An amplitude versus angle (AVA) method is presented for estimating density and velocities of a stratified elastic medium. The seismograms are multiple-free, intercept time-horizontal slowness domain Green’s functions of time length T assumed to obey the first order WKBJ model for elastic single P-wave scattering. The WKBJ method is known to apply when the wave appears to be propagating in a medium which is changing slowly relative to the vertical wavelength of the wave. The signal at the fundamental frequency f =1/ T where T is record length must be present in the seismograms, implying that ultra-low frequencies <1 Hz for T >1 s must be generated and recorded. A relation is found between planewave Green’s functions at each horizontal slowness and the medium properties in time. The main mathematical findings are illustrated by using simple model seismograms.

We present a stochastic inversion procedure for surface-based common-offset ground-penetrating radar (GPR) reflection data. The method is based on simulated annealing (SA) and conditioned to borehole information available along the GPR profile. Application to synthetic and field data indicates that the proposed method is capable of reliably recovering strongly heterogeneous porosity structures associated with surficial alluvial aquifers. Presentation Date: Wednesday, October 14, 2020 Session Start Time: 1:50 PM Presentation Time: 3:30 PM Location: 361A Presentation Type: Oral

The reflection waveform inversion (RWI) using the tomographic term of the sensitivity kernel could be an alternative to full waveform inversion (FWI), especially in the deep target area where diving wave is not available. In RWI, the reflection waveform residuals are minimized to invert for the low to intermediate wavenumber components of the subsurface model. Nevertheless, the RWI is a highly nonlinear problem requiring careful preconditioning to avoid the local minima and accelerate the convergence rate. The Hessian operator is the second-order derivative of the objective function, implying the quadratic convergence information for the inverse problem. Making use of the Hessian information through Gauss-Newton or Newton method, is a promising way to improve the accuracy and efficiency of RWI. Besides, using traveltime objective function can make the reflection-based inversion less prone to the cycle-skipping problem. Therefore, to facilitate the practical application of reflection data in velocity reconstruction, we design a two-stage workflow, in which reflection traveltime inversion (RTI) and RWI are cascaded and solved using the truncated Gauss-Newton method to obtain a quadratic convergence. The synthetic data example and the real data application show the effectiveness of the proposed method. Presentation Date: Tuesday, October 13, 2020 Session Start Time: 1:50 PM Presentation Time: 3:05 PM Location: Poster Station 3 Presentation Type: Poster

ABSTRACT Waveform inversion is difficult to apply to near-offset surface seismic data, with issues such as the absence of large lateral wavenumbers and diving waves tending to leave iterative methods exposed to local minima. Well-logs can mitigate this issue to some degree, either by supporting the construction of reliable starting models, or, as we show in this paper, by permitting a model-validation step to be included within each iteration. The extra stability conferred by model validation allows one-way wave operators to be used in place of reverse time migration operators in the construction of the update. The approach leads to remarkably accurate results and significant computational savings. Once a log-validated waveform procedure is set up along these lines, we address the unknown-wavelet issue. A process of updating of both the amplitude and phase of an initial wavelet estimate is set up to produce stable inversions in both synthetic and field environments. In the latter case, profiles extracted from a log-validated waveform inversion of the Hussar land data set, when compared to two blind validation wells, are observed to accurately reproduce structures in zones producing significant reflection energy. Presentation Date: Wednesday, September 18, 2019 Session Start Time: 9:20 AM Presentation Time: 10:10 AM Location: Poster Station 8 Presentation Type: Poster

ABSTRACT Multiples always introduce artifacts in reverse time migration (RTM). Especially for elastic RTM, the PP and PS images may contaminated by transmitted P-S (or S-P) wave. In this study, we propose an approach to reconstruct the primaries of PP and PS waves. The primaries means the wave (P-P or P-S) reflected only once at the interface in the subsurface. The approach mainly contains three steps, including wavemode decomposition, Marchenko redatuming, and convolutional interferometry. First, the P and S waves in the surface measurements are decomposed using decoupled propagation method. Second, two components of upgoing Green’s functions of PP and PS waves are retrieved using iterative Marchenko approach. At last, the first events picked from the upgoing Green’s functions are convolved with estimated direct P wave to reconstruct the primaries. The reconstructed primaries used in elastic RTM can avoid the artifacts generated by internal multiples and transmitted P-S (or S-P) wave. A numerical test proves the validity of this approach. The approach is supposed to be applied in more complex media. Presentation Date: Wednesday, September 18, 2019 Session Start Time: 9:20 AM Presentation Start Time: 10:35 AM Location: Poster Station 12 Presentation Type: Poster

ABSTRACT Reflection-waveform inversion (RWI) utilizes reflection data to recover the background velocity. Due to the limited apertures of reflection data illuminating targets, and the trade-off between the depth of reflectors and the average velocity above the reflectors, RWI is inherently ill-posed. One manifestation is the existence of characteristic artificial blob-shaped or column-like anomalies in the recovered velocity models. That erroneous background velocity, which still fits the traveltime of reflection arrivals in the record, can lead to inaccurate velocity models and distorted migration images in the subsequent processes. In order to mitigate those artifacts and improve the conditioning of RWI, we incorporate a piece of prior information in RWI, i.e. slow property variation along geological structures. This prior information is expressed mathematically as structure oriented smoothing. We achieved this smoothing by solving an anisotropic diffusion equation. Thus, we formulated a constrained RWI scheme by alternating the following three steps: building temporary reflectors, updating background velocity, and solving the diffusion equation. We tested successfully this scheme on the Marmousi model. The results show that the scheme yields a stable and accurate background velocity that is free of the aforementioned distortions and leads to a high-quality final velocity model with subsequently conventional full-waveform inversion. Presentation Date: Tuesday, September 17, 2019 Session Start Time: 1:50 PM Presentation Time: 3:55 PM Location: Poster Station 8 Presentation Type: Poster

ABSTRACT Reflection full-waveform inversion (RFWI) is a wave equation based model building approach that utilizes reflection data and can update deeper parts of a velocity model not accessible by diving waves of standard FWI. In this paper, we propose an efficient RFWI workflow that uses full-waveform information contained in reflection data to update kinematics of reflections. It is based on the linearized MBTT (Migration Based Travel Time) approach and employs (Least-Square Reverse-Time Migration) LSRTM type iterations to construct true-amplitude data-space reflectivity that can be re-used in several iterations of RFWI velocity updates. The approach uses a regular L2-norm data misfit objective function and provides a fully automatic workflow. We illustrate the approach with synthetic and real-data examples. Presentation Date: Monday, September 16, 2019 Session Start Time: 1:50 PM Presentation Time: 1:50 PM Location: 302B Presentation Type: Oral

ABSTRACT Although, with the usual seismic acquisition, much of the information about subsurface parameters is contained in the reflections data, many of the current Full Waveform Inversion applications still focus on the use of the transmitted energy (i.e. refractions). In order to reduce the dependency on refractions, in this work we propose to pre-process the recorded and the simulated signals with an exponential function in order to be able to exploit the Normalized Integration Method also for reflection data. Tests on synthetic data shows that the resulting new cost function is more robust with respect to the cycle skip compared to the standard least squares cost function. We show the results of the proposed method on two simple synthetic datasets and on a more realistic one characterized by complex geology and strong velocity contrasts Presentation Date: Thursday, October 18, 2018 Start Time: 8:30:00 AM Location: 207C (Anaheim Convention Center) Presentation Type: Oral

We analyze different velocity recovery mechanisms of full waveform inversion (FWI) and compare misfit functions based on the least-squares ( L 2 ) norm and optimal transport. The focus will be on recovering velocity even below reflecting interfaces. The inherent nonconvexity of the L 2 norm as misfit leads to many local minima by updating the high-wavenumber components first, which is good for migration but problematic for inversion. On the other hand, the "transport" property behind the optimal transport based misfit functions naturally generates low-wavenumber updates which are ideal for recovering the model kinematics. We will analyze the velocity recovery mechanisms of diving waves and for domains above reflecting layers to see the advantages of using optimal transport type of misfit. Multiple numerical examples with simple layered models as well as a realistic benchmark with salt inclusion demonstrate that optimal-transport FWI is able to update the low-wavenumber components. Presentation Date: Wednesday, October 17, 2018 Start Time: 8:30:00 AM Location: 207C (Anaheim Convention Center) Presentation Type: Oral

ABSTRACT Conventional full waveform inversion (FWI) needs long offset data to update the deep structure of a velocity and low-frequency information to avoid cycle skipping with diving or refraction waves. To reduce the data requirements, we propose an approach referred to as reflection intensity waveform inversion (RIWI), which fits the difference in seismic reflection intensity between modeled and field data, so that the starting model dependence of waveform inversion can be relaxed and long offset data is no longer required. The intensity inherently has low-frequency information when compared with the original data. It can be obtained by deconstructing the intensity into low-frequency and high-frequency information using Fourier transformation. Implementing multi-scale inversions starting from low-frequency reflection intensity data can largely avoid the cycle-skipping problem. We corroborate the proposed approach validity for data without low-frequency content and long-offset information with numerical examples. Presentation Date: Monday, October 15, 2018 Start Time: 1:50:00 PM Location: Poster Station 7 Presentation Type: Poster

We investigate the benefits of improving the quantitative estimation of reflectivity in reflection FWI (RFWI). This is an important step of the inversion process, since it not only affects the generation of the synthetic reflection data, but also the generation of the "rabbit ears" along the reflection wavepaths. In our approach, the quantitative estimation of reflectivity is performed using least-squares reverse time migration (LSRTM), where the Hessian matrix and its inverse are estimated in the curvelet domain. Using synthetic and field data sets, we show how this approach can improve the reflectivity model and, therefore, benefit the RFWI velocity update. Finally, we discuss some of the limitations of this approach and some of the challenges that are not addressed by it. Presentation Date: Thursday, October 18, 2018 Start Time: 8:30:00 AM Location: 207C (Anaheim Convention Center) Presentation Type: Oral

ABSTRACT We apply an acoustic multiple attenuation method to a marine OBC dataset from the Volve field in the North Sea. The method consists of estimating surface-to-subsurface virtual responses using the Marchenko method, and using interferometric integrals to compute prestack multiple estimates from these virtual responses. The prestack multiples are adaptively subtracted from the original reflection data, and then images are created. We provide detailed comparisons between the image obtained from the multiples-attenuated image, the migrated original dataset, and an image obtained by migrating only themultiples. We show that several structures are attenuated in our new images, evidencing that our multiple attenuation method is effective in field data. This adds to the body of evidence to suggest that some Marchenko methods are suitable for field data applications. Presentation Date: Monday, October 15, 2018 Start Time: 1:50:00 PM Location: 211A (Anaheim Convention Center) Presentation Type: Oral

ABSTRACT A modified implementation of Marchenko redatuming leads to a filter that removes internal multiples from reflection data. It produces local reflectivity at two-way travel time. The method creates new primary reflections resulting from emitted events that eliminate internal multiples. We call these non-physical primaries and their presence is a disadvantage. The advantage is that the filter is model free. We give the 3D filter and demonstrate with 1D arguments that starting the focusing wavefield with a unit impulse at zero time, while focusing below the bottom reflector, is the choice that leads to a model free implementation. The starting impulse generates the reflection data. Every later emitted pulse eliminates an internal multiple somewhere in the model and helps removing the transmission amplitude effects in a physical primary. We show that the amplitude of the non-physical primaries are a product of three reflections, making them generally smaller than those of the physical primaries. A 2D modeled shotgather at different stages of filtering the data shows that the filter works well. Presentation Date: Wednesday, September 27, 2017 Start Time: 4:45 PM Location: 370A Presentation Type: ORAL

ABSTRACT We present a Reflection FWI (RFWI) workflow to update the velocity model using the low-wavenumber component of the FWI gradient of reflection data. This is achieved by alternately using high-wavenumber and low-wavenumber components to update density and velocity models, respectively. With synthetic examples, we discuss the limitations and requirements of this approach and propose possible ways to overcome some of the limitations. Finally, the method is applied to a deep-water survey in the Gulf of Mexico, where improvement is observed both in the migrated image and gathers. Presentation Date: Wednesday, September 27, 2017 Start Time: 2:15 PM Location: 361F Presentation Type: ORAL

ABSTRACT Near surface models from refraction inversion contain several types of errors, which are partially compensated later in the data flow by reflection residual statics. In this work, we modify the dataflow to automatically include feedback information from reflection statics from stack-power maximization. This technique can work with any model based refraction solutions including grid based tomography model and layer based delay time methods. In this report we modify cost function of the refraction inversion by adding model and data weights computed from the long wavelength components of surface consistent residual statics. By using an iterative inversion, these weights allow us to update the near surface velocity model and to reject first arrival picks that do not fit the updated model. In this non-linear optimization work flow the refraction model is derived from maximizing the coherence of the reflection energy and minimizing the misfit between model arrival times and the recorded first arrival times. This approach can alleviate inherent limitations in shallow refraction data by using coherent reflection data. Presentation Date: Thursday, September 28, 2017 Start Time: 8:30 AM Location: 370C Presentation Type: ORAL

ABSTRACT The Green’s theorem wave-separation methods (e.g., separating the reference wave and the reflection data, and deghosting) have an important property of naturally accommodating an arbitrary measurement surface. However, for non-horizontal acquisition, those methods cannot locate the output point on the surface where the input data is acquired. For example, in order to effectively predict the receiver-side deghosted data, the current algorithm originating from Green’s theorem wave separation has to output the deghosted result at a depth that is shallower than the actual acquisition location. If the measurement surface is horizontal, the Green’s theorem deghosting algorithm can be expressed in the wavenumber domain, and is equivalent to the widely used PVz method, and it can locate the output result on the measurement surface. However, the PVz method is not applicable with a non-horizontal acquisition surface. To overcome this drawback, this paper develops a two-step method that can achieve receiver-side deghosting right on the measurement surface and without assuming the measurement surface to be horizontal. Therefore, it can deghost the actual acquired data. The new method derives from both Green’s theorem based wave separation and one-way wave prediction. The shape of the measurement surface is assumed known. This idea is also viable for source-side deghosting. We develop the method and illustrate with synthetic examples, considering a towed streamer in the water column. It is worth noting that onshore and ocean-bottom acquisition can often have a significantly variable topography and can also benefit from the new method in this paper. Presentation Date: Monday, September 25, 2017 Start Time: 2:40 PM Location: 360A Presentation Type: ORAL

ABSTRACT Seismic data are rarely adequately and regularly sampled in practice. This leads to spatial aliasing and artifacts that degrade the image. True amplitude imaging becomes especially problematic in such circumstance. We propose a strategy to alleviate the effect of incomplete seismic data on the image quality. The proposed method, formulated in an iterative manner, is able to correct the amplitudes, suppress the artifacts and recovers the missing data as a by-product. The success of this approach relies on the fact that the information of the missing data is actually preserved more or less in the model space. We demonstrate with two synthetic examples that the proposed approach can greatly improve the true amplitude imaging in the case of incomplete data. Presentation Date: Wednesday, September 27, 2017 Start Time: 3:05 PM Location: 361A Presentation Type: ORAL

ABSTRACT In a recent publication, we proposed a waveform inversion (WI) algorithm for attenuation analysis in heterogeneous VTI (transversely isotropic with a vertical symmetry axis) media. Here, we supplement that method with the local similarity technique designed to remove the time shifts between the simulated and observed data. In the presence of velocity errors, this technique substantially stabilizes computation of the WI gradients and improves parameter estimation. The gradients are derived with the adjoint-state method, and four parameters describing the attenuation of P- and SV-waves are updated simultaneously. The algorithm is applied to multicomponent reflection data generated for a modified section of the BP TI model. The inversion significantly reduces the data misfit and recovers the long-wavelength components of the attenuation parameters, especially in the upper part of the section. Presentation Date: Wednesday, September 27, 2017 Start Time: 10:35 AM Location: 360D Presentation Type: ORAL

ABSTRACT We construct a low-noise setup for experimental 1D wave propagation. Using the attenuation-corrected reflection response measured on one side of a three-layer tube, we successfully perform Marchenko focusing. This is the first time that the iterative Marchenko scheme is applied to laboratory data to physically focus a wavefield. The fundamental solutions of the Marchenko equation provide us with a focusing function that suppresses internal multiples and produces a purely downgoing pulse at an arbitrary depth. When re-emitting that focusing function in the physical model we are able to suppress 74 % of the internal multiple energy. Additionally, the data-driven Marchenko focusing function is compared to a model-driven approach. The latter is only superior if the model geometry is known very accurately, while the Marchenko approach only requires knowledge of the attenuation. Presentation Date: Monday, October 17, 2016 Start Time: 1:00:00 PM Location: 147/154 Presentation Type: ORAL

ABSTRACT Deghosting is a key step for ocean bottom seismic data processing. For measurements at the seafloor, notches can occur within the spectrum at much lower frequencies than for towed streamer data. Removing ghosts can improve seismic resolution. In addition, the subsequent steps (e.g., multiple removal, imaging and inversion) will all benefit from effective deghosting. In this paper, based on Green’s theorem, we provide distinct methods to separate (1) the pressure data that are collected just above ocean bottom, and (2) the multicomponent displacements that are acquired below the seafloor, into up and down waves. Synthetic tests demonstrate the promise and potential of this method for deghosting ocean bottom data. Presentation Date: Wednesday, October 19, 2016 Start Time: 10:20:00 AM Location: 140 Presentation Type: ORAL