**Source**

**Conference**

**Theme**

**Author**

**Chen, Hanming (13)**- Chen, Xiaohong (2)
- Chen, Yangkang (4)
- Dou, Yuzhao (1)
- Gan, Shuwei (1)
- Guan, Shoujun (2)
- Li, Qingqing (1)
- Lin, He (1)
- Liu, Wenling (1)
- Qu, Shan (2)
- Wang, Shangxu (1)
- Wang, Yufeng (1)
- Xia, Muming (1)
- Xiang, Kui (2)
- Xie, Chunlin (1)
- Zhang, Qi (1)
- Zhang, Qingchen (2)
- Zhi, Ling (1)
- Zhou, Hui (11)
- Zou, Yaming (2)
- Zu, Shaohuan (1)

**Concept Tag**

- absolute error (1)
- accuracy (2)
- acquisition (1)
- adjoint operator (1)
- algorithm (1)
- amplitude (1)
- annual meeting (3)
- application (1)
- artifact (1)
- Artificial Intelligence (5)
- AWWE (2)
- boundary (2)
- boundary condition (1)
- Chen (1)
- coefficient (1)
- constant fractional-order laplacian viscoacoustic (1)
- constant fractional-order laplacian wave equation (1)
- constraint (2)
- convolutional (2)
- convolutional operator (1)
- CPML (1)
- data quality (1)
- decomposition (1)
- deconvolution (1)
- Denote (1)
- discontinuity (1)
- discrete wavenumber (1)
- dispersion (1)
- Dubrule (1)
- elastic impedance (1)
- elastic parameter (1)
- elastic parameter inversion (1)
- elastic wave (1)
- entation implementation implementation procedure (1)
- equation (6)
- equation 11 (1)
- excitation source (1)
- expression (1)
- FD coefficient (1)
- FDM (1)
- finite-difference method (2)
- formulation (2)
- fractional laplacian (2)
- fractional laplacian viscoacoustic (1)
- fractional time derivative (1)
- fractional-order laplacian (1)
- fractional-order laplacian wave (1)
- fractional-order laplacian wave equation (1)
- frequency (4)
- full wave equation (1)
- full-waveform inversion (2)
- FWI (1)
- FWI iteration (1)
- Gaussian (1)
- geologic modeling (1)
- geological modeling (1)
- geological structure (1)
- geophysics (3)
- geostatistical inversion (1)
- gradient (1)
- Guddati (1)
- Heidari (1)
- impedance (1)
- Implementation (1)
- implementation implementation procedure procedu (1)
- implementation procedure (1)
- initial model (1)
- initial velocity model (1)
- interpolated velocity (1)
- interpolated velocity model (1)
- interpolation (1)
- inverse Fourier transform (1)
- inversion (5)
- inversion result (2)
- iteration (2)
- Komatitsch (1)
- Laplacian (1)
- Laplacian wave equation (1)
- LSM (1)
- Lsrtm (1)
- Martin (1)
- migration (3)
- Modeling & Simulation (1)
- operator (3)
- PML (1)
- Reservoir Characterization (13)
- scalar arbitrarily wide-angle (2)
- SGFD (1)
- SGFD method (1)
- Simulation (1)
- snapshot (2)
- Tlasssi (1)
- Upstream Oil & Gas (13)
- velocity model (2)
- Vibroseis (1)
- Vibroseis data (1)
- viscoacoustic wave equation (3)
- Wave Equation (6)
- wavefield (2)
- wide-angle wave equation (2)

**File Type**

We propose to estimate velocity and seismic quality factor (

Presentation Date: Wednesday, September 27, 2017

Start Time: 9:45 AM

Location: Exhibit Hall C/D

Presentation Type: POSTER

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Chen, Yangkang (University of Texas—Austin) | Xiang, Kui (China University of Petroleum—Beijing) | Chen, Hanming (China University of Petroleum—Beijing) | Chen, Xiaohong (China University of Petroleum—Beijing)

The simultaneous-source shooting technique can accelerate field acquisition and improve spatial sampling but will cause strong interferences in the recorded data. Direct imaging of blended simultaneous-source data has been demonstrated to be a promising research field since there is no need to separate the blended data before the subsequent processing and imaging. The key issue in direct imaging of blended data is the strong artifacts in the migrated image. Although the least-squares migration can help reduce some artifacts, there are still residual artifacts in the image. Those artifacts mainly appear in the shallow part of the image as spatially incoherent noise. Previously proposed structural smoothing operator can effectively attenuate the artifacts for relatively simple reflection structures during least-squares inversion, but it will cause damage to complicated reflection events such as the discontinuities. In order to preserve the discontinuities in the seismic image, we apply the singular spectrum analysis (SSA) operator to attenuate artifacts during least-squares inversion. Considering that global SSA cannot deal with over-complicated data well, we propose to use local SSA in order to remove noise and preserve steeply dipping components better. The local SSA operator corresponds to a local low-rank constraint applied in the inversion process. The migration operator used in the study is the reverse time migration (RTM) operator. We use the Marmousi model example to show the superior performance of the proposed algorithm.

Presentation Date: Wednesday, October 19, 2016

Start Time: 11:35:00 AM

Location: 171/173

Presentation Type: ORAL

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Recently, a decoupled fractional Laplacian viscoacoustic wave equation has been developed based on the constant-

Presentation Date: Thursday, October 20, 2016

Start Time: 8:30:00 AM

Location: 148

Presentation Type: ORAL

accuracy, constant fractional-order laplacian viscoacoustic, constant fractional-order laplacian wave equation, data quality, equation, equation 11, fractional laplacian, fractional-order laplacian, fractional-order laplacian wave, fractional-order laplacian wave equation, Laplacian, Laplacian wave equation, numerical solution, Reservoir Characterization, Upstream Oil & Gas, variable fractional-order laplacian, viscoacoustic wave equation, Wave Equation

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Chen, Yangkang (University of Texas–Austin) | Xiang, Kui (China University of Petroleum–Beijing) | Chen, Hanming (China University of Petroleum–Beijing) | Chen, Xiaohong (China University of Petroleum–Beijing)

Full waveform inversion (FWI) is a promising technique for inverting a high-resolution subsurface velocity model. The success of FWI highly depends on a fairly well initial velocity model. We propose a method for building a remarkable initial velocity model that can be put into the FWI framework for inverting nearly perfect velocity structure. We use a well log interpolated velocity model as a high-fidelity initial model for the subsequent FWI. The interpolation problem is solved via a least-squares method with a structural regularization. In order to obtain the geological structure of subsurface reflectors, an initial reverse time migration (RTM) with a fairly realistic initial velocity model is used to roughly calculate the local slope of subsurface structure. The well log interpolated initial velocity model can be very close to the true velocity while having small velocity anomaly or over-smoothing caused by the imperfect velocity interpolation, which however can be compensated during the subsequent FWI iterations. Regarding the field deployment, we suggest that future drilling should be seismic-oriented, which can help fully utilize the well logs for building initial subsurface velocity model and will facilitate a wide application of the proposed methodology.

Presentation Date: Wednesday, October 19, 2016

Start Time: 4:25:00 PM

Location: 162/164

Presentation Type: ORAL

full-waveform inversion, FWI, FWI iteration, geological structure, initial velocity model, interpolated velocity, interpolated velocity model, interpolation, inversion, inverted velocity, iteration, migrated image, multiple well, Reservoir Characterization, true velocity, Upstream Oil & Gas, velocity model, velocity structure, well log, well log interpolation

Chen, Hanming (China University of Petroleum, Beijing) | Zhou, Hui (China University of Petroleum, Beijing) | Zhang, Qingchen (China University of Petroleum, Beijing) | Zhang, Qi (China University of Petroleum, Beijing)

**Summary**

Two staggered-grid finite-difference (SGFD) methods with fourth- and sixth-order accuracy in time have been developed recently based on two new SGFD stencils. The SGFD coefficients are determined by Taylor-series expansion (TE), which is accurate only nearby zero wavenumber. We adopt the new two SGFD stencils and optimize the SGFD coefficients by minimizing the errors between the wavenumber responses of the SGFD operators and the first-order *k* (wavenumber)-space operator in a least-squares (LS) sense. We solve the LS problems by performing weighted pseudo-inverse of nonsquare matrices to obtain the SGFD coefficients, and to yield two LS based SGFD methods. Dispersion analysis and numerical examples demonstrate that our LS based SGFD methods can preserve the original fourth- and sixth-order temporal accuracy and achieve higher spatial accuracy than the existing TE based time-space domain SGFD methods.

**Introduction**

The staggered-grid finite-difference (SGFD) (Virieux, 1984) method has been widely used in seismic wave propagation modeling. Most of the SGFD applications adopt the traditional (2M, 2) scheme, which uses 2M-order Taylorseries expansion (TE) based FD operator to discretize spatial derivatives, and 2nd-order TE based FD operator to discretize temporal derivative. Although high-order spatial accuracy can be achieved by using a long stencil length, the temporal accuracy is only second-order. When a coarse time step is used, the traditional scheme suffers from obvious temporal dispersion during long time wave propagation.

Recently, Tan and Huang (2014a) propose two new SGFD methods with fourth-order and sixth-order accuracy in time respectively by incorporating a few of off-axial grid points into the standard SGFD stencil. The two methods are denoted as (2*M, * 4) and (2*M*, 6). The FD coefficients are determined in the time-space domain using TE approach. Althouth high-order temporal accuracy has been achieved, the TE based (2*M*, 4) and (*2M*, 6) methods still suffer from obvious spatial disperion when a large grid size or a short stencil length is adopted. Tan and Huang (2014b) continue to improve the spatial accuracy by using a nonlinear optimization to seek the optimal FD coefficients. However, the optimization requires repeated iterations, and the procedure may be time-consuming.

accuracy, coefficient, discrete wavenumber, dispersion, excitation source, FD coefficient, finite-difference method, lower subplot, operator, propagation, Reservoir Characterization, SGFD, SGFD method, sgfd stencil, spatial accuracy, stencil, stencil length, subplot, upper subplot, Upstream Oil & Gas, wavenumber

Wang, Yufeng (State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Lab of Geophysical Exploration, China University of Petroleum) | Zhou, Hui (State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Lab of Geophysical Exploration, China University of Petroleum) | Li, Qingqing (State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Lab of Geophysical Exploration, China University of Petroleum) | Chen, Hanming (State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Lab of Geophysical Exploration, China University of Petroleum) | Gan, Shuwei (State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Lab of Geophysical Exploration, China University of Petroleum) | Chen, Yangkang (The Unversity of Texas at Austin)

**Summary**

We apply the unsplit convolutional perfectly matched layer (CPML) absorbing boundary condition (ABC) to the viscoacoustic wave, which is derived from Kjartansson’s constant-Q model, with second-order spatial derivatives and fractional time derivatives, to annihilate spurious reflections from near-grazing incidence waves in the time domain. Computationally expensive temporal convolution in the unsplit CPML formulation are resolved by an effective recursive convolution update strategy which calculates time integration with the trapezoidal approximation, while the fractional time derivatives are computed with the Grünwald- Letnikov (GL) approximations. We verify the results by comparison with the 2D analytical solution obtained from wave propagation in homogeneous Pierre Shale.

**Introduction**

Perfectly matched layer (PML) absorbing boundary condition was introduced by Bérenger (1994) for the numerical simulations of electromagnetic waves in an unbounded medium. It can theoretically absorb the incident waves at the interface with the elastic volume, regardless of their incidence angle or frequency. However, the performance degrades upon the finite-difference time domain (FDTD) discretization, especially in the case of grazing incidence (Roden and Gedney, 2000; Bérenger, 2002a, 2002b). To deal with this problem, Kuzuoglu and Mittra (1996) proposed a general complex frequency shifted (CFS) method, in which a Butterworth-type filter is implemented in the layer. This approach is also known as convolutional PML (CPML) or complex frequency shifted PML (CFS-PML) (Bérenger, 2002a, 2002b), which has been proved to be more effective in absorbing the propagating wave modes at grazing incidence than the classical PMLs (Roden and Gedney, 2000; Komatitsch and Martin, 2007; Martin and Komatitsch, 2009; Drossaert and Giannopoulos, 2007a, 2007b).

Generally, the unsplit CPML has been applied to the wave equation recast as a first-order system in velocity and stress (Komatitsch and Martin, 2007; Martin and Komatitsch, 2009; Chen et. al., 2014). However, it was rarely used in numerical schemes based on the wave equation written as a second-order system in displacement. This form of wave equation is commonly used in finite-element methods (FEM), the spectral-element method (SEM) and some finite-difference methods. Several unsplit CPMLs have already been applied to the second-order wave equations (Li and Matar, 2010; René Matzen, 2011). Li and Matar (2010) presented an unsplit CPML for the second-order wave equation that contains auxiliary memory variables to avoid the convolution operators. Matzen (2011) developed a novel CPML formulation based on the second-order wave equation with displacements as the only unknowns, which is implemented by slightly modifying the existing displacement-based finite element framework.

annual meeting, convolutional, convolutional operator, equation, formulation, fractional time derivative, frequency, Komatitsch, Martin, operator, Reservoir Characterization, unsplit, unsplit convolutional, unsplit CPML, Upstream Oil & Gas, visco-acoustic wave, visco-acoustic wave equation, Wave Equation

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (0.72)

**Summary**

In this paper, the Lattice Spring Model (LSM) is adopted in forward modeling of elastic waves propagation in solid medium by combination with the Verlet Algorithm. Different from the traditional methods, such as Finite Difference Method (FDM), Finite Element Method (FEM) etc., LSM is a new method which is not based on the wave equations, but on the microcosmic mechanism that causes wave propagation. Firstly, the origin and history of LSM is introduced. Secondly, the theoretical framework of LSM is elaborated and a stability condition for the evolution of this system is deduced. Then, some numerical results of LSM are demonstrated and they are compared with the wave fields obtained by FDM. Finally, a brief conclusion is drawn based on the previous discussions.

**Introduction**

First devised by Grest and Webman in 1984, Lattice Spring Model (LSM) is a collection of linear springs connected at nodes distributing on a cubic lattice used for describing solid medium (Grest and Webman, 1984; Hassold and Srolovitz, 1989). In order to model materials of different Poisson’s ratios, angular springs are added to the original linear spring system (Wang, 1989). Ladd and Kinney (1997) developed this model by taking the idea of elastic element to improve its calculation precision. Such a simple model is sufficient to simulate heterogeneous elastic medium, and its application can be seen in modeling deformation and failure (Ladd and Kinney, 1997; Buxton et al., 2001; Zhao et al., 2011).

As is known to all, extensive research has been performed to solve the dynamic problems involving waves, and FDM is the most frequently used numerical method, which solves the wave equation by finite difference approximation of its partial derivative (Toomey and Bean, 2000). Yim and Sohn (2000) adopted a model similar to LSM for visualization of ultrasonic waves, but the evolution of wave fields are calculated by FDM. Pazdniakou and Adler (2012) made a further introduction of LSM and laid the foundation for its potential application in wave propagation in porous media in the low frequency band. Xia et al. (2014) modeled P waves from low frequencies (seismic frequency) to high frequencies (sonic log frequency) by importing a stability conditional for LSM dynamics.

**Summary**

Recently a time domain nearly constant *Q* (NCQ) wave equation derived from Kjartansson’s constant *Q* model has been developed for modeling viscoacoustic wavefield. The wave equation introduces decoupled attenuation and dispersion terms based on two separate fractional Laplacians, which can be easily calculated by spatial Fourier pseudo-spectral method. The fractional orders of the Laplacians are related to *Q*, and that means the orders are actually spatially varying. However, no desirable approach is presented in the current literatures to handle the varying orders. The fractional Laplacian with a spatially varying order can be exactly represented by a wavenumber-space domain operator. In this abstract we use a lowrank decomposition method to approximate the mixed-domain operator, thus making the NCQ wave equation adapt to large *Q* contrasts. Additionally, we reformulate the existing velocity-stress-strain NCQ formulation as an equivalent compact velocity-pressure system. The staggered-grid pseudo-spectral (SGPS) method and unsplit convolutional perfectly matched layer (CPML) are adopted in numerical simulations.

Artificial Intelligence, decomposition, equation, fractional laplacian, frequency, inverse Fourier transform, lowrank, lowrank approximation, lowrank decomposition, machine learning, Reservoir Characterization, spatially, time inverse fourier transform, Upstream Oil & Gas, viscoacoustic wave equation, Wave Equation, wavefield

**Summary**

Recently we have applied a classical split perfectly matched layer (PML) to the second-order scalar arbitrarily wide-angle wave equation (AWWE) in terms of displacement. However, the classical split PML increases computational cost obviously and has a poor performance at grazing incidence. The unsplit convolutional PML (CPML) has been proven to be more efficient in absorbing evanescent waves and propagating waves at grazing incidence. We reformulate the original AWWE as a first-order formulation and incorporate the CPML into the renewed formulation. The staggered-grid finite-difference (SGFD) method is adopted to discretize the first-order system. The presented first-order AWWE with the CPML is confirmed to be computationally more efficient than the original second-order AWWE with the classical split PML in wavefield depth continuation. Several numerical examples are presented to prove correctness of the SGFD method and the absorption effect of the CPML in AWWE numerical simulation and migration.

**Summary**

In this abstract, based on the blending matrix expression of different encoding methods deduced by using Principle of Stationary Phase, two separation methods are presented to separate the blended vibroseis data. In addition, before separation, we apply deconvolution to the blended vibroseis data as a preprocessing tool. The blending problem can be solved by an iterative method, which is extended from an iterative method proposed by Doulgeris (2010). A new pseudo-deblending matrix is defined to make it suitable to all encoding methods. The blending problem can also be treated as a regularization inversion problem with a sparse constraint after deconvolution. Both methods are effective and they have strong applicability to different encoding types. Deconvolution as a preprocessing tool is also very effective. Several numerical examples are given to show the effectiveness of the deconvolution preprocess and the two methods for different encoding types.

acquisition, deconvolution, equation, expression, inversion, inversion method, iteration, iterative method, matrix, pseudo-deblended result, Reservoir Characterization, seismic data, separation, shot record 1, simultaneous vibroseis, simultaneous vibroseis data, sparse, Upstream Oil & Gas, Vibroseis, Vibroseis data

Thank you!