2.5D forward modeling and inversion of frequency-domain airborne electromagnetic data

Frequency-domain airborne electromagnetics is a proven geophysical exploration method.Presently,the interpretation is mainly based on resistivity-depth imaging and onedimensional layered inversion;nevertheless,it is difficult to obtain satisfactory results for two- or three-dimensional complex earth structures using 1D methods.3D forward modeling and inversion can be used but are hampered by computational limitations because of the large number of data.Thus,we developed a 2.5D frequency-domain airborne electromagnetic forward modeling and inversion algorithm.To eliminate the source singularities in the numerical simulations,we split the fields into primary and secondary fields.The primary fields are calculated using homogeneous or layered models with analytical solutions,and the secondary（scattered） fields are solved by the finite-element method.The linear system of equations is solved by using the large-scale sparse matrix parallel direct solver,which greatly improves the computational efficiency.The inversion algorithm was based on damping leastsquares and singular value decomposition and combined the pseudo forward modeling and reciprocity principle to compute the Jacobian matrix.Synthetic and field data were used to test the effectiveness of the proposed method.

3D seismic forward modeling from the multiphysical inversion at the Ketzin CO_(2) storage site

From June 2008 to August 2013,approximately 67 kt of CO_(2) was injected into a deep saline formation at the Ketzin pilot CO_(2) storage site.During injection,3D seismic surveys have been performed to monitor the migration of sequestered CO_(2).Seismic monitoring results are limited by the acquisition and signal-to-noise ratio of the acquired data.The multiphysical reservoir simulation provides information regarding the CO_(2) fluid behavior,and the approximated model should be calibrated with the monitoring results.In this work,property models are delivered from the multiphysical model during 3D repeated seismic surveys.The simulated seismic data based on the models are compared with the real data,and the results validate the effectiveness of the multiphysical inversion method.Time-lapse analysis shows the trend of CO_(2) migration during and after injection.

UAV-based transient electromagnetic 3D forward modeling and inversion and analysis of exploration capability

Unmanned aerial vehicle transient electromagnetic(UAV-TEM)is a novel airborne exploration method that offers advantages such as low cost,simple operation,high exploration efficiency and suitability for near-surface exploration in complex terrain areas.To improve the accuracy of data interpretation in this method,the authors conducted a systematic three-dimensional(3D)forward modeling and inversion of the UAV-TEM.This study utilized the finite element method based on unstructured tetrahedral elements and employed the second-order backward Euler method for time discretization.This allowed for accurate 3D modeling and accounted for the effects of complex terrain.Based on these,the influence characteristics of flight altitudes and the sizes,burial depths,and resistivities of anomalies are compared and analyzed to explore the UAV-TEM systems’exploration capability.Lastly,four typical geoelectrical models of landslides are designed,and the inversion method based on the Gauss-Newton optimization method is used to image the landslide models and analyze the imaging effect of the UAV-TEM method on landslide geohazards.Numerical results showed that UAV-TEM could have better exploration resolution and fine imaging of nearsurface structures,providing important technical support for monitoring,early warning,and preventing landslides and other geological hazards.

3D time-domain forward modeling of airborne transient electromagnetism considering superparamagnetic effect

The superparamagnetic effect arises from the superparamagnetism exhibited by a multitude of nano-sized magnetic mineral particles under an external electric field.This phenomenon manifests in transient electromagnetic data primarily as a deceleration in the attenuation rate of late-stage signals,a characteristic difficult to discern directly from airborne transient electromagnetic signals,consequently leading to significant misinterpretations of subterranean electrical structures.This study embarks on 3D forward modeling of airborne electromagnetic responses in the frequency domain,accounting for the superparamagnetic effect,utilizing an unstructured finite element method.Superparamagnetic responses in the time domain were obtained through frequency-time conversion.This investigation explores the influence of various parameters-such as magnetic susceptibility,time constants,and flight altitude-on the superparamagnetic effect by examining the response characteristics of typical targets.Findings indicate that in its late stages,the superparamagnetic effect can induce a relative anomaly of up to 300%.There is a positive correlation between magnetic susceptibility and the strength of the superparamagnetic effect.The influence of the time constant's upper and lower limits on the superparamagnetic effect is minimal;however,the range between these limits significantly affects the effect,showing a negative correlation with its intensity.Higher flight altitudes weaken the superparamagnetic signal.The impact is most pronounced when superparamagnetic minerals are shallowly buried,effectively shielding the underlying geology with the characteristics of a good conductivity anomaly,but this effect diminishes with greater depth.The insights from this study provide a theoretical framework for a deeper understanding of the superparamagnetic effect in transient electromagnetic signals and for more accurate interpretations of subterranean geological and electrical structures.

Variable-coordinate forward modeling of irregular surface based on dual-variable grid

The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the calculation domain. The mapping method deals with the irregular surface and the low-velocity layer underneath it using a fine grid. For the deeper high-velocity layers, the use of a fine grid causes local oversampling. In addition, when the irregular surface is transformed to horizontal, the flattened interface below the surface is transformed to curved, which produces inaccurate modeling results because of the presence of ladder-like burrs in the simulated seismic wave. Thus, we propose the mapping method based on the dual-variable finite-difference staggered grid. The proposed method uses different size grid spacings in different regions and locally variable time steps to match the size variability of grid spacings. Numerical examples suggest that the proposed method requires less memory storage capacity and improves the computational efficiency compared with forward modeling methods based on the conventional grid.

Multicomponent seismic forward modeling of gas hydrates beneath the seafloor

We investigated the effect of microscopic distribution modes of hydrates in porous sediments, and the saturation of hydrates and free gas on the elastic properties of saturated sediments. We simulated the propagation of seismic waves in gas hydrate-bearing sediments beneath the seafloor, and obtained the common receiver gathers of compressional waves（P-waves） and shear waves（S-waves）. The numerical results suggest that the interface between sediments containing gas hydrates and free gas produces a large-amplitude bottomsimulating reflector. The analysis of multicomponent common receiver data suggests that ocean-bottom seismometers receive the converted waves of upgoing P- and S-waves, which increases the complexity of the wavefield record.

基于Forward-Modeling方法的黑河流域水储量变化特征研究

黑河流域陆地水储量变化对流域下游等周边区域水资源的合理利用以及经济和社会发展等有着重要的意义.本文利用2003年1月至2013年12月的GRACE RL05数据反演了黑河流域陆地水储量长时间序列的变化,并针对重力场模型和数据处理中产生的信号泄漏问题,采用Forward-Modeling方法进行了改正并恢复泄漏信号;将GRACE获得的泄漏信号恢复前后的黑河流域水储量变化结果与全球水文模型GLDAS和CPC进行比较分析,结果表明泄漏信号改正后的结果与水文模型结果的时间序列相关性均有明显提高,从其空间分布结果可以看出Forward-Modeling方法有效地恢复初始信号、增强被湮没的信号,泄漏信号误差减小;通过分析黑河流域水储量变化的长时间序列结果,发现其具有明显的阶段性变化特征,即2003—2006年呈明显下降趋势,约为-0.86cm·a-1,在2007—2010年趋于平衡状态,而2011—2013年则呈现缓慢上升趋势约为0.14cm·a-1;联合GRACE数据和GLDAS数据反演了黑河流域地下水储量变化,并与全球降雨数据GPCC进行了比较分析,两者相关性可达到0.88以上.

Forward modeling of marine DC resistivity method for a layered anisotropic earth

Since the ocean bottom is a sedimentary environment wherein stratification is well developed, the use of an anisotropic model is best for studying its geology. Beginning with Maxwell＇s equations for an anisotropic model, we introduce scalar potentials based on the divergence-free characteristic of the electric and magnetic （EM） fields. We then continue the EM fields down into the deep earth and upward into the seawater and couple them at the ocean bottom to the transmitting source. By studying both the DC apparent resistivity curves and their polar plots, we can resolve the anisotropy of the ocean bottom. Forward modeling of a high-resistivity thin layer in an anisotropic half-space demonstrates that the marine DC resistivity method in shallow water is very sensitive to the resistive reservoir but is not influenced by airwaves. As such, it is very suitable for oil and gas exploration in shallowwater areas but, to date, most modeling algorithms for studying marine DC resistivity are based on isotropic models. In this paper, we investigate one-dimensional anisotropic forward modeling for marine DC resistivity method, prove the algorithm to have high accuracy, and thus provide a theoretical basis for 2D and 3D forward modeling.

AVO forwarding modeling in two-phase media: multiconstrained matrix mineral modulus inversion

AVO forward modeling is based on two-phase medium theory and is considered an effective method for describing reservoir rocks and fluids. However, the method depends on the input matrix mineral bulk modulus and the rationality of the two-phase medium model. We used the matrix mineral bulk modulus inversion method and multiple constraints to obtain a two-phase medium model with physical meaning. The proposed method guarantees the reliability of the obtained AVO characteristicsin two-phase media. By the comparative analysis of different lithology of the core sample, the advantages and accuracy of the inversion method can be illustrated. Also, the inversion method can be applied in LH area, and the AVO characteristics can be obtained when the porosity, fluid saturation, and other important lithology parameters are changed. In particular, the reflection coefficient amplitude difference between the fast P wave and S wave as a function of porosity at the same incidence angle, and the difference in the incidence angle threshold can be used to decipher porosity.

Behavioral modeling of RF power amplifiers with time-delay feed-forward neural networks

A novel behavioral model using three-layer time-delay feed-forward neural networks （TDFFNN）is adopted to model radio frequency （RF）power amplifiers exhibiting memory nonlinearities. In order to extract the parameters, the back- propagation algorithm is applied to train the proposed neural networks. The proposed model is verified by the typical odd- order-only memory polynomial model in simulation, and the performance is compared with different numbers of taped delay lines（TDLs） and perceptrons of the hidden layer. For validating the TDFFNN model by experiments, a digital test bench is set up to collect input and output data of power amplifiers at a 60 × 10^6 sample/s sampling rate. The 3.75 MHz 16-QAM signal generated in the vector signal generator（VSG） is chosen as the input signal, when measuring the dynamic AM/AM and AM/PM characteristics of power amplifiers. By comparisons and analyses, the presented model provides a good performance in convergence, accuracy and efficiency, which is approved by simulation results and experimental results in the time domain and frequency domain.

1-D Controlled source electromagnetic forward modeling for marine gas hydrates studies

We discuss the feasibility of using controlled-source electromagnetic （CSEM） in the frequency domain for prospecting marine gas hydrates. Based on the Ocean Drilling Program （ODP） Leg 164 log data, we have established several 1-D resistivity models which have different gas hydrate concentrations. Meanwhile, we analyzed the electromagnetic response of marine gas hydrates in the frequency domain based on these models. We also studied the relationship between electrical field magnitude or phase and parameters such as receiver-transmitter distance and frequency. Our numerical modeling results provide us with a quantitative reference for exploration and resource evaluation of marine gas hydrates.

Irregular surface seismic forward modeling by a body-fitted rotated–staggered-grid finite-difference method

Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid(SSG) with interpolation, nonstaggered grid, rotated staggered grid(RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the firstorder stress–velocity equation in the curvilinear coordinates system and introduce the highprecision adaptive, unilateral mimetic finite-difference(UMFD) method to process the freeboundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.

Frequency domain wave equation forward modeling using gaussian elimination with static pivoting

Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting （GESP） method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.

Three-dimensional land FD-CSEM forward modeling using edge finite-element method

A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.

The parallel 3D magnetotelluric forward modeling algorithm

The workload of the 3D magnetotelluric forward modeling algorithm is so large that the traditional serial algorithm costs an extremely large compute time. However, the 3D forward modeling algorithm can process the data in the frequency domain, which is very suitable for parallel computation. With the advantage of MPI and based on an analysis of the flow of the 3D magnetotelluric serial forward algorithm, we suggest the idea of parallel computation and apply it. Three theoretical models are tested and the execution efficiency is compared in different situations. The results indicate that the parallel 3D forward modeling computation is correct and the efficiency is greatly improved. This method is suitable for large size geophysical computations.

One-way wave equation seismic prestack forward modeling with irregular surfaces

Mathematical geophone （MG） and equal-time stacking （ETS） principles are used to implement seismic prestack forward modeling with irregular surfaces using the oneway acoustic wave-equation. This method receives seismic primary reflections from the subsurface using a set of virtual MGs. The receivers can be located anywhere on an irregular observing surface. Moreover, the ETS method utilizes the one-way acoustic wave equation to easily and quickly image and extrapolate seismic reflection data. The method is illustrated using high single-noise ratio common shot gathers computed by numerical forward modeling of two simple models, one with a flat surface and one with an irregular surface, and a complex normal fault model. A prestack depth migration method for irregular surface topography was used to reoroduce the normal fault model with high accuracy.

Three-dimensional forward modeling and inversion of borehole-to-surface electrical imaging with different power sources

Borehole-to-surface electrical imaging （BSEI） uses a line source and a point source to generate a stable electric field in the ground. In order to study the surface potential of anomalies, three-dimensional forward modeling of point and line sources was conducted by using the finite-difference method and the incomplete Cholesky conjugate gradient （ICCG） method. Then, the damping least square method was used in the 3D inversion of the formation resistivity data. Several geological models were considered in the forward modeling and inversion. The forward modeling results suggest that the potentials generated by the two sources have different surface signatures. The inversion data suggest that the low- resistivity anomaly is outlined better than the high-resistivity anomaly. Moreover, when the point source is under the anomaly, the resistivity anomaly boundaries are better outlined than when using a line source.

Forward modeling to improve seismic reflection energy of a protective coal seam based on Zoeppritz equation

In seismic exploration for coal, seismic waves are very difficult to transmit downward because of high velocity protective layers, making the reflection information very hard to receive above ground. Based on the Snell law and the Zoeppritz equation, we studied the relationship between the incidence angle and reflection seismic wave energy using a forward model of level media. The result shows that the seismic wave energy has a sudden increase at the critical angle. Based on the energy propagation rule, using big offset to receive the seismic wave energy under a protective layer can effectively reduce its protection effect.

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.

Three-dimensional forward modeling and response characteristics analysis of foundation pit leakage electric-field considering electrokinetic effect

The traditional ground direct current method is not suitable for leakage detection of underground diaphragm walls in foundation pits because of its low accuracy and poor anti-noise ability.Here,we propose a joint surface-borehole observation device for leakage electric fi eld detection to achieve rapid measurement of the electric fi eld distribution characteristics at ground level in the foundation pit,thus enabling rapid localization of leakage points.We first establish the mechanism and basic equation of the leakage electric field response by combining the electric field formed by electrokinetic effect(EK)and the stable electric fi eld formed by conduction current in a combined leakage channel.Then,the fi nite–infi nite element coupling method is used to solve the electric fi eld equation to simulate the responses of a three-dimensional foundation pit leakage model.Furthermore,we conduct numerical simulations of diff erent pit models to investigate the infl uencing factors of the detection device and response characteristics of the change in the properties of the leakage channel.The results demonstrate that the proposed joint surface-borehole observation device can effi ciently reveal anomalous potential caused by leakage,and the amplitude of the electric fi eld generated by EK can eff ectively strengthen the leakage electric fi eld signal at the leakage,thus improving detection accuracy and effi ciency.