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 forward modeling and response characteristics of low-resistivity overburden of the CFS-PML absorbing boundary for ground-well transient electromagnetic method

This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field.The absorption boundary condition of complex frequency-shifted perfectly matched layer(CFS-PML)was used for truncation so that the low-frequency electromagnetic wave can be better absorbed at the model boundary.A typical three-dimensional(3D)homogeneous half-space model was established and a low-resistivity cube model was analyzed under the half-space condition.The response patterns and drivers of the low-resistivity cube model were discussed under the influence of a low-resistivity overburden.The absorption boundary conditions of CFS-PML significantly affected the low-frequency electromagnetic waves.For a low-resistivity cube around the borehole,its response curve exhibited a single-peak,and the extreme point of the curve corresponded to the center of the low-resistivity body.When the low-resistivity cube was directly below the borehole,the response curve showed three extreme values(two high and one low),with the low corresponding to the center of the low-resistivity body.The total field response of the low-resistivity overburden was stronger than that of the uniform half-space model due to the low-resistivity shielding effect of electromagnetic waves.When the receiving-transmitting distance gradually increased,the effect of the low-resistivity overburden was gradually weakened,and the response of the low-resistivity cube was strengthened.It was affected by the ratio of the overburden resistivity to the resistivity of the low-resistivity body.

Estimation of Displacement and Extension due to Reverse Drag of Normal Faults: Forward Method

In the case of reverse drag of normal faulting, the displacement and horizontal extension are determined based on the established equations for the three mechanisms: rigid body, vertical shear and inclined shear. There are three sub-cases of basal detachment for the rigid body model: horizontal detachment, antithetic detachment and synthetic detachment. For the rigid body model, the established equations indicate that the total displacement on the synthetic base (Dt2) is the largest, that on the horizontal base (Dt1) is moderate, and that on the antithetic base (Dt3) is the smallest. On the other hand, the value of (Dt1) is larger than the displacement for the vertical shear (Dt4). The value of (Dt1) is larger than or less than the displacement for the inclined shear (Dt5) depending on the original fault dip δ0, bedding angle θ, and the angle of shear direction β. For all original parameters, the value of Dt5 is less than the value of Dt4. Also, by comparing three rotation mechanisms, we find that the inclined shear produces largest extension, the rigid body model with horizontal detachment produces the smallest extension, and the vertical shear model produces moderate extension.

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.

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.

Multi-wave forward modeling of a reservoir and AVO analysis

In the process of accurate interpretation of multi-wave seismic data,we wanted to solve the problem of multi-wave information recognition.Based on techniques of elastic wave forwarding,targeting the geological model of a reservoir of an oil field exploration area,we used a high-order staggered-grid difference technology to simulate many shots of seismic records of nonzero offset shots,implemented multi-wave seismic data processing to acquire the CMP of P waves and converted waves,NMO traces of CCP pre stacks,including AVA information and superposition profiles.Based on the AVA calculation of the model,the layer parameters of the model and the forwarding wave field relations of the P-S wave,we also compared and studied the correspondence between P waves and converted waves.The results of our analysis show that the results from simulation and from the AVO analysis are consistent.Significant wave field differences between P waves and converted waves in the same reservoir were found,which are helpful in recognizing and interpreting the multi-wave information in this area.We made use of the multi-wave data to provide the important guidelines for reservoir prediction.

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.

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 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.

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.

Forward modeling for “earth-ionosphere” mode electromagnetic field

A fixed artificial source(greater than 200 kW) was used and the source location was selected at a high resistivity region to ensure high emission efficiency. Some publications used the "earth-ionosphere" mode in modeling the electromagnetic(EM) fields with the offset up to a thousand kilometer, and such EM fields still have a signal/noise ratio of 10-20 dB. This means that a new EM method with fixed source is feasible, but in their calculation, the displacement in air was neglected. In this work, some three-layer modeling results were presented to illustrate the basic EM fields' characteristics in the near, far and waveguide areas under "earth-ionosphere" mode, and a standard is given to distinguish the boundary of near, far and waveguide areas. Due to the influence of the ionosphere and displacement current in the air, the "earth-ionosphere" mode EM fields have an extra waveguide zone, where the fields' behavior is very different from that of the far field zone.

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.

A Gravity Forward Modeling Method based on Multiquadric Radial Basis Function

It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.