Ajo-Franklin, J., G. Alves, O. Barak, G. Barnier, B. Biondi, E. Biondi, K. Bjella, A. Cabrales-Vargas, J. Chang, J. Claerbout, R. Clapp, S. Constable, T. Dahlke, T. Daley, S. Dou, E. Dunham, S. Fomel, B. Freifeld, F. Huot, J. Jennings, K. Key, H. Le, S. Levin, N. Lindsey, Y. Ma, M. Maharramov, E. Martin, M. Robertson, S. Ronen, R. Sarkar, C. Ulrich, A. Wagner, and L. Watson.
Wave-mode separation in the complex wavelet domain using combined translational and rotational data (pdf)
Ohad Barak and Shuki Ronen
Rotations are medium strains induced by seismic waves, which are independent of the commonly-recorded translational motions. We use combined translational data from geophones and rotational data from rotation sensors to identify and separate particular wave modes from a six-component (6C) field dataset. We develop a polarization filter in the complex wavelet domain in order to identify and subsequently attenuate shear and surface wave modes. Our method does not rely on spatial continuity parameters, and can therefore be applied to spatially aliased data.
The elastic forward and adjoint operators involve the computation and storage of many wave fields and models. I present two solutions to speed up the computation time of elastic operators. The first one uses multithread parallelization, while the second introduces Intel's Single Program Multiple Data Program Compiler (ISPC). Each solution shows a speed-up of about three times when compared to the original algorithm. I combine these improvements with better memory usage procedures that allow the processing of larger data sets. I show results of an Elastic Reverse Time Migration (ERTM) applied to the 2D synthetic Marmousi2 data set.
Ettore Biondi, Biondo Biondi, and Robert Clapp
We introduce the concept of a wavefield-based amplitude variation with offset (AVO) inversion scheme. With this approach we do not make use high-frequency ray approximation or planar-reflector assumption used in most of the AVO inversion algorithms. We illustrate a method to compute elastic images by simple acoustic propagation of pressure waves, and demonstrate the equivalence with those obtained by full elastic wavefield modeling.
Robert G. Clapp and Gustavo Alves
Elastic migration, due to both sampling requirements and the need for additional wavefields, requires significantly more storage per saved time step than acoustic migration. Using random boundaries that are time reversible is a solution to minimize storage requirements. We construct a random boundary for elastic modeling using randomly sized grains with increasingly random Lamé parameters away from the computational domain. We demonstrate that the elastic random boundary is more effective than an acoustic random boundary due to mode conversions.
Ohad Barak, Kerry Key, Steven Constable, and Shuki Ronen
Induction-coil magnetometers generate current when they are rotated within the Earth's magnetic field. The current is proportional to the amount of rotation. We show how to obtain seismic rotations from magnetometer recordings. To validate the method, we performed a seismic survey where both magnetometers and inertial rotation sensors were used to record waves generated by an active source. Our results indicate that seismic rotations can be derived from induction-coil magnetometers if the ambient magnetic noise level is low and if the rotation axis is not coincident with the Earth's ambient magnetic field's direction.
The recently proposed concept of energy imaging condition is an alternative method for the attenuation of low-wavenumber artifacts that arise in reverse-time migration. It can be set in terms of energy conservation of the wave equation solution, or using the impedance kernel, and can be implemented in acoustic and elastic media. I introduce an implementation of the energy imaging condition in vertical transverse isotropic media. The performance of the energy imaging condition is evaluated in 2-D synthetic data, both isotropic and anisotropic.
Eileen R. Martin, Nate Lindsey, Shan Dou, Jonathan B. Ajo-Franklin, Anna Wagner, Kevin Bjella, Tom Daley, Barry Freifeld, Michelle Robertson, and Craig Ulrich
In the summer of 2015 a shallow trenched distributed acoustic sensing (DAS) array was deployed along a road north of Fairbanks, Alaska as part of an effort to develop a low-cost system to monitor permafrost thaw under infrastructure. The dominant vibration sources were cars passing on a nearby road parallel to the array's dominant direction. Source analysis including beamforming over small frequency intervals and of the broadband recordings confirms that most noise was coming from the direction of Fairbanks or from cars. Cross-correlations of the data show unusual apparent copies of the primary Green's function, and limiting data to times with no more than one car only slightly helps these issues. Another virtual source response estimation method, cross-coherence, yields better results even with no filtering applied to the data.
Jason P. Chang
Using the passive portion of the continuous recordings from the Apache Forties data set, I characterize the marine ambient noise field and perform ambient noise cross-correlations on multicomponent ocean-bottom node data. Spectrograms from nodes near and far from the operating platform suggest that the platform dominates the ambient noise field for frequencies up to 40 Hz, particularly in the vertical geophones. Plots of spectral power at each node as a function of distance from the operating platform support this observation. Beamforming of the ambient noise field across different subsections of the array confirms this widespread influence of the platform. As Love waves often have higher signal-to-noise ratio than corresponding Rayleigh waves, I apply the ambient noise cross-correlation method to multicomponent ocean-bottom node recordings. In the microseism band, I am able to recover coherent Scholte waves in the radial-radial correlations and coherent Love waves in the transverse-transverse correlations. For frequencies between 5 and 10 Hz, Love-wave energy appears to be just as coherent as Scholte-wave energy. Additionally, there are signs of an acoustic wave traveling on the hydrophone and vertical geophone components at very high frequencies (40-80 Hz). The presence of these acoustic waves is potentially promising for future work in passive fathometry.
Noise gradiometry is a special case of wavefield reconstruction inversion when the propagating wavefield is recorded at every point within the domain of interest. In this favorable, but typically unrealistic, case the method provides accurate and high-resolution estimates of seismic velocities. It can recover both the short and long wavelengths of unknown velocity perturbations. However, if the data are irregularly sampled, or the recording is limited to the boundary of the domain (surface), the quality of the velocity estimate depends on the quality of the wavefield reconstruction. A simple synthetic-data example in which the wavefield is randomly subsampled by a factor of two shows the challenges encountered by the method by poor reconstruction of the wavefield.
In 1989 using cast-off industrial gear we at SEP set up for just one night a square 2-D array of 4056 10 Hz geophones. To our utter surprise we found noise arriving from the east all night long with an emergent velocity greater than 8 km/sec. Stratified media seismology implies the source is continuous microearthquakes directly under Stanford Campus at 10-20 km depth.
Guillaume Barnier and Biondo Biondi
We present an approach to identify and quantify patterns in migrated subsalt images caused by small-scale velocity errors in the vicinity of the top-salt interface. These velocity anomalies, which behave as point diffractors, generate artifacts in subsalt reflectors that have coherent moveout information. We show that the signature of a given velocity error in the image is the same as the impulse response of a migration with one source at the surface and a single virtual receiver placed at the velocity error location. Our final goal is to use the moveout information of these patterns to gradually extract them from the image and translate them into velocity model updates (close to the salt interface) by applying a wave equation migration velocity analysis (WEMVA) optimization scheme.
I develop a time-domain method for anisotropic full waveform inversion based on the second-order system of pseudo-acoustic wave equations in vertical transverse isotropic media. I use a synthetic model with both reflections and diving waves to test the method's performance. Three inversion passes are carried out in a frequency continuation manner using three source wavelets with peak frequencies at 5 Hz, 10 Hz, and 20 Hz. The residual is reduced significantly after each pass, and the inverted models converge toward the true ones. I also investigate the use of the Hessian to precondition the objective function's gradient and to reduce crosstalks between different parameters. The synthetic examples show that the inverse of the Hessian spatially balances the amplitude of the gradients, focuses energy to the actual model perturbations' locations, and reduces parameter crosstalks.
Taylor Dahlke, Biondo Biondi, and Robert Clapp
Interpretation of sharp salt boundaries can be achieved by using level sets to define the boundary as an isocontour of a higher dimensional implicit surface. Using shape optimization, we can evolve this surface and the boundary it represents. We derive an update for the implicit surface that uses second-order information in the Hessian of the FWI objective function, taking into account the effects of the acquisition, as well as scattering and transmission energy. This approach helps us avoid local minima and more effectively converges on the true model, both in terms of the data and model residual norms. We demonstrate this idea using a Gauss-Newton approximation of the Hessian on synthetic examples.
Yinbin Ma, Musa Maharramov, Robert Clapp, and Biondo Biondi
We implement multiparameter full-waveform inversion (FWI) in the isotropic acoustic media with the nonlinear conjugate gradient (CG) method. The performance of the FWI is evaluated using different combinations of acoustic parameters, including velocity, density and acoustic impedance. Simultaneous inversion of velocity and density leads to smoother results, when compared with the inversion results for velocity and acoustic impedance. We discuss the crosstalk between parameters for different parameterizations of FWI. We show the second order method can be used to reduce the crosstalk by applying the approximated inverse of the Hessian to the gradient.
Alejandro Cabrales-Vargas, Biondo Biondi, and Robert Clapp
Current implementations of linearized waveform inversion rely on an optimum background model, and only allow updating the high wavenumber component, a.k.a. reflectivity. We attempt to take one step further allowing controlled perturbations in the background model. We propose constraining such perturbations in a way that maximizes the stacking power, therefore improving the estimated reflectivity even further. We introduce theoretical insight about what we have called linearized waveform inversion with velocity updating.
Musa Maharramov and Stewart A. Levin
We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve L1/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of Multipliers (ADMM) with a Conjugate Directions technique in a way that allows reusing conjugate search directions constructed by the algorithm across multiple iterations of the ADMM. The new method achieves fast convergence by trading off multiple applications of the modeling operator for the increased memory requirement of storing previous conjugate directions. We illustrate the new method with a series of imaging and inversion applications.
A constant Q earth model attenuates amplitude inversely with the number of wavelengths propagated, so the attenuation factor is e-| ω | (z/v)/Q. We call an impulse response in this model a Futterman wavelet. A collection of Futterman wavelets F for all depths is a seismogram modeling operator. Applying FT to the data converts a collection of Futterman responses to a collection of symmetric autocorrelations. In this way it recovers event arrival time while (unfortunately) squaring the frequency response. We build a unitary operator that compensates Futterman phase response without changing the data spectrum. We build a quasi-analytic inverse that considers data precision while attempting to restore pulses that are late-arriving hence high frequency weak.
Separation of simultaneous source blended data using radiality and source similarity attributes (pdf)
Joseph Jennings and Shuki Ronen
Deblending data from simultaneous sources is an underdetermined problem. This problem cannot be solved based on fitting blended data to unknown deblended data without more assumptions. Useful such assumptions are, for example, that the deblended data are continouos in common receiver gathers, or that both blended and deblended data fit one earth reflectivity model. We point to the opportunity to use multi-component data and different sources in addition to such assumptions. We developed a method that assigns a probability to the existence of simultaneous source interference indicating the likelihood that at certain times, the interference originated from another active source. To estimate this probability we compute two attributes which we call radiality and source-signature similarity. Radiality is calculated for multi-component data with horizontal components such as ocean bottom seismometers or multi-sensor streamers. Source signature similarity is useful when sources have different source signatures. The end goal of this work is to use this probability as additional information in deblending and imaging simultaneous source data.
Cycling around Galilee (pdf)
Stewart A. Levin
Inspired by loop tie interpretation of intersecting 2D seismic lines, I adjust the depths of individual tracks from the venerable Sea of Galilee depth soundings in order to make their depth readings (more) consistent at crossing points. I also explore the notion that moveout along tracks is more reliable than absolute depths.
A time-adaptive deconvolution filter is estimated and used in a streaming manner.
Sergey Fomel, Jon Claerbout, Stewart A. Levin, and Rahul Sarkar
A PEF can be updated as each new data value arrives. The update costs only one dot product of vectors the size of the PEF. Typical PEF applications do not require storing the PEF; it can be used on the fly. This streaming notion could be merged with a multidimensional helix to produce a nonstationary multidimensional PEF.
Prediction error filters (PEFs) have found applications in several important areas of geophysics, including noise removal and interpolation of seismic data. Non-stationary time variant PEFs or TV-PEFs are special in this family of filters because they can model non-stationary processes which allow us to more accurately capture most seismic data. However, computing and applying the TV-PEFs using the usual method of least squares, becomes prohibitively expensive for large data sets. This paper investigates a recent computationally efficient streaming formulation designed to overcome this difficulty. I show with 1D examples, that the TV-PEFs obtained using streaming are capable of producing results comparable or better than other existing algorithms. I generalize the streaming result to an arbitrary path based update scheme for the TV-PEF coefficients in 2D. It is also shown with numerical examples that the results depend on the path traversed through the data. The performance of the streaming algorithm when applied to the 2D missing data interpolation problem is also considered.
Fantine Huot and Robert Clapp
Strong localized heterogeneities in the subsurface, such as karst caverns and sinkholes, cause scattering of seismic waves, thereby degrading the images obtained in conventional processing. We explore the possibility of using pattern recognition techniques for detecting these strong heterogeneities from seismic data. Through synthetic models, we generate training data with significant scattering and demonstrate how to decompose it into elementary shapes fit for machine learning algorithms by applying continuous wavelet transforms. We then provide an overview of support vector machine classification and present how we intend to apply it to our problem.
Leighton M. Watson, Eric M. Dunham, and Shuki Ronen
There is significant interest in understanding the dynamics of seismic airguns and the coupling between the bubble produced when the airgun discharges and the pressure waves excited in the water. It is desirable to increase the low frequency content of the signal, which is beneficial for imaging, especially for sub-salt and sub-basalt exploration, and to reduce the high frequency content, which, due to attenuation and scattering, is less useful as seismic signal, yet is thought to be damaging to marine life. It has been argued that a new style of airgun, with drastically lower pressure and larger volume than conventional airguns, will achieve these improvements. We develop a numerical model of a seismic airgun and compare the simulation results to lake data for validation. We perform numerical simulations for a range of airgun firing parameters and demonstrate that the proposed low pressure source (4000 in3, 600 psi) is able to reduce the high frequency noise by 6 dB at 150 Hz compared to a 1000 in3 airgun at 2000 psi, while maintaining the low frequency content. Therefore, the low pressure source is more environmentally friendly without compromising survey quality.
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Robert G. Clapp