic data. Recently, various deep learning methods have been introduced into pre-stack inversion, effectively capturing the vertical correlations of seismic data. However, existing deep learning methods face challenges such as insufficient feature extraction, poor lateral continuity, and unclear inversion details. We introduce the atrous spatial pyramid pooling (ASPP) module into the pre-stack inversion process, modifying the connection order and mode of its three components. Additionally, we incorporate a triplet attention module to extract features at different scales and utilize a gate recurrent unit (GRU) module to extract global information. During the network training stage, we employ a multi-gather simultaneous inversion method, combining one-dimensional and two-dimensional inversions. The proposed method is named as IGIT (I for Improved ASPP, G for GRU, I for Initial model and T for Triplet attention). To verify the feasibility of this network model, we evaluate it using the Marmousi2 model, SEAM model, and field data, comparing the results with other deep learning methods. Experimental results demonstrate that the IGIT not only improves lateral continuity but also delivers accurate and clear inversion details. Notably, the inversion effect for density parameters shows significant enhancement.

Joint PP and PS AVA inversion using an acceleration algorithm and a multi-trace strategy

Abstract Exploration utilizing converted wave (PS) technology has garnered considerable interest in recent years owing to its ability to provide distinct insights into subsurface properties compared to compressional waves (PP). PS wave is particularly advantageous for accurately determining S-wave velocity (${V}_S$) and bulk density ($\rho $), whereas PP wave is better suited for assessing P-wave velocity (${V}_P$). Thus, theoretically, joint PP and PS AVA inversion can yield precise results for ${V}_P$, ${V}_S$, and $\rho $. However, a critical step before joint inversion is PP and PS registration, which is prone to causing lateral discontinuity in the inversion outcomes. To mitigate this issue, we present a simultaneous multi-trace joint inversion method. The method can improve the lateral consistency of inversion results by imposing lateral continuity constraints on the elastic parameters being inverted. Nevertheless, this simultaneous multi-trace inversion method inherently increases computational burden. To enhance algorithmic efficiency without sacrificing inversion precision, we implement an acceleration strategy. Synthetic and real data examples demonstrate that the proposed method offers remarkable performance in enhancing computational efficiency and lateral continuity compared to the conventional methods.

Adjoint Synthesis for Trans‐Oceanic Tsunami Waveforms and Simultaneous Inversion of Fault Geometry and Slip Distribution

AbstractTsunamis propagate over long distances and can cause widespread damage even after crossing ocean basins. Prediction of tsunamis in distant areas based on observations near their sources is critical to mitigating damage. In recent years, the accuracy of numerical models of trans‐oceanic tsunami propagation has improved significantly due to the incorporation of effects such as the solid earth response to tsunami loading and wave dispersion. However, these models are computationally expensive and have not been fully utilized for real‐time prediction. Here, we derive the adjoint operator for the linear set of equations describing deep‐ocean tsunami propagation and show how a pre‐computed database of adjoint states can achieve rapid synthesis of tsunami waveforms at target sites from nonpoint arbitrary tsunami sources. The adjoint synthesis method allows for an exhaustive parameter search for tsunami source estimation. A method for simultaneous inversion of fault geometry and slip distribution using adjoint synthesis with Sequential Monte Carlo method was proposed and applied to the 2012 Haida Gwaii earthquake tsunami. The influence of model accuracy and the amount of observed data on the estimation of tsunami sources and waveforms was examined. It was found that with a highly accurate propagation model, using only a limited amount of observed data produced source and waveform estimates very similar to the final models obtained with much larger data sets. The final inferred fault model involved megathrust slip distributed between the Haida Gwaii trench and the Queen Charlotte fault. The proposed method can also quantify the uncertainty of the waveform forecasts.

Classification and Prediction Method for Dolomite Reservoirs in the Permian Maokou Formation in the Sichuan Basin

The Lower Permian Maokou Formation in the Hechuan area is one of the key horizons for natural gas exploration in the Sichuan Basin, showing a low degree of exploration and great exploration potential. The Lower Permian gas reservoir is mainly controlled by the reservoir, therefore it is subject to the development of the Maokou Formation reservoir. However, due to the strong heterogeneity and significant variations in physical properties of the Maokou Formation dolomite reservoir in the Hechuan area, there are significant differences in seismic response characteristics of reservoirs with different porosities. Through comprehensive analysis of gas testing wells in the Maokou Formation, criteria for reservoir classification were established based on lithology, average porosity, plane porosity, and thickness of dolomite reservoirs. The effective reservoirs in the Maokou Formation were divided into two types: high-porosity reservoirs and medium-porosity reservoirs. On the basis of establishing a physical quantity model for the Lower Permian carbonate rock in the research area, the rock physical characteristics and seismic response characteristics of reservoirs with different pores are determined through model forward modeling, and appropriate methods are selected for prediction. By using the optimization processing method of gathers and wavelet decomposition to remove sidelobes, the issue of seismic abnormal response caused by lateral velocity changes in the underlying Maokou Formation has been solved. The relative strength relationship of seismic response amplitude can effectively characterize the true situation of reservoir development. Then, by using post-stack inversion and pre-stack simultaneous inversion methods, the high-porosity and medium-porosity dolomite reservoirs in the Maokou Formation are classified and predicted, thereby to effectively improve the prediction accuracy of reservoirs, ultimately providing a reliable basis for the exploration and development of the Maokou Formation in the Hechuan area in the later stage.

A non-stationary iterative Tikhonov regularization method for simultaneous inversion in a time-fractional diffusion equation

The present paper is devoted to recovering the source term and the initial data simultaneously for a time-fractional diffusion equation from additional temperature data at two fixed times t=T1 and t=T2. Firstly, we prove the uniqueness result for the direct problem. And then we apply a non-stationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm. Three numerical examples in both one-dimensional and two-dimensional cases are provided to demonstrate the effectiveness and feasibility of the proposed method.

The 3-D Global Prestack Seismic Inversion in the Time–Frequency Mixed Domain

Traditional seismic inversion has the problems of low lateral resolution and poor anti-noise performance. To address these challenges, the advantages of inversion methods in time and frequency domains are combined; the Lp norm that can preserve more sparsity information is introduced into seismic inversion. Meanwhile, multi-trace simultaneous inversion has become the mainstream of inversion methods, which can effectively improve the quality of pre-stack seismic inversion. However, traditional multi-trace simultaneous inversion methods have high computational costs and are difficult to obtain the 3D result. Ensuring spatial continuity of inversion results is a challenging task. To address this issue, a 3D global pre-stack inversion method in the time-frequency mixed domain is proposed. The proposed method adds a frequency domain fidelity constraint the objective function of traditional time domain inversion to improve the resolution of the inversion results. To improve the computational efficiency of multi-trace simultaneous inversion, the anisotropic total variation regularization method under Lp norm constraint is employed. In addition, the 2D Sylvester equation is extended to 3D space to enable 3D global inversion. The method not only improves computational efficiency, but also ensures spatial continuity of the results. The stability and feasibility of the proposed method have been demonstrated through its application on both the 3D overthrust model and field pre-stack seismic data.

Simultaneous Inversion for Reflectivity and Q Using Nonstationary Seismic Data With Deep-Learning-Based Decoupling

Building reflectivity and quality factor (Q) using nonstationary post-stack seismic data is important for vertical resolution enhancement of seismic data and reservoir identification. However, it is well-known that both reflectivity and Q affect the waveform of seismic data, leading to the fact that simultaneously estimating them is a strong ill-posed multi-parameter inverse problem which faces the crosstalk problem. In this paper, we propose a new method for simultaneous inversion of reflectivity and Q. A deep-learning-based data decoupling operator is proposed to decouple the effects of the two parameters on nonstationary seismic data. Based on the decoupled data, we transform the original multi-parameter inverse problem into two independent singe-parameter inverse problems that are immune to crosstalk and can build reasonable initial models for reflectivity and Q. Then alternative iteration is conducted to update the two built initial models to obtain the final models. A few well-logs are used to train the deep learning architecture and specific regularization terms are constructed for the inverse problem to ensure physically reasonable results. Synthetic and field data examples verify the effectiveness of the proposed method and its advantages over a conventional model-driven joint inversion method.

Transdimensional simultaneous inversion of velocity structure and event locations in downhole microseismic monitoring

In downhole microseismic monitoring, the velocity model plays a vital role in accurate mapping of the hydraulic fracturing image. For velocity model uncertainties in the number of layers or interface depths, the conventional velocity calibration method has been shown to effectively locate the perforation shots; however, it introduces nonnegligible location errors for microseismic events, especially for complex geologic formations with inclinations. To improve the event location accuracy, we have exploited the advantages of the reversible jump Markov chain Monte Carlo approach in generating different dimensions of velocity models and adopted a transdimensional Bayesian simultaneous inversion framework for obtaining the effective velocity structure and event locations simultaneously. The transdimensional inversion changes the number of layers during the inversion process and selects the optimal interface depths and velocity values to improve the event location accuracy. The confidence intervals of the simultaneous inversion event locations estimated by Bayesian inference enable us to evaluate the location uncertainties in the horizontal and vertical directions. Two synthetic examples and a field test are presented to illustrate the performance of our methodology, and the event location accuracy is shown to be higher than that obtained using the conventional methods. With less dependence on prior information, our transdimensional simultaneous inversion method can be used to obtain an effective velocity structure for facilitating highly accurate hydraulic fracturing mapping.

Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation

Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation

Bayesian Theorem Application to Model Reservoir Facies Distribution on Deltaic Depositional Environment, Case Study of Browse Basin

Successful Hydrocarbon exploration and reservoir characterization always related with good understanding of geology and geophysics aspect. One of the fundamental issues is to get reliable parameter distribution and quantify the confidence level of the parameter model in 3D. The case study in this paper will be applied in Browse field that and the result will be a distribution model in 3D of facies and hydrocarbon fluid. The workflow that will be introduced in this paper is the combination between rock physics analysis, simultaneous seismic inversion and Bayesian estimation theorem. Rock physics analysis includes well log conditioning and correlation analysis between reservoir parameter (porosity, saturation, Vshale, etc) with seismic parameter (acoustic impedance, vp/vs, shear impedance, etc) to obtain facies classification in well log scale. The simultaneous seismic inversion method is used to obtain seismic parameter cube to be correlated with rock physics result to drive the facies distribution. Bayesian estimation theorem assembles initial knowledge about a model before observing the inversion attributes. The probability density function later will be used to drive the facies distribution combined with well log data and seismic data; and also estimate the confidence level distribution in 3D. The result can be used to identify new play in the Browse field.

Simultaneous inversion ofQand reflectivity using dictionary learning

Quality factor ( Q) and reflectivity are two important subsurface properties in seismic data processing and interpretation. They can be calculated simultaneously from a seismic trace corresponding to an anelastic layered model by a simultaneous inversion method based on the nonstationary convolutional model. However, the conventional simultaneous inversion method calculates the optimum Q and reflectivity based on the minimum of the reflectivity sparsity by sweeping each Q value within a predefined range. As a result, the accuracy and computational efficiency of the conventional method depend heavily on the predefined Q value set. To improve the performance of the conventional simultaneous inversion method, we have developed a dictionary learning-based simultaneous inversion of Q and reflectivity. The parametric dictionary learning method is used to update the initial predefined Q value set automatically. The optimum Q and reflectivity are calculated from the updated Q value set based on minimizing not only the sparsity of the reflectivity but also the data residual. Synthetic data and two field data sets are used to test the effectiveness of our method. The results demonstrate that our method can effectively improve the accuracy of these two parameters compared to the conventional simultaneous inversion method. In addition, the dictionary learning method can improve computational efficiency up to approximately seven times when compared to the conventional method with a large predefined dictionary.

Conductive polyethersulfone membrane facilely prepared by simultaneous phase inversion method for enhanced anti-fouling and separation under low driven-pressure

Electrically conductive membranes have been regarded as a new alternative to overcome the crucial drawbacks of membranes, including permeability-selectivity trade-off and fouling. It is still challenging to prepare conductive membranes with good mechanical strength, high conductivity and stable separation performance by reliable materials and methods. This work developed a facile method of simultaneous phase inversion to prepare electrically conductive polyethersulfone (PES) membranes with carboxylic multiwalled carbon nanotubes (MWCNT) and graphene (Gr). The resultant MWCNT/Gr/PES nanocomposite membranes are composed of the upper MWCNT/Gr layer with good conductivity and the base PES layer providing mechanical support. MWCNT as nanofillers effectively turns the insulting PES layers to be electrically conductive. With the dispersing and bridging functions of Gr, the MWCNT/Gr layer shows an enhanced electric conductivity of 0.10 S/cm. This MWCNT/Gr/PES membrane in an electro-filtration cell achieves excellent retention of Cu(II) ions up to 98 % and a high flux of 94.5 L m−2∙h−1∙bar−1 under a low driven-pressure of 0.1 MPa. The conductive membrane also shows improved anti-fouling capability during protein filtration, due mainly to the electrostatic repulsion and hydrogen evolution reaction on the electrode. This facile strategy has excellent potential in electro-assistant membrane filtration for fouling control and effective separation.

Simultaneous joint migration inversion with calendar-time constraints as a processing tool for semi-continuous surveys

Nowadays, to obtain a better understanding of dynamic time-lapse changes, frequent seismic monitoring is necessary, although it will generate a considerable cost increase. Therefore, low-cost frequent monitoring, e.g., sparse and/or nonrepeated surveys, is desired. The simultaneous inversion-based method allows the baseline and monitor parameters to communicate and compensate with each other during inversion via constraints and helps to reduce the artifacts caused by sparse acquisition. These features make it largely independent of the used low-cost acquisition geometry and suitable for inexpensive frequent monitoring surveys. Therefore, we have used this simultaneous inversion-based method as an effective time-lapse processing tool for data sets acquired from inexpensive, semi-continuous time-lapse monitoring surveys, which are based on the so-called instantaneous 4D (i4D) technology. We choose a specific simultaneous inversion method called simultaneous joint migration inversion (S-JMI), which combines a simultaneous processing strategy with the JMI method. In i4D technology, inexpensive localized/sparse surveys, called i4D surveys, are deployed frequently between the conventional full-field surveys. This technology can be treated as a special case of changing geometries during monitoring. In this case, the simultaneous strategy allows the information of the full-field survey to compensate for the insufficient illumination of the localized/sparse i4D surveys during processing. Furthermore, we apply constraints on the reflectivity and velocity differences between the baseline and monitor vintages along the calendar-time axis called calendar-time constraints. These constraints take advantage of the feature that time-lapse effects develop (semi-)continuously along the calendar-time axis, when the monitoring surveys are deployed (semi-)continuously over calendar time. Based on a complex synthetic example, we determined that S-JMI is a promising tool to process the data sets from the semi-continuous monitoring surveys based on i4D technology. Finally, we found that the calendar-time constraints significantly improve the quality of time-lapse effects.

Simultaneous inversion for S-wave velocity and density from the SV-SV wave

Knowledge of the S-wave velocity ([Formula: see text]) and density ([Formula: see text]) is essential for oil and gas reservoir detection and characterization. However, reliable recovery of both parameters, especially density, from the reflected PP-wave data is a difficult issue because this inverse problem is highly ill-conditioned. The reflected SV-SV wave is easier to process than the PS-wave, and it can provide better estimates of [Formula: see text] and [Formula: see text] than the PP-wave because it is more sensitive to these parameters than the PP-wave. I have developed a simultaneous inversion for [Formula: see text] and [Formula: see text] based on a modified approximation of the SV-SV wave reflection coefficient. The modified equation includes only two parameters (natural logarithms of [Formula: see text] and [Formula: see text]) to be inverted, and it has high accuracy even at large incident angles and for strong impedance contrasts. I find that simultaneous inversion based on the modified approximation is well-posed when using data of small-to-moderate incident angle (20o–30o) and that the misfit function can be easily regularized. The new simultaneous inversion method is applied to an SV-SV wave prestack data set acquired from a 2D nine-component survey. The field data example demonstrates that the new method can recover stable and high-resolution density and S-wave velocity information, which can be used to investigate rock mineral composition, porosity, and fluid content.

Identification of lithology and fluid content using simultaneous inversion in the “IM” field of the North Sumatra Basin

The “IM” field is an oil and gas exploration field located in the North Sumatra Basin. It was previously identified that in this field hydrocarbons were found in the form of gas condensate. This study aims to characterize the reservoir in terms of lithological distribution and fluid content. The research includes carbonate reservoir targets located in Middle Miocene Malacca Limestone. The data used in this study are 3D seismic data and two wells data. The simultaneous inversion method is applied to process data so that research objectives can be achieved. The simultaneous inversion method produces Acoustic Impedance (Zp), Shear Impedance (Zs). The results show that in the gas reservoir the acoustic impedance (Zp) value is around 16542 - 18917 (ft/s*g/cc) and the shear impedance(Zs) is around 8375 (ft/s*g/cc) while in the water reservoir the acoustic impedance (Zp) value is around 21292 - 23667 (ft/s*g/cc) and the shear impedance (Zs) is around 18500-20525 (ft/s*g/cc). The results showed that the reservoir distribution has a North West-South East orientation.

OpenMP Implementation of a Novel Potential-Field-Data Source-Growth-Based Inversion Approach for 3D Salt Imaging in Deepwater Gulf of Mexico

Potential-field-data imaging of complex geological features in deepwater salt-tectonic regions in the Gulf of Mexico remains an open active research field. There is still a lack of resolution in seismic imaging methods below and in the surroundings of allochthonous salt bodies. In this work, we present a novel three-dimensional potential-field-data simultaneous inversion method for imaging of salt features. This new approach incorporates a growth algorithm for source estimation, which progressively recovers geological structures by exploring a constrained parameter space; restrictions are posed from a priori geological knowledge of the study area. The algorithm is tested with synthetic data corresponding to a real complex salt-tectonic geological setting commonly found in exploration areas of deepwater Gulf of Mexico. Due to the huge amount of data involved in three-dimensional inversion of potential field data, the use of parallel computing techniques becomes mandatory. In this sense, to alleviate computational burden, an easy to implement parallelization strategy for the inversion scheme through OpenMP directives is presented. The methodology was applied to invert and integrate gravity, magnetic and full tensor gradient data of the study area.

High‐resolution seismic velocity field estimation techniques and their application to geohazard, lithology and porosity prediction

ABSTRACTSeismic velocity is an attractive parameter for geohazard interpretation, pore pressure analysis, play and prospect evaluations, and other geological studies, but ordinary seismic processing velocities often do not have a good enough resolution. We adapt a dynamic time warping algorithm to estimate geologically reasonable high‐resolution velocities from average‐quality seismic data that can be used for geohazard analysis based on 3D seismic data. To predict free gas and/or excess pore water pressure in thin shallow layers, we use velocity inversion. It is a method for simultaneous inversion of velocity data to geological attributes. It runs in the depth domain, uses a background velocity model for balancing of input velocities to wells and a normal compaction trend model to simultaneously estimate lithology, pore pressure and net apparent erosion attributes, while porosity is calculated from a sandstone–porosity relationship. The overall workflow is applied for geohazard analysis at two marine sites. The first example is a deep‐water one from the Norwegian Sea, where thin and possibly overpressured or gas‐filled layers are identified in the Pleistocene section. The second example is in a region with limestone‐dominated lithology, where thin overpressured shales can cause severe drilling problems. In both examples, the thicknesses of the layers prone to geohazards are estimated to be about half of the wavelength. Dedicated high‐resolution velocity estimations, such as those obtained through the proposed workflow with dynamic time warping, applied to standard 3D seismic data and followed by dedicated velocity inversion routines, are, therefore, a necessity for proper geohazard assessment.

Mapping the Distribution and Characterization of Sandstone Reservoir Using Simultaneous Inversion Method in “OA” Field at Northern Bonaparte Basin

The sandstone reservoir in the “OA” Field is situated in the Northern Bonaparte Basin, which is gas-saturated sandstone. Mineral diagenesis is also causing several reservoir zone areas to become tight sand. The inversion method using acoustic impedance (AI) is less sensitive in distinguishing sandstone and clay rock lithology since they have almost the same impedance. Simultaneous Inversion overcomes this problem by simultaneously inversing partial angle data (near, mid, far) to obtain physical parameters besides acoustic impedance which are expected to be more sensitive in distinguishing lithology and predicting the presence of gas fluids such as shear impedance (SI) and density. These three parameters can be derived as Lame (LMR) parameters. Cross plot analysis shows sensitive physical parameters to predict the distribution of lithology and the presence of gas fluid. Density sensitive in distinguishing lithology which is then inverted, obtaining sandstone cutoff values are 2.3-2.5 (g/cc), tight sand with cutoff 2.5-2.625 (g/cc) and clay stones with cutoff 2.625-2.8 (g/cc). The presence of gas fluid is predicted by inversing the parameter Vp/Vs which has a cutoff of >1.6 and Lambda-rho cutoff of >25 (Gpa)*(g/cc). Analysis of the parameter distribution map shows the distribution of sandstones and the presence of dominant gas fluids in the northern area of the research zone with relatively clean sandstone, compared to relatively more southern regions.

Seismic facies-controlled prestack simultaneous inversion of elastic and petrophysical parameters for favourable reservoir prediction

Comprehensive utilisation of elastic and petrophysical parameters to predict favourable reservoirs can help reduce the possibility of misidentification of resources. Existing simultaneous inversion methods for estimating the elastic and petrophysical parameters are typically based on either the Gassmann equation, with which these parameters are inverted from prestack seismic data through stochastic optimisation methods, or Wyllie’s modified equation, with which these parameters are inverted from poststack seismic data using deterministic optimisation methods. The purpose of this work is to develop a strategy for estimating the elastic and petrophysical parameters based on the Gassmann equation using deterministic prestack inversion. We employ the Gassmann equation to construct the relationship between the prestack seismic data and petrophysical parameters. We treat the joint posterior probability of elastic and petrophysical parameters as the objective function under a Bayesian framework. Given the macroscopic geological background and the poor-quality prestack seismic data, seismic facies regularisation constraints were introduced to improve the robustness and accuracy of the inversion. The very fast-simulated annealing method is used to quickly find the optimal solutions for the elastic and petrophysical parameters. Based on a model test and the application of real data demonstrates that the proposed inversion method has high accuracy and strong reliability.

Application of simultaneous prestack inversion in reservoir facies identification

Poststack inversion is purely acoustic because there is no mode conversion at normal incidence. Therefore, P-wave impedance is the only information that can be estimated from poststack inversion of P-wave data. In full prestack inversion, both the low- and high-frequency components of the P-wave acoustic impedance can be extracted from the seismic data. In addition to the P-wave acoustic impedance, S-wave information or Poisson's ratio can also be estimated from prestack data. This provides fluid information for the reservoirs; thus, prestack inversion has an advantage over poststack inversion. We determined k, KC, m, and mC which are, respectively, the slope of the natural logarithm of shear impedance against the natural logarithm of acoustic impedance, the intercept of the natural logarithm of shear impedance against the natural logarithm of acoustic impedance, the slope of the natural logarithm of density against the natural logarithm of acoustic impedance, and the intercept of the natural logarithm of shear impedance against the natural logarithm of acoustic impedance. We also needed a set of angle-dependent wavelets, which are derived from angle stacks. Hence, we built three angle stacks; the near-angle stack (0–11 degrees), middle-angle stack (11–20 degrees), and far-angle stack (20–29 degrees). Using these angle stacks, we built three statistical angle-dependent wavelets. Finally, with log information we built an initial model for acoustic impedance, and tried to solve the inversion matrix using the conjugate gradient method. By solving this, we could simultaneously derive the acoustic impedance, shear impedance, and density sections from prestack data. Simultaneous inversion used the assumption of a constant shear wave to compressional wave velocity ratio, and the generalized Garnder equation, which are only valid in clastic rocks. The simultaneous prestack inversion method was used for the identification of reservoir facies in one of the hydrocarbon fields in Iran. With this method, four facies were identified; these were confirmed by reservoir geological information and well data.