Numerical Inversion Research Articles

Simultaneous waveform inversion of seismic-while-drilling data for P-wave velocity, density, and source parameters

Full-waveform inversion (FWI), as an optimization-based approach to estimating subsurface models, is limited by incomplete acquisition and illumination of the subsurface. The incorporation of additional data from new and independent raypaths should be expected to result in significant increase in the accuracy of FWI models. In principle, seismic-while-drilling (SWD) technology can supply these additional raypaths; however, it introduces a new suite of unknowns, namely precise source locations (i.e., drilling path), source signature, and radiation characteristics. A new FWI algorithm is formulated in which the source radiation patterns and positions join the velocity and density values of the grid cells as unknowns to be determined. Several numerical inversion experiments are then conducted with different source settings using a synthetic model. The SWD sources are supplemented by explosive sources and multicomponent receivers at the surface, simulating a conventional surface acquisition geometry. The subsurface model and SWD source properties are recovered and analyzed. The analysis is suggestive that SWD involvement can enhance the accuracy of FWI models, with varying degrees of enhancement depending on factors such as trajectory inclination, source density, and drill path extension. The impact of SWD-FWI over standard FWI is reduced when low-frequency data are missing, but improvements over the models constructed with no subsurface sources remain. This formulation permits general source information, such as position and moment tensor components, to be independently obtained. This inversion scheme may lead to a range of potential applications for which medium properties and source information are required.

Two-temperature generalized magneto-thermic-viscoelastic response problem considering non-local and memory effects

Based on the two-temperature generalized magneto-thermal-viscoelastic theory considering scale effects and fractional time derivatives, the dynamic response of generalized magneto-thermal-viscoelastic theory in homogeneous isotropic semi-infinite elastic media with infinite conductivity is studied. Laplace Fourier integral transform and numerical inverse transform are used to solve the general solution of dimensionless physical equations. Based on the numerical results, the effects of time factor, fractional parameter and scale effect on the transient magneto thermic viscoelastic response of the structure are discussed respectively. The above results are visually expressed in the form of graphs. The results show that the temperature and displacement are less affected by each parameter, the stress increases with the increase of time, non-local and viscosity parameters, and decreases with the increase of fractional order parameters. This result is of great significance to the application of different physics fields, and provides some theoretical guidance for solving practical engineering problems.

Temperature field of multi-barrier with gap layer in nuclear waste repository

A three-dimensional four-layer thermal conduction model including an air layer was developed to analyze temperature evolution in nuclear waste repository. Laplace-domain temperature solutions for each layer were obtained using finite Fourier transform and Laplace transform. The Laplace-domain solutions were transformed into time-domain semi-analytical solutions by numerical inversion. The surface temperature of central canister was obtained by superimposing the temperature increments of air and buffer layers on rock wall temperature caused by every canister in one disposal panel. The effects of the geometrical parameters, thermal parameters and nuclear waste parameters on surface temperature of canister were studied based on the obtained semi-analytical solution. The results indicate that the presence of air layer has little effect on temperature distribution in bentonite while its effect on temperature at surface of canister is significant. Thickness of air layer has a greater effect on temperature than that of its thermal conductivity. The burn-up value and cooling time also have significant influence on the temperature. Finally, the influences of repository’s geometric size on temperature in this model were analyzed.

An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs, the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network. It has been proven to cause inaccurate production evaluations because of the absence of matrix–macrofracture communication. In addition, most of the existing models are solved analytically based on Laplace transform and numerical inversion. Hence, an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation, the simultaneous matrix depletion is divided into two parts: one part feeding the macrofractures and the other part feeding the microfractures. Then, a series of partial differential equations (PDEs) describing the transient flow and boundary conditions are constructed and solved analytically by integration. Finally, a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models. When the microfracture system and matrix–macrofracture communication is neglected, the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model, respectively. Certainly, the new model also has an excellent agreement with the numerical model. The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin. After identifying the flow regime, the solution suitably matches the field production data, and the model parameters are determined. Through these output parameters, we can accurately forecast the production and even estimate the petrophysical properties.

Analytical model for CO2 geo-sequestration in deep saline aquifers considering the effect of heterogeneity and matrix-fracture interaction

Deep saline aquifers are considered to be the best storage option for long-term CO2 geo-sequestration because such geological formation has the largest identified storage potential that can securely trap CO2 under its low-permeability caprock layers. Many analytical models have been proposed to rapidly detect the CO2 leakage from the storage aquifers. However, the heterogeneity and matrix-fracture interaction of storage layers have not been taken into consideration in previous studies. In this paper, we develop an analytical model to determine the dimensionless leakage rate and pressure build-up due to CO2 leakage from the heterogeneous, dual-porosity and multi-layer bounded storage aquifer. Based on the model description and assumptions, the analytical solution is obtained by means of dimensionless transformation, Laplace transform and numerical inversion. Afterwards, our model is verified by comparing with existing analytical model. In order to determine the effect of heterogeneity and the matrix-fracture interaction on the dimensionless leakage rate and pressure change, we conducted sensitivity analysis taking account of the heterogeneous factors. Based on the obtained results, increasing layer number and layer thickness from the bottom layer to the upper layer will delay the CO2 leakage. Furthermore, each layer in storage aquifer with greater fluid mobility is not conductive to CO2 storage but the overall effect is not obvious. As for the matrix-fracture fluid transfer processes, when the ratio of the matrix permeability to the fracture permeability is small, the fast flow of CO2 through the fracture system without significant storage in the matrix. Obviously, the resistance along the leakage path is decreasing with the decrease of the caprock thickness, which leads to greater leakage between the two aquifers. The derived analytical solutions considering heterogeneity and dual media is practical and helpful for CO2 geo-sequestration site selection and storage risk assessment.

An Elementary Formula for the Initial Relaxation Modulus from the Creep Compliance for Asphalt Mixtures.

The conversion between the relaxation modulus and creep compliance is a traditional research topic in viscoelastic materials. Generally, different methods have been used to solve the numerical solution based on convolution theory. However, the initial relaxation modulus (relaxation modulus at t = 0) has been difficult to obtain. This paper aimed to propose a fast calculation method to derive the initial relaxation modulus from the creep compliance. First, three groups of uniaxial static creep tests of asphalt mixtures were conducted to determine the creep compliance of the experimental data. Then, the calculation of the initial relaxation modulus from the creep compliance by three inversion methods (midpoint method, approximate method, and Laplace numerical inversion method) was evaluated. The results indicate that approximate method and Laplace numerical inversion method cannot calculate the initial relaxation modulus value, and the calculation results of the midpoint method can only approach the exact value infinitely, for which calculating the relaxation modulus at 0.0005 s requires 2000 s. The results can only approach the exact value infinitely and take a lot of computing time. Finally, a fast calculation method for the initial relaxation modulus is proposed and verified by Laplace initial value theorem, and this method can directly derive a simple expression for calculating the initial relaxation modulus without requiring computational time. The proposed calculation methods of the initial relaxation modulus for various viscoelastic models were then put forward. The research results provide an effective tool for obtaining the initial relaxation modulus accurately.

A closed‐form solution of DPL bioheat transfer problem with time‐periodic boundary conditions

AbstractA closed‐form (long‐time) solution of one‐dimensional dual‐phase lag bioheat transfer problem with consistent time‐periodic boundary conditions (BCs) is presented in this paper for planar, cylindrical, and spherical skin tissue for a newly developed solution methodology. The steady‐periodic solution is composed of a steady‐state part and an oscillating part; corresponding to the constant and oscillating parts of BCs, respectively. Using the superposition principle, these two parts are split into two problems, which are solved separately. The steady‐state part is fairly straightforward to obtain, while for the oscillating part, an alternate Laplace transform (LT) approach is proposed in this work. It is demonstrated that for sinusoidal BCs, a closed‐form solution in the time domain can be obtained by evaluating an approximate convolution integral, which emulates the effect of the inverse LT. The obtained closed‐form solution is free of any series summation or numerical inversion, thereby, making it computationally very efficient compared with conventional LT and eigenfunctions‐based approaches. The current methodology is verified with the established eigenfunctions expansion‐based methodology. It can be seen that the long‐time solutions obtained by these two approaches are almost identical. The verified methodology is further extended for the time‐periodic nonsinusoidal BCs. The ease of implementation and simplicity of the new methodology for both sinusoidal and nonsinusoidal BCs is demonstrated using a few test cases. It is evident from the results that the developed methodology leads to an efficient and accurate solution.

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model.

This paper elaborates on the significance of liquid chromatography for a single-component reactive linear general rate model. The model equations consist of a set of two coupled partial differential equations, which include diffusion, interfacial mass transfer, axial dispersion, external and intraparticle pore diffusivity, and heterogeneous chemical reaction of the first order with two sets of boundary conditions. The model equations are solved by the Laplace transformation. The actual time domain solution is obtained by numerical Laplace inversion, as analytical inversion cannot be obtained. The graphical sketch of different physical parameters is presented to analyze the dynamics of the elution profiles. The result indicates that the chromatographic reactor works more efficiently on increasing the value of the heterogeneous-type first-order reaction. To check the analytical results, a second-order high-resolution finite volume scheme is used. Both results are in good agreement and indicate the correctness of the numerical scheme. The current work is also compared with the previously available numerical schemes, which shows that the proposed numerical scheme is better for elaborating the chromatographic reactor performance. A comparison table is also presented to compute error analysis and computational run time for analyzing the efficiency of the reactor. A graphical sketch of the numerical temporal moment analysis is also presented, which gives significant information about the performance and the shape of the concentration profiles.

Effect of Magnetic Field and Inclined Load on a Two-Dimensional Thermoelastic Medium Under Gravity

This work aims to investigate the effects of magnetic field and inclined load on a two-dimensional thermoelastic medium under gravitational field. The problem is formulated in the context of refined dual-phase-lag Green–Naghdi (DPL GN) model. The bounding plane surface is heated by a non-Gaussian laser beam. The inclined load is supposed to be a linear combination of a normal load and a tangential load. Analytical formulas for several physical quantities are generated on the transformed domain using the Laplace and Fourier transform techniques. The inversion of double transform has been done numerically by using MATHEMTICA 10. The numerical inversion of Laplace transform is done by using the Zakian method (Halsted and Brown [Zakians technique for inverting Laplace transforms, J. Chem. Eng. 3 (1972) 312–313]). All physical quantities have been graphically depicted for the dual-phase-lag Green–Naghdi type III model (DPL GN-III), simple Green–Naghdi type III model (simple GN-III), Lord–Shulman model (LS) and classical thermoelasticity theory (CTE) to indicate the effect of magnetic field and the angle of inclination of the medium.

Fusing Numerical Weather Prediction Ensembles with Refractivity Inversions during Surface Ducting Conditions

Abstract This study investigates the use of numerical weather prediction (NWP) ensembles to aid refractivity inversion problems during surface ducting conditions. Thirteen sets of measured thermodynamic atmospheric data from an instrumented helicopter during the Wallops Island field experiment are fit to a two-layer parametric surface duct model to characterize the duct. This modeled refractivity is considered “ground truth” for the environment and is used to generate the synthetic radar propagation loss field that then drives the inversion process. The inverse solution (refractivity derived from the synthetic radar data) is compared with this ground truth refractivity. For the inversion process, parameters of the two-layer model are iteratively estimated using genetic algorithms to determine which parameters likely produced the synthetic radar propagation field. Three numerical inversion experiments are conducted. The first experiment utilizes a randomized set of two-layer model parameters to initialize the inversion process, while the second experiment initializes the inversion using NWP ensembles, and the third experiment uses NWP ensembles to both initialize and restrict the parameter search intervals used in the inversion process. The results show that incorporation of NWP data benefits the accuracy and speed of the inversion result. However, in a few cases, an extended NWP ensemble forecast period was needed to encompass the ground truth parameters in the restricted search space. Furthermore, it is found that NWP ensemble populations with smaller spreads are more likely to hinder the inverse process than to aid it.

Nonequilibrium Electrochemical Phase Maps: Beyond Butler-Volmer Kinetics.

Accurate models of electrochemical kinetics at electrode-electrolyte interfaces are crucial to understanding the high-rate behavior of energy storage devices. Phase transformation of electrodes is typically treated under equilibrium thermodynamic conditions, while realistic operation is at finite rates. Analyzing phase transformations under nonequilibrium conditions requires integrating nonlinear electrochemical kinetic models with thermodynamic models. This had only previously been demonstrated for Butler-Volmer kinetics, where it can be done analytically. In this work, we develop a software package capable of the efficient numerical inversion of rate relationships for general kinetic models. We demonstrate building nonequilibrium phase maps, including for models such as Marcus-Hush-Chidsey that require computation of an integral, and also discuss the impact of a variety of assumptions and model parameters, particularly on high-rate phase behavior. Even for a fixed set of parameters, the magnitude of the critical current can vary by more than a factor of 2 among kinetic models.

Optimizing tight oil extraction from low permeability tight reservoirs: a study on stress sensitivity effects and applications in carbon capture, utilization, and storage

This paper takes into consideration the impact of stress sensitivity on bioenergy production from low permeability tight reservoirs, focusing on the post-fracturing phase. This paper established a trilinear flow model that effectively takes into account the dynamics of such reservoirs. This model incorporates stress sensitivity parameters and uses the perturbation transformation and Laplace transformation to solve the productivity prediction formula. The final productivity prediction curve post-fracturing is achieved through a numerical inversion method. This study shows that the stress sensitivity effect significantly diminishes the productivity of fractured horizontal wells used in bioenergy extraction. By introducing stress sensitivity effect parameters, this paper manages to uncover the influence law of mobility and artificial fracture parameters on productivity. Notably, as the reservoir mobility increases, the cumulative bioenergy production from fractured horizontal wells improves significantly. In addition to the above, this paper also scrutinizes the sensitivity of artificial fracture parameters and optimize both the quantity and length of these fractures. This plays a crucial role in enhancing the productivity and efficiency of bioenergy extraction from these tight reservoirs. The applicability and reliability of this method are extensively tested, thereby establishing its potential in guiding the development of low permeability reservoirs post-fracturing. Importantly, this research sets the groundwork for combining bioenergy production with Carbon Capture, Utilization, and Storage (CCUS) technologies. By focusing on optimization and stress management in tight reservoirs, this paper contributes to the sustainable production of bioenergy and reduce carbon emissions, moving a step closer to a cleaner and sustainable future.

Theoretical study on dynamic stress redistribution around circular tunnel with different unloading paths

This study presents a solution for stress redistribution induced by dynamic excavation of a rock tunnel in hydrostatic and non-hydrostatic stress states. Considering rock as an elastic medium, the analytical solution of dynamic excavation unloading was derived in the Laplace transform space utilizing the wave function expansion method and mode decomposition, and transformed into the time domain using the approximate numerical inversion method. The effects of the unloading path (linear, cosine, and exponential), unloading rate, and initial stress state on stress redistribution were analyzed. The analytical results indicated that a high unloading rate led to a high stress concentration and oscillations around the tunnel, and instantaneous dynamic unloading caused 20–30% stress concentration. When dynamic unloading is complete, the stress state around the tunnel converges to the Kirsch solution. The 3D numerical results indicated that deformation of the tunnel boring face increased as the initial stress increased. Moreover, the accumulation and release of strain energy and stress state change paths were analyzed and discussed. The results of this study provide a theoretical basis for understanding the stress adjustment and failure of surrounding rock induced by excavation of deep-buried openings in hydrostatic and non-hydrostatic stress states.

Performance Analysis of Zhao and Durbin Numerical Inversion Methods of Laplace Transform

The Laplace transform is essential to satisfy the independence of time for the analysis of the transient response of the composite or functionally-graded materials. The time independent boundary value problem may be solved then either by numerically or analytically. The solutions should be inverted to the physical plane using inverse Laplace transform. Therefore, the selected numerical inversion method may be crucial to obtain the high accuracy throughout the whole analysis steps. In the present study, Zhao’s Method I, Zhao’s Method II, Durbin’s Method and Modified Durbin’s Method are applied to dynamic loading conditions. The analysis results show that the accurate and stable solutions even for long time inversion have been obtained by Modified Durbin’s Method and Zhao’s Methods. However, compared with the methods of Zhao’s, the computational and programing load of Durbin’s Methods are minimum.

Mathematical modelling of micropolar thermoelastic problem with nonlocal and hyperbolic two-temperature based on Moore–Gibson–Thompson heat equation

The aim of this article is to study a problem of thermomechanical deformation in a homogeneous, isotropic, micropolar thermoelastic half-space based on the Moore–Gibson–Thompson heat equation under the influence of nonlocal and hyperbolic two-temperature (HTT) parameters. The problem is formulated for the considered model by reducing the governing equations into 2D and then converting to dimensionless form. Laplace transform and Fourier transform techniques are employed to obtain the system of differential equations. In the transformed domain, the physical quantities like displacement components, stresses, thermodynamic temperature, and conductive temperature are calculated under the specific types of normal force and thermal source at the boundary surface. A numerical inversion technique is used to recuperate the equations in the physical domain to exhibit the influence of nonlocal and HTT in the form of graphs. Particular cases of interest are also discussed in the present problem. The present study finds applications in a wide range of problems in engineering and sciences, control theory, vibration mechanics, and continuum mechanics.

Investigation on the thermoelastic response of a porous microplate in a modified fractional-order heat conduction model incorporating the nonlocal effect

In recent years, the application of porous materials in practical engineering has become increasingly common. Under extreme thermal conditions, how to accurately describe the heat conduction and structural response of porous materials is a key issue in the structural safety and functional design of porous materials. Among them, it is particularly important to consider the size-dependent and memory-dependent effects for small-sized structures or microdevices of porous materials. To address these issues of porous structures and to guide their applications as well as optimization, this paper first investigates the thermoelastic transient response of porous microplates subjected to thermal and stress shocks at the left boundary based on the Atangana-Baleanu (AB) fractional-order generalized thermoelastic theory by considering nonlocal effects and fractional-order strain, which is combined with the thermoelasticity theory of porous materials and the dual-phase-lag (DPL) heat conduction model. The governing equations are then established and solved using the Laplace transform and its numerical inversion. Finally, the effects of newly defined fractional order parameters, nonlocal parameters and the initial magnitude of the mechanical shock on the dimensionless temperature, volume fraction field, displacement and stress distribution are discussed and displayed graphically.

Analytical solutions of fractal and anomalous diffusion models for pressure and rate transient analysis

In this study, we examine the modeling of the naturally fractured reservoirs based on the fractal, Metzler, and Raghavan anomalous diffusion models which are different from Darcy flux law. The governing equations of these models are presented for a vertical well producing at either a constant rate (CR) or constant bottomhole pressure (CBHP) production in an infinite-acting reservoir. New analytical and early- and late-time asymptotic approximate solutions were derived for the finite-wellbore problem for the Raghavan anomalous model. The approximate solutions identify the fractal and anomalous diffusion parameters that influence behaviors of the early- and late-time pressure and rate transient data. The method of Laplace transformation is used to find the solutions in dimensionless forms which are then inverted to the real-time domain using a numerical inversion algorithm. In addition, we compare the solutions for the fractal, Metzler anomalous, and Raghavan anomalous models and delineate the similarities and differences among these solutions. We show the effect of fractal parameters on diffusion models, the relationship between the fractal model, and Raghavan and Metzler anomalous models, in terms of dimensionless pressure and dimensionless pressure derivative responses in the reservoir. We show that the “dimensionless” pressure defined by Raghavan is not a dimensionless quantity unless the Euclidean dimension d=2 (or for a fractal structure with the mass fractal dimension df=2). To the best of our knowledge, in the literature, there exists no study providing a detailed review and comparing the applicability of each diffusion model on real field well-test data as well as providing new analytical solutions and early- and late-time asymptotic approximate solutions for the anomalous diffusion for both the CR and CBHP cases for the finite-wellbore problem. Hence, this study fills this gap. In addition, we apply the three diffusion models to an interference well test data from the Kizildere geothermal reservoir in Turkey by using the ensemble smoother with multiple data assimilation (ES-MDA) method. The results show that the fractal model in terms of the goodness of fit (root-mean-square error – RMSE) best matches the field test data.

Transient non-Fourier thermal interactions of two parallel cracks in porous metal foam

Experimental evidence shows heat conduction in the porous media would be non-Fourier under specific circumstances. The novelty of this research lies in considerations of the non-Fourier effect and the interactions of two parallel thermally insulated cracks in the porous metal foam. The transient propagation characteristics are examined by utilizing the Dual-phase-lag model, which incorporates the certain time required to establish local thermal equilibrium between the solid framework and surrounding pores. Fourier transform and Laplace transform are employed to solve the mathematical model simulating a porous strip subjected to abrupt thermal shock. After reducing the problem to two groups of singular integral equations, the transient temperature distributions and heat flux intensity factors are determined with the help of numerical Laplace inversion. Numerical calculations are carried out to evaluate the impacts of crack positions, the relative density, phase lags, and two crack lengths on the thermal characteristics, which would contribute to a thorough understanding of the ultrafast process of porous materials operating in extreme conditions.

Pressure-Transient Behavior of Vertical Wells Considering Dynamic Water Hammer and Dynamic Induced Fracture: Theory and Case Studies.

Water injection can result in the creation of induced fracture by connecting natural fractures. The induced fracture penetrates the entire reservoir, leading to the interconnection of injection and production wells and ultimately resulting in water breakthrough and the abandonment of production wells. During well work, the induced fracture exhibits dynamic behavior characterized by extension and closure, known as the dynamic-induced fracture phenomena. During the shut-in process, fracture closure phenomena are often accompanied by water hammer phenomena, which can be detected bottom hole pressure data. However, numerical simulation methods are difficult to describe their dynamic processes. Therefore, we urgently need a mathematical model to fill this gap. In this work, we developed a waterflooding-induced dynamic fracture (WIDF) model. Dynamic water hammer phenomena, multi-dynamic closure phenomena, and fracture storage phenomena are introduced into the WIDF model to describe the induced fracture dynamic behavior. Field cases demonstrate that the WIDF model can improve the accuracy of interpreted parameters and correct incorrect model selection. Green function and Newman product method are used to characterize single-phase water flows within tight reservoirs. Then, the induced fracture is discrete into N segments through the boundary element method. Discrete-induced fractures are divided into n parts. Based on the induced fracture bending property, conductivity variation is independent in each part. The feature line method is used to solve the pressure response of the dynamic water hammer. The Duhamel principle is applied to couple the storage effects and reservoir pressure response. The Laplace transform method transforms the model into Laplace space so that it can be solved easily, and the Stehfest numerical inversion method transforms the model into real space to obtain the final solution. Our results show that the dynamic water hammer flow (DWH) regime with an oscillation curve and the multi-dynamic closure flow (MDCF) regime with peaks exist on the type curve. Resistance coefficient (f) and inertia coefficient (I) control the DWH regime. Fracture storage coefficient (Cf), dynamic fracture closure rates (Delpatm), and induced fracture closure half-lengths (xdfm) control the MDCF regime. It is worth noting that the peak position can be adjusted by the Delpatm and xdfm parameters, achieving a more accurate match to the field cases. The Cf is identified, which corrected for the amplified wellbore storage coefficient. Obtained permeability is also in a reasonable range of permeability for tight reservoirs. In summary, a series of mathematical methods are used to develop and solve an injection well model to identify the dynamic behavior of the induced fracture. Numerical simulation methods are used to verify the accuracy of the WIDF model. Two field cases from X Oilfield demonstrate the practicability of the WIDF model. Dynamic identification of the induced fracture would help engineers develop appropriate injection schemes to prevent water breakthroughs.

High-quality genome assembly and multi-omics analysis of pigment synthesis pathway in Auricularia cornea.

Owing to its great market potential for food and health care, white Auricularia cornea, a rare edible fungus, has received increased attention in recent years. This study presents a high-quality genome assembly of A. cornea and multi-omics analysis of its pigment synthesis pathway. Continuous Long Reads libraries, combined with Hi-C-assisted assembly were used to assemble of white A. cornea. Based on this data, we analyzed the transcriptome and metabolome of purple and white strains during the mycelium, primordium, and fruiting body stages. Finally, we obtained the genome of A.cornea assembled from 13 clusters. Comparative and evolutionary analysis suggests that A.cornea is more closely related to Auricularia subglabra than to Auricularia heimuer. The divergence of white/purple A.cornea occurred approximately 40,000 years ago, and there were numerous inversions and translocations between homologous regions of the two genomes. Purple strain synthesized pigment via the shikimate pathway. The pigment in the fruiting body of A. cornea was γ-glutaminyl-3,4-dihydroxy-benzoate. During pigment synthesis, α-D-glucose-1P, citrate, 2-Oxoglutarate, and glutamate were four important intermediate metabolites, whereas polyphenol oxidase and other 20 enzyme genes were the key enzymes. This study sheds light on the genetic blueprint and evolutionary history of the white A.cornea genome, revealing the mechanism of pigment synthesis in A.cornea. It has important theoretical and practical implications for understanding the evolution of basidiomycetes, molecular breeding of white A.cornea, and deciphering the genetic regulations of edible fungi. Additionally, it provides valuable insights for the study of phenotypic traits in other edible fungi.