Many engineering problems involve learning hidden dynamics from indirect observations, where the ... more Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered scalable and efficient to learn hidden dynamics. However, one of the most time-consuming and error-prone tasks is to derive and implement the gradients, especially in systems of PDEs where gradients from different systems must be correctly integrated together. To that purpose, we present a novel technique, called intelligent automatic differentiation (IAD), to leverage the modern machine learning tool TensorFlow for computing gradients automatically and conducting optimization efficiently. Moreover, IAD allows us to integrate specially designed state adjoint method codes to achieve better performance. Numerical tests demonstrate the feasibility of IAD for learning hidden dynamics in complicated systems of PDEs; additionally, by incorporating custom built state adjoint method codes in IAD, we significantly accelerate the forward and inverse simulation.
Inverse problems are usually ill-posed in such a way that it is necessary to use some method to r... more Inverse problems are usually ill-posed in such a way that it is necessary to use some method to reduce their deficiencies. For this purpose, we use the regularization by derivative matrices, known as Tikhonov regularization. There is a crucial problem in regularization, which is the selection of the regularization parameter 𝜆. In this work, we use generalized cross validation (GCV) as a tool for the selection of 𝜆. GCV is used here for an application in geophysical diffraction tomography, where the objective is to obtain the 2-D velocity distribution from the measured values of the scattered acoustic field. The results are compared to those obtained using L-curve, and also Θ-curve, which is an extension of L-curve. We present several simulation results with synthetic data, and in general the results using GCV are equal or eventually better than the other two approaches.
Background In the last two annual reports on CO2 storage monitoring, we discussed the feasibility... more Background In the last two annual reports on CO2 storage monitoring, we discussed the feasibility of using different geophysical options for subsurface CO2 monitoring, and described an innovative approach for near-continuous subsurface monitoring. We also discussed special challenges and requirements with continuous and leak detection of CO2. We chose seismic methods for subsurface monitoring primarily because they are broadly applicable in a variety of geological settings and sensitive to changes in CO2 saturation. To further develop seismic methods, for this particular application, we have proposed adaptive sparse data acquisition to address the problem of cost-effective time-lapse monitoring. We focused our work on leak detection and have proposed data gathering and processing concepts for dynamic imaging and model-based inversion. Developments reported in previous reports included a suite of seismic modeling tools to simulate monitoring and a small-scale field example on seismic...
It is desirable to use Finite Element (FE) or Finite Difference (FD) method to simulate elastic d... more It is desirable to use Finite Element (FE) or Finite Difference (FD) method to simulate elastic data for cross-hole seismic surveys. But FE and FD are computationally intensive and time-expensive for full wave-field modeling of large cross-hole survey. The computation cost -space and time-of elastic data modeling inhibits the use of synthetic data for providing solution to cross-hole geophysics problems .On the other hand, acoustic synthetic data require less computation time but lacks some of seismic arrivals seen in the field data. In this study a recursive reflectivity method incorporating P and S wave properties and attenuation effects is formulated to model cross-hole seismic data. The model is tested using a set of field data acquired in Green Wood field, USA. The visco-acoustic data modeled by the recursive reflectivity method show improvement over the acoustic data and gave a perfect match to the elastic and field data. The visco-acoustic data featured the different seismic arrivals seen in the field and elastic synthetic data. The data simulation method is stable, efficient, and fast. The inclusion of a scheme for determining the optimum layer model further reduced the computation time without compromising the quality of the results: only about one-eight of the time require for elastic data is needed to produce the equivalent visco-acoustic data. Because of its low computation cost, the study highlights the strong potentials for solving the problem of inefficient algorithm for processing and imaging cross-hole data, with a consequence of using cross-hole technology as a routine in oil and gas industry.
Proceedings of the 6 Simpósio Brasileiro de Geofísica, 2014
) estimation with attenuation-compensated reverse time migration (Q-RTM). We review the approach ... more ) estimation with attenuation-compensated reverse time migration (Q-RTM). We review the approach (theory and algorithm), and present results from a field application of Q-compensated imaging using borehole seismic data. The goal of Q-compensated imaging is to restore pre-stack amplitude loss, improve signal bandwidth, and improve pre-stack balance of amplitude and phase in an effort to improve stack coherency and subsequently image resolution. To this end, we developed and tested a consistent approach for Q estimation and forward-time and reverse-time simulation for waves in constant Q media. This approach incorporates robust and practical algorithms for Q-compensated imaging. The approach is tested on a crosswell field dataset from west Texas, USA where improved spatial resolution and improved spatial continuity can be observed in the Q-compensated image.
Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be... more Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be easily trapped in a local minimum. On the other hand, the inversion results may exhibit strong artifacts and reduced resolution because of inadequate constraint from data. Proper regularizations are necessary to reduce such artifacts and steer the inversion towards a good direction. In this study, we propose a novel adaptive sparsity-promoting regularization for FWI in the model-derivative domain which exploits nonlocal similarity in the model. This regularization can be viewed as a generalization of total variation (TV) with multi-class learning-based dictionaries. The dictionaries incorporate the prior information of nonlocal similarity into the inversion, exploiting the fact that geological patterns at different places are similar to some others up to affine transformations (translation, rotation and scaling). Such nonlocal similarity priors effectively reduce the degrees of freedom in model parameters, and may also mitigate the problem of local minima. The formulated optimization problem is solved by the Alternating Direction Method of Multipliers (ADMM). By interpreting the iterative scheme, we find our method closely connected with image processing techniques and convolutional neural networks (CNN). We test our proposed method on a modified BP 2004 velocity model and a smoothed Marmousi model. Compared with traditional FWI, our technique can better reconstruct sharp edges such arXiv:1803.11391v2 [physics.geo-ph] 6 Aug 2018 2 D. Li & J. Harris as salt body boundaries, and is also able to effectively reduce artifacts. Compared with TV, our result is less blocky and more geologically realistic. Quantitatively, our result has the highest structural similarity index (SSIM) and also the lowest model mean square error. This proposed method provides a general framework for incorporating nonlocal similarity priors into inversion, and can be applied to other (transformed) domains with the double-sparsity strategy.
We present a novel earthquake location method using acoustic wave-equation-based traveltime inver... more We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation (δt 0 , δx s ) and the resulting traveltime residual δt of a particular seismic phase, represented by the traveltime sensitivity kernel K(t 0 , x s ) with respect to the earthquake location (t 0 , x s ), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K(t 0 , x s ) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake-receiver geometry but also accurately honors the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.
The coseismic electromagnetic signals observed during the 2004 M w 6 Parkfield earthquake are sim... more The coseismic electromagnetic signals observed during the 2004 M w 6 Parkfield earthquake are simulated using electrokinetic theory. By using a finite fault source model obtained via kinematic inversion, we calculate the electric and magnetic responses to the earthquake rupture. The result shows that the synthetic electric signals agree with the observed data for both amplitude and wave shape, especially for early portions of the records (first 9 s) after the earthquake, supporting the electrokinetic effect as the reasonable mechanism for the generation of the coseismic electric fields. More work is needed to explain the magnetic fields and the later portions of the electric fields. Analysis shows that the coseismic electromagnetic (EM) signals are sensitive to both the material properties at the location of the EM sensors and the electrochemical heterogeneity in the vicinity of the EM sensors and can be used to characterize the underground electrochemical properties.
SEG Technical Program Expanded Abstracts 1993, 1993
The elastic constants that control P-and SV-wave propagation in a transversely isotropic media ca... more The elastic constants that control P-and SV-wave propagation in a transversely isotropic media can be estimated by using P-and SV-wave traveltimes from either cross-well or VSP geometries. The procedure consists of two steps. First, elliptical velocity models are used to fit the traveltimes near one axis. The result is four elliptical parameters that represent direct and normal moveout velocities near the chosen axis for P-and SV-waves. Second, the elliptical parameters are used to solve a system of four equations and four unknown elastic constants. The system of equations is solved analytically yielding simple expressions for the elastic constants as a function of direct and normal moveout velocities. For S&waves the estimation of the corresponding elastic constants is easier because the phase velocity is already elliptical. The procedure, introduced for homogeneous media, is generalized to heterogeneous media by using tomographic techniques. The technique is illustrated with synthetic and field data examples from cross-well geometries.
SEG Technical Program Expanded Abstracts 2003, 2003
Borehole seismic data often contain strong tube waves and tube-wave-related arrivals due to the e... more Borehole seismic data often contain strong tube waves and tube-wave-related arrivals due to the effects of the presence of the borehole. A basic requirement for accurate single-well, cross-well and VSP modeling is inclusion of these events. We use a velocity-stress variable-grid finite-difference code for cross-well field data modeling with inclusion of the two perforated cased boreholes. The synthetics resemble the field observations in terms of arrival times not only on P-and S-waves but also on tube waves and tubewave-related arrivals generated by perforations in receiver and source wells.
SEG Technical Program Expanded Abstracts 1998, 1998
The availability and use of seismic data in reservoir development is increasing. This paper descr... more The availability and use of seismic data in reservoir development is increasing. This paper describes the analysis of reflections, for elastic and porous medium considering variations in the petrophysical parameters of porosity, permeability and viscosity. Three types of seismic waves are analyzed: P fast , P slow and S for frequencies common to surface seismic (60 Hz) and crosswell seismic (2000 Hz) surveys. We use a system of equations derived for porous media by Chen and Quan (1995) which are analogous to Zoeppritz (1919) equations for a pure elastic solid media. We also use an elastic biphase finitedifference modeling program to compare and match the results. Final conclusions indicate a greater sensitivity of the seismic reflection response to porosity variations. Also, variations in the value of the critical angle can be a diagnosis of porosity in reservoir analysis. This effect was called "critical angle migration". S waves are more sensitive than P fast waves. Reflections are less sentive to variations with permeability and viscosity; and, the two have inverse dependence and are indistinct. P slow waves carry more information concerning to the petrophysical parameters but those waves can not be recorded in conventional seismic surveys.
SEG Technical Program Expanded Abstracts 2013, 2013
We present a constant-Q time-domain wave equation. It is derived from Kjartansson's constant-Q co... more We present a constant-Q time-domain wave equation. It is derived from Kjartansson's constant-Q constitutive stressstrain relation in combination with the mass and momentum conservation equations. Our wave equation, expressed by a second order temporal derivative and two fractional Laplacian operators, models attenuation and dispersion effects. The temporal derivative is solved by the staggered-grid finite-difference approach. The fractional Laplacian is easily calculated in the spatial frequency domain using say a Fourier pseudo-spectral implementation. The advantage of using our fractional Laplacian formulation over the traditional fractional time derivative approach is the avoidance of storing the time history of variables and thus more economic in computational costs. In numerical simulations, we incorporate PML (perfectly matched layer) absorbing boundaries. Furthermore, we verify the accuracy of numerical results through comparisons with theoretical constant-Q attenuation and dispersion solutions, McDonal's measurements in the Pierre shale, and results from 2-D viscoacoustic analytical modeling for the homogeneous Pierre shale. We then generalize our rigorous formulation for viscoacoustic waves in homogeneous media to an approximate equation for heterogeneous media. We demonstrate the applicability and efficiency of our constant-Q time-domain approach wave equation in a heterogeneous medium with highly atttenuative formation.
SEG Technical Program Expanded Abstracts 2009, 2009
An approach for quasi-continuous, geophysical time-lapse monitoring with sparse seismic data is p... more An approach for quasi-continuous, geophysical time-lapse monitoring with sparse seismic data is proposed. This approach takes advantage of the small changes in the seismic property of a geological reservoir that are expected to occur in a small time interval. The goal of this approach is to obtain high temporal and spatial resolution in reconstructed, time-lapse geophysical images using comparable resources that would have provided high spatial but low temporal resolution images with conventional approaches. This is done by acquiring spatially sparse data at small time intervals. In this case, a spatially sparse dataset refers to that dataset which is a small fraction (as little as 5%) of what would be acquired to reconstruct a high spatial resolution tomographic image of the subsurface. The high spatial resolution obtained by the proposed approach occurs because unrecorded data are predicted from future and past data. With high temporal and spatial resolution, early detection of important reservoir changes is more likely to occur.
SEG Technical Program Expanded Abstracts 2008, 2008
A stochastic approach to seismic inversion using the ensemble Kalman filter (EnKF) is proposed. S... more A stochastic approach to seismic inversion using the ensemble Kalman filter (EnKF) is proposed. Seismic depth and time image data are used as the input for EnKF stochastic seismic inversion. The sonic log is used to estimate source wavelet and create initial models for the inversion, which provides an efficient integration of sonic log data and seismic data. We use both travel time and waveform data for the inversion and obtain the absolute seismic velocity instead of the relative impedance. EnKF can continuously update the model using time-lapse data. A synthetic example is used to demonstrate the possible application to seismic monitoring.
SEG Technical Program Expanded Abstracts 2000, 2000
Over the last five years as part of DOE's Fossil Energy Program, Lawrence Berkeley National Labor... more Over the last five years as part of DOE's Fossil Energy Program, Lawrence Berkeley National Laboratory (LBNL), i n conjunction with industry, has been developing and applying methods of extending the penetration of conventional seismic logging from a few meters out to tens if not hundreds of meters. The use of borehole seismic sources and sensor strings, capable of exciting frequencies from 10s to 1000s of Hz, on a single cable is termed single well seismic imaging (SWSI). The SWSI acquisition work within our project has progressed through various field tests to a current system capable of CMP type borehole surveys with multiple borehole source and receiver options. Recent field experiments have been aimed at salt dome imaging from wells within and outside of a salt dome.
SEG Technical Program Expanded Abstracts 2011, 2011
proposed a strategy, called True4D, for quasi-continuous reservoir monitoring with sparse data. T... more proposed a strategy, called True4D, for quasi-continuous reservoir monitoring with sparse data. True4D introduced two concepts for processing sparse but continuously recorded datasets: (1) dynamic imaging and inversion, (2) data evolution, and (3) model evolution. Harris (2009, 2010) presented an approach to data evolution, i.e., inversion or imaging using data estimated from sparse recordings. In this paper, we examine the practicability of their approach, and present its application to full trace synthetic and field surface seismic data. The True4D approach is implemented by acquiring as little as 5% of the conventional 3-D survey data volume at small time intervals. Unrecorded data at each time interval are then estimated using recorded data at all intervals to produce an image with good spatial resolution of the subsurface. The high temporal resolution obtained using the True4D approach is its main benefit.
SEG Technical Program Expanded Abstracts 1994, 1994
A crosswell dataset, collected at Conoco' s Borehole Test Facility in Oklahoma, was first process... more A crosswell dataset, collected at Conoco' s Borehole Test Facility in Oklahoma, was first processed using a tomography algorithm based on an isotropic velocity model. The resulting 2-D velocity tomogram was found to have huge artifacts believed to be caused by nonuniform ray coverage and possibly anisotropy. A comparison of the zero offset crosswell velocities (Horizontal Path Log) with the log-derived sonic velocities (Vertical Path Log) indicated nearly 25% P-wave anisotropy in some formations. Despite the artifacts, a good interpretation of the 2-D isotropic tomogram was made with the help of synthetic data. The data were then inverted using an algorithm that incorporates a model of elliptical transverse isotropy. This anisotropy model produced an unambiguous image for two components of velocity that simultaneously match the sonic log and the crosswell data. Both inversions support a final interpretation of 1-D vertical stratification of layers, some of which exhibit significant P-wave anisotropy. This interpretation is consistent with the sonic logs, crosswell data, and available geological information.
SEG Technical Program Expanded Abstracts 1996, 1996
The generalized reflection and transmission coefficient method with modal expansion is developed ... more The generalized reflection and transmission coefficient method with modal expansion is developed to calculate the elastic wave field for the acoustic logging simulation and the crosswell seismic simulation in complex radially symmetric media. Our model consists of an arbitrary number of cylindrical layers and each cylindrical layer has arbitrary layers in the z-direction. This model can be used to simulate a variety of borehole geophysics problems: borehole casing with perforations, faults, source array, open and cased boreholes embedded in layered media, The simulation based on this method gives direct waves, reflections, transmissions, tube waves, tube wave conversions generated at casing perforations and horizontal interfaces, and the radiation pattern for a complicated borehole-formation structure. A general configuration of the problem considered in this study is shown in Figure , where the formation consists of several vertically heterogeneous cylinders, the source is located inside the borehole, while receivers are located either inside or outside the borehole. Although this model looks complicated, it still exhibits nice axial symmetric property. Taking the advantage of this symmetry we can derive a set of formulas to simulate the elastic wave propagation in this complex boreholeformation model. Since the model is radially symmetric, i.e., independent of in cylindrical coordinates, we can write the displacement for the jth cylindrical layer as
Many engineering problems involve learning hidden dynamics from indirect observations, where the ... more Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered scalable and efficient to learn hidden dynamics. However, one of the most time-consuming and error-prone tasks is to derive and implement the gradients, especially in systems of PDEs where gradients from different systems must be correctly integrated together. To that purpose, we present a novel technique, called intelligent automatic differentiation (IAD), to leverage the modern machine learning tool TensorFlow for computing gradients automatically and conducting optimization efficiently. Moreover, IAD allows us to integrate specially designed state adjoint method codes to achieve better performance. Numerical tests demonstrate the feasibility of IAD for learning hidden dynamics in complicated systems of PDEs; additionally, by incorporating custom built state adjoint method codes in IAD, we significantly accelerate the forward and inverse simulation.
Inverse problems are usually ill-posed in such a way that it is necessary to use some method to r... more Inverse problems are usually ill-posed in such a way that it is necessary to use some method to reduce their deficiencies. For this purpose, we use the regularization by derivative matrices, known as Tikhonov regularization. There is a crucial problem in regularization, which is the selection of the regularization parameter 𝜆. In this work, we use generalized cross validation (GCV) as a tool for the selection of 𝜆. GCV is used here for an application in geophysical diffraction tomography, where the objective is to obtain the 2-D velocity distribution from the measured values of the scattered acoustic field. The results are compared to those obtained using L-curve, and also Θ-curve, which is an extension of L-curve. We present several simulation results with synthetic data, and in general the results using GCV are equal or eventually better than the other two approaches.
Background In the last two annual reports on CO2 storage monitoring, we discussed the feasibility... more Background In the last two annual reports on CO2 storage monitoring, we discussed the feasibility of using different geophysical options for subsurface CO2 monitoring, and described an innovative approach for near-continuous subsurface monitoring. We also discussed special challenges and requirements with continuous and leak detection of CO2. We chose seismic methods for subsurface monitoring primarily because they are broadly applicable in a variety of geological settings and sensitive to changes in CO2 saturation. To further develop seismic methods, for this particular application, we have proposed adaptive sparse data acquisition to address the problem of cost-effective time-lapse monitoring. We focused our work on leak detection and have proposed data gathering and processing concepts for dynamic imaging and model-based inversion. Developments reported in previous reports included a suite of seismic modeling tools to simulate monitoring and a small-scale field example on seismic...
It is desirable to use Finite Element (FE) or Finite Difference (FD) method to simulate elastic d... more It is desirable to use Finite Element (FE) or Finite Difference (FD) method to simulate elastic data for cross-hole seismic surveys. But FE and FD are computationally intensive and time-expensive for full wave-field modeling of large cross-hole survey. The computation cost -space and time-of elastic data modeling inhibits the use of synthetic data for providing solution to cross-hole geophysics problems .On the other hand, acoustic synthetic data require less computation time but lacks some of seismic arrivals seen in the field data. In this study a recursive reflectivity method incorporating P and S wave properties and attenuation effects is formulated to model cross-hole seismic data. The model is tested using a set of field data acquired in Green Wood field, USA. The visco-acoustic data modeled by the recursive reflectivity method show improvement over the acoustic data and gave a perfect match to the elastic and field data. The visco-acoustic data featured the different seismic arrivals seen in the field and elastic synthetic data. The data simulation method is stable, efficient, and fast. The inclusion of a scheme for determining the optimum layer model further reduced the computation time without compromising the quality of the results: only about one-eight of the time require for elastic data is needed to produce the equivalent visco-acoustic data. Because of its low computation cost, the study highlights the strong potentials for solving the problem of inefficient algorithm for processing and imaging cross-hole data, with a consequence of using cross-hole technology as a routine in oil and gas industry.
Proceedings of the 6 Simpósio Brasileiro de Geofísica, 2014
) estimation with attenuation-compensated reverse time migration (Q-RTM). We review the approach ... more ) estimation with attenuation-compensated reverse time migration (Q-RTM). We review the approach (theory and algorithm), and present results from a field application of Q-compensated imaging using borehole seismic data. The goal of Q-compensated imaging is to restore pre-stack amplitude loss, improve signal bandwidth, and improve pre-stack balance of amplitude and phase in an effort to improve stack coherency and subsequently image resolution. To this end, we developed and tested a consistent approach for Q estimation and forward-time and reverse-time simulation for waves in constant Q media. This approach incorporates robust and practical algorithms for Q-compensated imaging. The approach is tested on a crosswell field dataset from west Texas, USA where improved spatial resolution and improved spatial continuity can be observed in the Q-compensated image.
Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be... more Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be easily trapped in a local minimum. On the other hand, the inversion results may exhibit strong artifacts and reduced resolution because of inadequate constraint from data. Proper regularizations are necessary to reduce such artifacts and steer the inversion towards a good direction. In this study, we propose a novel adaptive sparsity-promoting regularization for FWI in the model-derivative domain which exploits nonlocal similarity in the model. This regularization can be viewed as a generalization of total variation (TV) with multi-class learning-based dictionaries. The dictionaries incorporate the prior information of nonlocal similarity into the inversion, exploiting the fact that geological patterns at different places are similar to some others up to affine transformations (translation, rotation and scaling). Such nonlocal similarity priors effectively reduce the degrees of freedom in model parameters, and may also mitigate the problem of local minima. The formulated optimization problem is solved by the Alternating Direction Method of Multipliers (ADMM). By interpreting the iterative scheme, we find our method closely connected with image processing techniques and convolutional neural networks (CNN). We test our proposed method on a modified BP 2004 velocity model and a smoothed Marmousi model. Compared with traditional FWI, our technique can better reconstruct sharp edges such arXiv:1803.11391v2 [physics.geo-ph] 6 Aug 2018 2 D. Li & J. Harris as salt body boundaries, and is also able to effectively reduce artifacts. Compared with TV, our result is less blocky and more geologically realistic. Quantitatively, our result has the highest structural similarity index (SSIM) and also the lowest model mean square error. This proposed method provides a general framework for incorporating nonlocal similarity priors into inversion, and can be applied to other (transformed) domains with the double-sparsity strategy.
We present a novel earthquake location method using acoustic wave-equation-based traveltime inver... more We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation (δt 0 , δx s ) and the resulting traveltime residual δt of a particular seismic phase, represented by the traveltime sensitivity kernel K(t 0 , x s ) with respect to the earthquake location (t 0 , x s ), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K(t 0 , x s ) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake-receiver geometry but also accurately honors the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.
The coseismic electromagnetic signals observed during the 2004 M w 6 Parkfield earthquake are sim... more The coseismic electromagnetic signals observed during the 2004 M w 6 Parkfield earthquake are simulated using electrokinetic theory. By using a finite fault source model obtained via kinematic inversion, we calculate the electric and magnetic responses to the earthquake rupture. The result shows that the synthetic electric signals agree with the observed data for both amplitude and wave shape, especially for early portions of the records (first 9 s) after the earthquake, supporting the electrokinetic effect as the reasonable mechanism for the generation of the coseismic electric fields. More work is needed to explain the magnetic fields and the later portions of the electric fields. Analysis shows that the coseismic electromagnetic (EM) signals are sensitive to both the material properties at the location of the EM sensors and the electrochemical heterogeneity in the vicinity of the EM sensors and can be used to characterize the underground electrochemical properties.
SEG Technical Program Expanded Abstracts 1993, 1993
The elastic constants that control P-and SV-wave propagation in a transversely isotropic media ca... more The elastic constants that control P-and SV-wave propagation in a transversely isotropic media can be estimated by using P-and SV-wave traveltimes from either cross-well or VSP geometries. The procedure consists of two steps. First, elliptical velocity models are used to fit the traveltimes near one axis. The result is four elliptical parameters that represent direct and normal moveout velocities near the chosen axis for P-and SV-waves. Second, the elliptical parameters are used to solve a system of four equations and four unknown elastic constants. The system of equations is solved analytically yielding simple expressions for the elastic constants as a function of direct and normal moveout velocities. For S&waves the estimation of the corresponding elastic constants is easier because the phase velocity is already elliptical. The procedure, introduced for homogeneous media, is generalized to heterogeneous media by using tomographic techniques. The technique is illustrated with synthetic and field data examples from cross-well geometries.
SEG Technical Program Expanded Abstracts 2003, 2003
Borehole seismic data often contain strong tube waves and tube-wave-related arrivals due to the e... more Borehole seismic data often contain strong tube waves and tube-wave-related arrivals due to the effects of the presence of the borehole. A basic requirement for accurate single-well, cross-well and VSP modeling is inclusion of these events. We use a velocity-stress variable-grid finite-difference code for cross-well field data modeling with inclusion of the two perforated cased boreholes. The synthetics resemble the field observations in terms of arrival times not only on P-and S-waves but also on tube waves and tubewave-related arrivals generated by perforations in receiver and source wells.
SEG Technical Program Expanded Abstracts 1998, 1998
The availability and use of seismic data in reservoir development is increasing. This paper descr... more The availability and use of seismic data in reservoir development is increasing. This paper describes the analysis of reflections, for elastic and porous medium considering variations in the petrophysical parameters of porosity, permeability and viscosity. Three types of seismic waves are analyzed: P fast , P slow and S for frequencies common to surface seismic (60 Hz) and crosswell seismic (2000 Hz) surveys. We use a system of equations derived for porous media by Chen and Quan (1995) which are analogous to Zoeppritz (1919) equations for a pure elastic solid media. We also use an elastic biphase finitedifference modeling program to compare and match the results. Final conclusions indicate a greater sensitivity of the seismic reflection response to porosity variations. Also, variations in the value of the critical angle can be a diagnosis of porosity in reservoir analysis. This effect was called "critical angle migration". S waves are more sensitive than P fast waves. Reflections are less sentive to variations with permeability and viscosity; and, the two have inverse dependence and are indistinct. P slow waves carry more information concerning to the petrophysical parameters but those waves can not be recorded in conventional seismic surveys.
SEG Technical Program Expanded Abstracts 2013, 2013
We present a constant-Q time-domain wave equation. It is derived from Kjartansson's constant-Q co... more We present a constant-Q time-domain wave equation. It is derived from Kjartansson's constant-Q constitutive stressstrain relation in combination with the mass and momentum conservation equations. Our wave equation, expressed by a second order temporal derivative and two fractional Laplacian operators, models attenuation and dispersion effects. The temporal derivative is solved by the staggered-grid finite-difference approach. The fractional Laplacian is easily calculated in the spatial frequency domain using say a Fourier pseudo-spectral implementation. The advantage of using our fractional Laplacian formulation over the traditional fractional time derivative approach is the avoidance of storing the time history of variables and thus more economic in computational costs. In numerical simulations, we incorporate PML (perfectly matched layer) absorbing boundaries. Furthermore, we verify the accuracy of numerical results through comparisons with theoretical constant-Q attenuation and dispersion solutions, McDonal's measurements in the Pierre shale, and results from 2-D viscoacoustic analytical modeling for the homogeneous Pierre shale. We then generalize our rigorous formulation for viscoacoustic waves in homogeneous media to an approximate equation for heterogeneous media. We demonstrate the applicability and efficiency of our constant-Q time-domain approach wave equation in a heterogeneous medium with highly atttenuative formation.
SEG Technical Program Expanded Abstracts 2009, 2009
An approach for quasi-continuous, geophysical time-lapse monitoring with sparse seismic data is p... more An approach for quasi-continuous, geophysical time-lapse monitoring with sparse seismic data is proposed. This approach takes advantage of the small changes in the seismic property of a geological reservoir that are expected to occur in a small time interval. The goal of this approach is to obtain high temporal and spatial resolution in reconstructed, time-lapse geophysical images using comparable resources that would have provided high spatial but low temporal resolution images with conventional approaches. This is done by acquiring spatially sparse data at small time intervals. In this case, a spatially sparse dataset refers to that dataset which is a small fraction (as little as 5%) of what would be acquired to reconstruct a high spatial resolution tomographic image of the subsurface. The high spatial resolution obtained by the proposed approach occurs because unrecorded data are predicted from future and past data. With high temporal and spatial resolution, early detection of important reservoir changes is more likely to occur.
SEG Technical Program Expanded Abstracts 2008, 2008
A stochastic approach to seismic inversion using the ensemble Kalman filter (EnKF) is proposed. S... more A stochastic approach to seismic inversion using the ensemble Kalman filter (EnKF) is proposed. Seismic depth and time image data are used as the input for EnKF stochastic seismic inversion. The sonic log is used to estimate source wavelet and create initial models for the inversion, which provides an efficient integration of sonic log data and seismic data. We use both travel time and waveform data for the inversion and obtain the absolute seismic velocity instead of the relative impedance. EnKF can continuously update the model using time-lapse data. A synthetic example is used to demonstrate the possible application to seismic monitoring.
SEG Technical Program Expanded Abstracts 2000, 2000
Over the last five years as part of DOE's Fossil Energy Program, Lawrence Berkeley National Labor... more Over the last five years as part of DOE's Fossil Energy Program, Lawrence Berkeley National Laboratory (LBNL), i n conjunction with industry, has been developing and applying methods of extending the penetration of conventional seismic logging from a few meters out to tens if not hundreds of meters. The use of borehole seismic sources and sensor strings, capable of exciting frequencies from 10s to 1000s of Hz, on a single cable is termed single well seismic imaging (SWSI). The SWSI acquisition work within our project has progressed through various field tests to a current system capable of CMP type borehole surveys with multiple borehole source and receiver options. Recent field experiments have been aimed at salt dome imaging from wells within and outside of a salt dome.
SEG Technical Program Expanded Abstracts 2011, 2011
proposed a strategy, called True4D, for quasi-continuous reservoir monitoring with sparse data. T... more proposed a strategy, called True4D, for quasi-continuous reservoir monitoring with sparse data. True4D introduced two concepts for processing sparse but continuously recorded datasets: (1) dynamic imaging and inversion, (2) data evolution, and (3) model evolution. Harris (2009, 2010) presented an approach to data evolution, i.e., inversion or imaging using data estimated from sparse recordings. In this paper, we examine the practicability of their approach, and present its application to full trace synthetic and field surface seismic data. The True4D approach is implemented by acquiring as little as 5% of the conventional 3-D survey data volume at small time intervals. Unrecorded data at each time interval are then estimated using recorded data at all intervals to produce an image with good spatial resolution of the subsurface. The high temporal resolution obtained using the True4D approach is its main benefit.
SEG Technical Program Expanded Abstracts 1994, 1994
A crosswell dataset, collected at Conoco' s Borehole Test Facility in Oklahoma, was first process... more A crosswell dataset, collected at Conoco' s Borehole Test Facility in Oklahoma, was first processed using a tomography algorithm based on an isotropic velocity model. The resulting 2-D velocity tomogram was found to have huge artifacts believed to be caused by nonuniform ray coverage and possibly anisotropy. A comparison of the zero offset crosswell velocities (Horizontal Path Log) with the log-derived sonic velocities (Vertical Path Log) indicated nearly 25% P-wave anisotropy in some formations. Despite the artifacts, a good interpretation of the 2-D isotropic tomogram was made with the help of synthetic data. The data were then inverted using an algorithm that incorporates a model of elliptical transverse isotropy. This anisotropy model produced an unambiguous image for two components of velocity that simultaneously match the sonic log and the crosswell data. Both inversions support a final interpretation of 1-D vertical stratification of layers, some of which exhibit significant P-wave anisotropy. This interpretation is consistent with the sonic logs, crosswell data, and available geological information.
SEG Technical Program Expanded Abstracts 1996, 1996
The generalized reflection and transmission coefficient method with modal expansion is developed ... more The generalized reflection and transmission coefficient method with modal expansion is developed to calculate the elastic wave field for the acoustic logging simulation and the crosswell seismic simulation in complex radially symmetric media. Our model consists of an arbitrary number of cylindrical layers and each cylindrical layer has arbitrary layers in the z-direction. This model can be used to simulate a variety of borehole geophysics problems: borehole casing with perforations, faults, source array, open and cased boreholes embedded in layered media, The simulation based on this method gives direct waves, reflections, transmissions, tube waves, tube wave conversions generated at casing perforations and horizontal interfaces, and the radiation pattern for a complicated borehole-formation structure. A general configuration of the problem considered in this study is shown in Figure , where the formation consists of several vertically heterogeneous cylinders, the source is located inside the borehole, while receivers are located either inside or outside the borehole. Although this model looks complicated, it still exhibits nice axial symmetric property. Taking the advantage of this symmetry we can derive a set of formulas to simulate the elastic wave propagation in this complex boreholeformation model. Since the model is radially symmetric, i.e., independent of in cylindrical coordinates, we can write the displacement for the jth cylindrical layer as
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Papers by Jerry Harris