Search

In the last decade, a significant shift in the marine seismic acquisition business has been made where ocean bottom nodes gained a substantial market share from streamer cable configurations. Ocean bottom node acquisition (OBN) can acquire wide azimuth seismic data over geographical areas with challenging deep and shallow bathymetries and complex subsurface regimes. When the water bottom is rugose and has significant elevation differences, OBN data processing faces a number of challenges, such as denoising of the vertical geophone, accurate wavefield separation, redatuming the sparse receiver nodes from ocean bottom to sea level and multiple attenuation. In this work, we review a number of challenges using real OBN data illustrations. We demonstrate corresponding solutions using processing workflows comprising denoising the vertical geophones by using all four recorded nodal components, cross-ghosting the data or using direct wave to design calibration filters for up- and down-going wavefield separation, performing one-dimensional reversible redatuming for stacking QC and multiple prediction, and designing cascaded model and data-driven multiple elimination applications. The optimum combination of the mentioned technologies produced cleaner and high-resolution migration images mitigating the risk of false interpretations.

During ocean bottom seismic acquisition, seafloor multicomponent geophones located in rugose and sloping water bottom can be affected by skewed energy distribution, such as leaked shear energy on the vertical geophones and leaked compressional energy on the horizontal geophones. To correct for the tilted energy distribution, which is one of most effective preprocessing steps, a geophone reorientation step is applied. This is a simple and straightforward process that applies a 3‐dimensional rotation matrix with respect to the orientation angles. Since the reorientation process highly affects the outcome of the entire data processing workflow, it has to be accompanied by a careful quality control process to verify its validity for the whole survey area. In this study, we propose a quality control workflow for the geophone reorientation by using unsupervised machine learning. A correlation analysis is employed to compare numerical versus analytical solutions of both the azimuth and the incidence angles for the direct arrivals. A comparison of both solutions aims to generate correlation coefficients that are indicative of the accuracy of geophone orientation. The correlation coefficients are subsequently investigated by the k‐means clustering algorithm to differentiate and identify normally and abnormally deployed/reoriented geophones. Numerical experiments on a field ocean bottom seismic data set confirm that the proposed workflow effectively provides reliable labels for normally and abnormally deployed/reoriented geophones. The labelling assigned by the proposed quality control workflow is a suitable indicator for abnormalities in the geophone reorientation step and will be helpful for further investigation, such as re‐correction or removal of abnormally reoriented geophones.

This study introduces a new attribute to identify seismic erratic noise, i.e. outlier, in the context of unsupervised anomaly detection and is defined as local outlier probabilities. The local outlier probabilities calculate scores of degrees of isolation, i.e. outlier‐ness, for each object in a data set, which represents how far an object is deviated from its surrounding objects. Since the local outlier probabilities combines a density‐based outlier detection method with a statistically oriented scheme, its scoring system provides regularized outlier‐ness, which is an outlier probability, to be used for making a binary decision to do inclusion or exclusion of an object; such a decision only requires a simple and straightforward threshold on a probability. Based on the binary decision that flags outliers versus non‐outliers, local outlier probabilities‐denoising workflows are developed by combining multiple steps to complete an application of the local outlier probabilities to attenuate seismic erratic noise. Higher stability and improved robustness in the detection and rejection of seismic erratic noise have been achieved by implementing moving windows and decision tree‐based processes. To avoid loss of useful signal energy, signal enhancement applications are additionally suggested. Numerical experiments on synthetic data investigate the applicability of the proposed algorithms to seismic erratic noise attenuation. Field data examples demonstrate the feasibility of a local outlier probabilities‐denoising application as an effective tool in seismic denoising portfolio.

Numerous field acquisition examples and case studies have demonstrated the importance of recording, processing, and interpreting broadband land data. In most seismic acquisition surveys, three main objectives should be considered: (1) dense spatial source and receiver locations to achieve optimum subsurface illumination and wavefield sampling; (2) coverage of the full frequency spectrum, i.e., broadband acquisition; and (3) cost efficiency. Consequently, an effort has been made to improve the manufacturing of seismic vibratory sources by providing the ability to emit both lower (approximately 1.5 Hz) and higher frequencies (approximately 120 Hz) and of receivers by utilizing single, denser, and lighter digital sensors. All these developments achieve both operational (i.e., weight, optimized power consumption) and geophysical benefits (i.e., amplitude and phase response, vector fidelity, tilt detection). As part of the effort to reduce the acquisition cycle time, increase productivity, and improve seismic imaging and resolution while optimizing costs, a novel seismic acquisition survey was conducted employing 24 vibrators generating two different types of sweeps in a 3D unconstrained decentralized and dispersed source array field configuration. During this novel blended acquisition design, the crew reached a maximum of 65,000 vibrator points during 24 hours of continuous recording, which represents significantly higher productivity than a conventional seismic crew operating in the same area using a nonblended centralized source mode. Applying novel and newly developed deblending algorithms, high-resolution images were obtained. In addition, two data sets (i.e., low-frequency and medium-high-frequency sources) were merged to obtain full-bandwidth broadband seismic images. Data comparisons between the distributed blended and nonblended conventional surveys, acquired by the same crew during the same time over the same area, showed that the two data sets are very similar in the poststack and prestack domains.

A number of deblending methods and workflows have been reported in the past decades to eliminate the source interference noise recorded during a simultaneous shooting acquisition. It is common that denoising algorithms focusing on optimizing coherency and weighting down/ignoring outliers can be considered as deblending tools. Such algorithms are not only enforcing coherency but also handling outliers either explicitly or implicitly. In this paper, we present a novel approach based on detecting amplitude outliers and its application on deblending based on a local outlier factor that assigns an outlier‐ness (i.e. a degree of being an outlier) to each sample of the data. A local outlier factor algorithm quantifies outlier‐ness for an object in a data set based on the degree of isolation compared with its locally neighbouring objects. Assuming that the seismic pre‐stack data acquired by simultaneous shooting are composed of a set of non‐outliers and outliers, the local outlier factor algorithm evaluates the outlier‐ness of each object. Therefore, we can separate the data set into blending noise (i.e. outlier) and signal (i.e. non‐outlier) components. By applying a proper threshold, objects having high local outlier factors are labelled as outlier/blending noise, and the corresponding data sample could be replaced by zero or a statistically adequate value. Beginning with an explanation of parameter definitions and properties of local outlier factor, we investigate the feasibility of a local outlier factor application on seismic deblending by analysing the parameters of local outlier factor and suggesting specific deblending strategies. Field data examples recorded during simultaneous shooting acquisition show that the local outlier factor algorithm combined with a thresholding can detect and attenuate blending noise. Although the local outlier factor application on deblending shows a few shortcomings, it is consequently noted that the local outlier factor application in this paper obviously achieves benefits in terms of detecting and attenuating blending noise and paves the way for further geophysical applications.

We propose a workflow of deblending methodology comprised of rank‐reduction filtering followed by a signal enhancing process. This methodology can be used to preserve coherent subsurface reflections and at the same time to remove incoherent and interference noise. In pseudo‐deblended data, the blending noise exhibits coherent events, whereas in any other data domain (i.e. common receiver, common midpoint and common offset), it appears incoherent and is regarded as an outlier. In order to perform signal deblending, a robust implementation of rank‐reduction filtering is employed to eliminate the blending noise and is referred to as a joint sparse and low‐rank approximation. Deblending via rank‐reduction filtering gives a reasonable result with a sufficient signal‐to‐noise ratio. However, for land data acquired using unconstrained simultaneous shooting, rank‐reduction–based deblending applications alone do not completely attenuate the interference noise. A considerable amount of signal leakage is observed in the residual component, which can affect further data processing and analyses. In this study, we propose a deblending workflow via a rank‐reduction filter followed by post‐processing steps comprising a nonlinear masking filter and a local orthogonalization weight application. Although each application shows a few footprints of leaked signal energy, the proposed combined workflow restores the signal energy from the residual component achieving significantly signal‐to‐noise ratio enhancement. These hierarchical schemes are applied on land simultaneous shooting acquisition data sets and produced cleaner and reliable deblended data ready for further data processing.

An intrinsic problem during migration and imaging of seismic wavefields using the two-way wave equation is the crosstalk interference between the up/down propagation of the corresponding source and receiver wavefields. To mitigate this crosstalk, the downgoing source and upgoing receiver wavefield imaging condition (IC) is adopted at an early stage of the inversion process, improving convergence and obtaining cleaner reflection images. A wavefield decomposition methodology can also be incorporated into a least-squares reverse time migration (LSRTM) algorithm. The separation of wavefields based on the propagation direction in the early iterations of LSRTM is to reduce interference noise during the inversion process given that the IC considers only primary reflections. Wavefields decomposed with respect to the vertical direction can be easily obtained by Fourier transforms on the time and vertical axes; however, they usually require significantly higher computational effort especially for 3D applications. Vertical wavefield decomposition by a complex-valued analytic signal is an alternative method implemented by the Hilbert transform, which can be conducted by 1D Fourier transform only on the vertical axis. An LSRTM algorithm adopting this decomposition method has a disadvantage in that it requires two additional wave modelings at each iteration. However, by adapting the deprimary IC into LSRTM, only one more modeling is additionally required in the backward wavefield propagation as compared with conventional LSRTM. Our LSRTM using wavefield decomposition has the ability to produce broader band reflectivity images than conventional LSRTM. This is demonstrated with numerical examples using synthetic and real data resulting artifact-free migration results and broadband reflectivity images.

P-wave and S-wave separation methods have been widely applied to recorded and modelled multi-component wavefields in the time- and space-domains. Traditional methodologies, which employ divergence and curl operators, have given reasonable results; however, substantial residual energy or crosstalk remains. Application of the divergence and curl operators will alter the physical properties of the respective separated wavefields in terms of amplitude and phase information. Numerous studies have suggested more robust methods to separate P- and S-waves, such as decoupled wave equations to preserve the physical properties of the decomposed wavefields. These formulations produce intrinsic artifacts from S-wave reflections and conversions at where the non-smoothed velocity exists. In this paper, we introduce a filtering methodology using signal and noise orthogonalization to reduce unwanted artifacts occurring during the P-wave and S-wave separation. By combining robust wavefield separation and orthogonalization filtering, the residual reflection events, mainly from the S-wave conversions and reflections, are attenuated. We demonstrate using synthetic and real data examples a decoupled elastic wave propagation modelling scheme followed by local orthogonalization filtering and show its application in elastic full waveform inversion (FWI), which attempts to handle interference noise between mode-converted waves. Consequently, from the numerical examples presented, it is shown that using cleaner and separated P- and S-wavefields obtained from the filtered elastic wave propagation modelling and inversion, the solution converges faster and reduces the risk of falling into local minima during elastic multi-parametric inversion.

Summary One of the key advantage of multicomponent seafloor seismic acquisition is to suppress receiver side ghost and water-layer multiples by PZ processing. It is well known that the success of PZ processing is heavily rely on the processing/pre-conditioning of the vertical geophone component. In this study, we propose a pre-conditioning workflow for applying a vertical geophone de-noise process to enhance compressional wave signal free from shear energy contamination. The proposed workflow is a fully automated process and is comprised by three steps: 1) Masking filter, 2) Adaptive subtraction and 3) Envelope matching. Numerical examples show that the proposed methodology highly enhances signal-to-noise ratio of the vertical geophone component exhibiting high coherency with the hydrophone. The denoising result indicates the effectiveness of the proposed workflow, which will serve as a pre-conditioning step prior to the subsequent application of PZ processing as well as conventional data processing.

Summary In the oil industry, ocean bottom node acquisition (OBN) is one of the technologies utilized to help in deep marine exploration and development. It has also allowed us to acquire data over areas with more complex shallow bathymetry. Like many new techniques, it has its advantages and limitations. In this abstract, we will discuss some of them by showing examples from a recently acquired large, high density and full azimuth OBN survey.

The main objective of the full waveform inversion (FWI) is to deliver a velocity model which produces accurate and high resolution depth images. An integral part of FWI is the iterative optimization process aiming at minimizing an objective function describing the misfit between the observed and modelled data with respect to the velocity model parameters. However, FWI commonly suffers from local minima due to errors in data fitting and the starting velocity model. In this study, we develop a methodology to enhance convergence and mitigate the risk of having solutions falling into local minima. We employ optical flow to decompose the source and residual receiver wavefields and map them into the subsurface angle domain. Having evaluated the propagation vectors of the respective cleaner wavefields, subsurface reflection and azimuth angles can be robustly computed. Using such information we can apply angle-dependent preconditioning within the inversion algorithm. During a conventional FWI workflow, larger angles (i.e., transmission wavepaths) are mainly responsible for long wavelength velocity anomalies whereas narrow angles (i.e., reflection wavepaths) influence short wavelength velocity anomalies. In the proposed FWI methodology, we apply an optimized weighting function based on these estimated subsurface reflection angles in order to weight certain angle directions needed for gradient estimation using in parameter updating. Following a hierarchical approach, allowing for larger angles at the early stage of the FWI application, we initially solve for the smooth and longer wavelength velocity updates. Relaxing the opening angle from large to mid to narrow, the gradient direction will first estimate long wavelength velocity model updates (transmission-based wavepaths), following by short wavelength velocity model updates (reflection-based wavepaths). Moreover, angle-dependent-based gradient preconditioning can reduce cycle skips and improve convergence during FWI iterations.

The key objective of an imaging algorithm is to produce accurate and high-resolution images of the subsurface geology. However, significant wavefield distortions occur due to wave propagation through complex structures and irregular acquisition geometries causing uneven wavefield illumination at the target. Therefore, conventional imaging conditions are unable to correctly compensate for variable illumination effects. We propose a generalised wave-based imaging condition, which incorporates a weighting function based on energy illumination at each subsurface reflection and azimuth angles. Our proposed imaging kernel, named as the directional-oriented wavefield imaging, compensates for illumination effects produced by possible surface obstructions during acquisition, sparse geometries employed in the field, and complex velocity models. An integral part of the directional-oriented wavefield imaging condition is a methodology for applying down-going/up-going wavefield decomposition to both source and receiver extrapolated wavefields. This type of wavefield decomposition eliminates low-frequency artefacts and scattering noise caused by the two-way wave equation and can facilitate the robust estimation for energy fluxes of wavefields required for the seismic illumination analysis. Then, based on the estimation of the respective wavefield propagation vectors and associated directions, we evaluate the illumination energy for each subsurface location as a function of image depth point and subsurface azimuth and reflection angles. Thus, the final directionaloriented wavefield imaging kernel is a cross-correlation of the decomposed source and receiver wavefields weighted by the illuminated energy estimated at each depth location. The application of the directional-oriented wavefield imaging condition can be employed during the generation of both depth-stacked images and azimuth–reflection angle-domain common image gathers. Numerical examples using synthetic and real data demonstrate that the new imaging condition can properly image complex wave paths and produce high-fidelity depth sections.

Summary A key advantage of acquiring multi-component data using ocean bottom sensors is the ability to separate the full wavefield into up-going and down-going wavefields. To achieve clean up/down separation we need to eliminate the noise recorded by various components of the sensors. Unlike the hydrophone component, the geophone components recorded at the ocean floor are usually contaminated by a various noise modes, including Scholte waves, backscattering noise, converted shear waves and other various types of noise. In particular, converted shear waves cause a number of challenges during data processing and degrade the effectiveness of up/down separation. In this paper, a de-noising methodology is developed to obtain cleaner vertical geophone components. It uses all recorded components to suppress shear wave energy and comprises three steps: 1) design and apply a masking filter to decompose the vertical geophone traces into less sensitive and mutually dependent parts with the horizontal geophone traces; 2) adaptive subtraction of the horizontal geophone traces from the vertical geophone traces; and 3) matching the signal envelope between hydrophone and vertical geophone traces. This de-noising process serves as a pre-conditioning step before the subsequent critical seafloor data processing steps including PZ summation, up/down deconvolution, and multiple removal.

Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l 1-norm-based objective functions. However, the l 1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l 2-norm and l 1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l 2-norm is sensitive to noise, whereas the l 1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l 1- and l 2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l 1- and l 2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution.

In this study, we suggest least-squares reverse-time migration (LSRTM) with wavefield decomposition method. Conventional imaging condition is comprised with the wavefields traveling upward and downward for source and receiver sides, respectively. Robust imaging condition can be obtained by separating those wavefields with respect to the vertical direction, however, it usually requires extremely heavy cost in computation in the 3D application due to Fourier transforms on both time and vertical axes. Wavefield decomposition by an analytic signal, i.e. complex signal, is an alternative method which is implemented by Hilbert transform. Since the analytic signal has only positive frequency component, wavefield decomposition can be more efficiently done by 1D Fourier transform only on the vertical axis. Taking the wavefields traveling opposite direction into account by decomposition for source and receiver sides, respectively, suppresses low wavenumber backscattered noise which is an intrinsic problem of two-way reverse-time migration (RTM) while LSRTM increases spatial resolution and frequency spectrum of the image. Thus, combining this wavefield decomposition method with existing LSRTM yields a robust depth imaging method.

Full waveform inversion (FWI) is based on updating process by a gradient direction which is dependent on the difference between the observed and modelled data. However, the gradient direction of the misfit function suffers from local minima due to errors in the data residual and starting velocity model, then FWI derives the solution which is no longer the optimum ones. In this paper, we present a new approach to decompose wavefields into angle domain using optical flow. Having direction of the wavefields by optical flow, it allows to compute the reflection angle between both forward and backward wavefields. This new FWI algorithm can use large reflection angles help retrieving long wavelength structures and attempt to reduce uncertainties of falling into local minima, and minimize cycle skipping and migration footprint in the gradient direction. Thus, the application of optical flow in FWI can play a role that makes FWI be more robust and stable by the angle-dependent gradient computation.

We develop an inversion strategy for seismic full waveform inversion (FWI) for 2D vertical transversely isotropic media (VTI). In our strategy, we use LamA© constants (I» and I¼) instead of C33 (= I» + 2I¼) and C44 (= I¼). For C11 and C13, we redefine them by LamA© constants and residuals between anisotropic parameters (C11 and C13) and LamA© constants. Accordingly, these residuals represent anisotropic characteristics. In FWI, we invert LamA© constants and residuals, and then we extract C11, C13, C33 and C44 from the inverted parameters. We validate our new strategy by comparing inversion results obtained by the new inversion strategy to those obtained by the isotropic inversion and the conventional VTI inversion for a modified version of the overthrust geological model. Results obtained by the isotropic inversion are reliable only for isotropic layers. On the other hand, anisotropic layers cannot be recovered well by only I» and I¼. In case of the conventional VTI inversion, C33 and C44 are well inverted. These results agree well with the isotropic inversion results. The C11 and C13 models inverted by the conventional VTI inversion are reasonable, but their resolutions are poorer than those of the C33 and C44. On the other hand, the C11 and C13 models inverted by the new inversion strategy are much improved compared to those of the conventional VTI inversion. From these results, we note that anisotropic properties in subsurface media cannot be recovered by the isotropic inversion, whereas the developed inversion strategy can provide reasonable anisotropic characteristics. In addition, elastic parameters by the new inversion strategy are more precise and stable than those of the conventional isotropic and VTI FWIs.

SUMMARY To interpret subsurface structures properly, elastic wave propagation must be considered. Because elastic media are described by more parameters than acoustic media, elastic waveform inversion is more likely to be affected by local minima than acoustic waveform inversion. In a conventional elastic waveform inversion, P- and S-wave velocities are properly recovered, whereas density is difficult to reconstruct. For this reason, most elastic full-waveform inversion studies assume that density is fixed. Although several algorithms have been developed that attempt to describe density properly, their results are still not satisfactory. In this study, we propose a two-stage elastic waveform inversion strategy to recover density properly. The Lame constants are first recovered while holding density fixed. While the Lame constants and density are not correct under this assumption, the velocities obtained using these incorrect Lame constants and constant density may be reliable. In the second stage, we simultaneously update density and Lame constants using the wave equations expressed through velocities and density. While density is updated following the conventional method, the Lame constants are updated using the gradient obtained by applying the chain rule. Among several parameter-selection strategies tested, only this strategy gives reliable solutions for both velocities and density. Our elastic full waveform inversion algorithm is based on the finite-element method and the backpropagation technique in the frequency domain. We demonstrate our inversion strategy for the modified Marmousi-2 model and the SEG/EAGE salt model. Numerical examples show that this new inversion strategy enhances density inversion results.

Department of Energy Systems Engineering, Seoul National University, Seoul 151-744, KoreaAbstact:r Recently as the interest in the development of domestic ore deposits has increased, we can easily find somestudies on exploration geophysics-based ore-deposit survey in literature. Based on the fact that mineralized zone aregenerally more conductive than surrounding media, electrical resistivity survey among several geophysical surveys hasbeen applied to investigate metallic ore deposits. Most of them are grounded on 2-D survey. However, 2-D inversion maylead to some misinterpretation for 3-D geological structures. In this study, we investigate the feasibility of the 3-Delectrical resistivity survey to 3-D vein-type ore deposits. We first simulate 2-D dipole-dipole survey data for survey linesnormal to the strike and 3-D pole-pole survey data, and then perform 3-D inversion. For 3-D ore-body structures, weassume a width-varying dyke, a wedge-shaped, and a fault model. The 3-D inversion results are compared to 2-Dinversion results. By comparing 3-D inversion results for 2-D dipole-dipole survey data to 3-D inversion results for 3-Dpole-pole survey data, we could note that the 2-D dipole-dipole survey data yield better inversion results than the 3-Dpole-pole data, which is due to the main characteristic of the pole-pole array. From these results, we are convinced that ifwe have certain information on the direction of the strike, it would be desirable to apply 2-D dipole-diple survey for thesurvey lines normal to the strike. However, in most cases, we do not have any information on the direction of the strike,because we already developed the ore deposit with the outcrops and the remaining ore deposits are buried under thesurface. In that case, performing 3-D pole-pole electrical resistivity survey would be a reasonable choice to obtain moreaccurate interpretation on ore body structure in spite of low resolution of pole-pole array. 3-D, dipole-dipole array, pole-pole array, electrical resistivity survey, inversion : ! "# $ ' %& * () +,- & / . 0 12 . 34 56 , / 7 89 :; > @ AB * C, E D, FG > : * ,- HI J M KL& , NO EP R Q 2 ST / U2 HI .X VW 34 R Q Y ' RZ, M 1' , Y [ 2\X 9 Y ]^ ; ` _ 1-$ a6 bc 3 ST d * e2 . fg 3 ST hd ,E 2 ST 2 ST j ;i k HI 56 U lm

Simultaneous-source technique has been mainly employed for the l2-norm-based full waveform inversion. Considering that real field data are noisy, however, it would be preferable to use robust objective function such as the l1-norm objective function. When we combine the simultaneous-source technique and the l1-norm objective function, there are several problems to be resolved. In case of the l2-norm-based full waveform inversion, the gradient direction of the simultaneous-source inversion has an identical form with that of the individual-source inversion if the crosstalk terms are excluded. In case of the l1-norm-based simultaneous-source inversion, however, the gradient direction is not coincident with that of the individual-source inversion. For this reason, the meaning and the crosstalk reduction of the l1-norm-based simultaneous-source inversion are questionable. In this study, we investigate the gradient direction of the l1-norm-based simultaneous-source inversion and verify the way how the crosstalk noise is suppressed through the statistical approach. Numerical example shows that the l1-norm-based simultaneous-source efficiently reduces the crosstalk and can give reasonable inversion results for noisy data.

Since seismic modelling is widely used in seismic inversion and migration, the accuracy of seismic modelling is important. As a practical full waveform inversion, acoustic waveform inversion is preferred because of computational burden. Most of the acoustic waveform inversion and migration are based on the acoustic wave equation for homogeneous media. However, because real earth media are not homogeneous, density variation of subsurface media needs to be considered in acoustic modelling, inversion, and migration. In this study, we compare numerical modelling results obtained by the finite-difference and finite-element modelling algorithms based on the conventional and heterogeneous wave equations for the Marmousi-2 model. As long as the modelling algorithm is based on the same (conventional or heterogeneous) wave equation, modelling results are compatible with each other. On the other hand, modelling results based on the heterogeneous wave equation are different from those based on the conventional wave equation. Considering that real earth media are heterogeneous, we suggest using acoustic wave modelling based on the heterogeneous wave equation in seismic inversion and migration.

Summary In this paper, we propose a new objective function that incorporates both simultaneous-source technique and robust norm in the frequency domain. The proposed objective function is defined to measure the residual of the super-shot consisting of encoded shot gathers. Although the objective function does not exactly simulate the ordinary l1norm objective function without source encoding, it has the same robustness as the least-absolute criteria. To confirm the robustness of our algorithm, we performed the full waveform inversion (FWI) using data with outliers and random noise. Based on the inversion results, we confirmed that our algorithm possesses the robust characteristics of the l1-norm objective function as well as the efficiency of the simultaneous source inversion.

Summary To make a reasonable interpretation of seismic data, anisotropic features should be considered. Although there are numerous studies on migration with anisotropic features taken into account, for anisotropic waveform inversion only a few studies are encountered in literature. Because many parameters are needed to describe anisotropic media, anisotropic waveform inversion has not been successful. In this study, we develop a 2D frequency-domain elastic full waveform inversion algorithm using the finite-element method for vertically transversely isotropic media (VTI). Our inversion algorithm is mainly based on the backpropagation technique. Source wavelet is also estimated in addition to elastic constants. We investigate the feasibility of our inversion algorithm for synthetic data of the anisotropic overthrust model. Our inversion results are better than previous inversion results obtained by the finitedifference method for some parts of the model, which may be due to boundary conditions. Nevertheless, further improvement should be made on anisotropic waveform inversion to obtain reliable information through anisotropic waveform inversion.

c constants in the VTI inversion than in the isotropic case, it is more prone to obtain local minimum solutions. To compensate for the weakness of the anisotropic inversion, we couple a few of elastic constants based on Thomsen’s relationships between elastic constants and anisotropy parameters. Our coupling method leads to inversion results compatible with true models except for C13. To enhance inversion results for C13, we conduct the waveform inversion at two steps. First we perform either the isotropic or the anisotropic waveform inversion by using linearly increasing models for initial guesses. Then the anisotropic waveform inversion is carried out once more by using the inversion results obtained at the first stage for initial models. By applying these techniques to a part of the 2D overthrust model, we could properly recover the subsurface elastic constants.