Wavefield Inversion Research Articles

Sequence Stratigraphy of Subcontinental Reservoirs of the Upper Part of the Tanopcha Formation of the Minkhov Field (North of Western Siberia)

Abstract ––The purpose of this paper is to present the results of sequence stratigraphic modeling of subcontinental reservoirs of the Tanopcha Formation upper part (Lower Cretaceous) of the Minkhov field, located in the northern part of the Messov oil and gas region of the Gydan oil and gas region. The study is vital due to the need for additional exploration and commissioning of hydrocarbon reserves in the lower part of the Pokur suprahorizon in the north of Western Siberia. The modeling is based on sedimentological columns for four wells, in which the object of study was characterized by a core with sufficient completeness. The structure of seven sequences has been studied. Sequences PK 2-2, 2-3, 2-4, 2-5, 2-6, and PK 3-1, in accordance with the classical concept, are divided into three systems tracts: lowstand (LST), transgressive (TST), highstand (HST). The boundaries of the sequences are outlined along the erosive surfaces in the bottom of the alluvial complexes. LST tops – on contacts of alluvial facies with tidal, marsh, lake sediments, indicating flooding of the coastal plain at the beginning of transgressions. TST tops – on contacts of facies of the tidal plain with alluvial deposits, indicating the beginning of normal regressions. The main reservoirs of the object are large belts and covers of alluvium of amalgamating channels as part of the LST. Additional reservoirs are thin bodies of tidal genesis in the composition of TST, and alluvial genesis in the composition of HST. The bottom of the PK 3-2 sequence was outlined on the contacts of coastal-marine TST sandstones with tidal and marsh facies, indicating the event transgression of the coastline. One of the main reservoirs of the field, the TP1 formation, is connected to the TST of the PK 3-2 sequence. The boundaries of the selected sequences can be traced on seismic sections of acoustic impedance. Depending on the temporary thickness in the impedance field, the sequences are displayed as two-, three- and four-layer sequences of layers, which opens up the possibility of their further study by the method of wave field inversion.

A fast pseudo-3D model for inversion of full SH waves in layered half-spaces

SH and Love waves have certain advantages over P-SV and Rayleigh waves when inverting shear-wave velocity (VS) profiles. They can also supplement Rayleigh waves to provide better model constraints on characterizing anisotropic media. Since the true 3D forward solution of full SH waves requires intensive computation, we propose, in this paper, a simple 2D wavefield solution and further modify it as an efficient pseudo-3D solution. This is achieved by applying an empirical amplitude correction function for geometric attenuation. In the transformed domain, this newly proposed pseudo-3D solution yields a dispersion image (frequency-velocity spectrum, FVS) practically equivalent to that of the true 3D solution which is also developed by the authors. Furthermore, this pseudo-3D solution is significantly more accurate than the modal summation method. Thanks to its fast computation speed and accuracy, the pseudo-3D algorithm is demonstrated to be an excellent surrogate for full wavefield inversion based on FVS. The FVS of SH waves is shown to be much more sensitive to embedded thin weak layers than that of P-SV waves. The superiority of FVS inversion over fundamental mode inversion is further demonstrated by examining their corresponding error functions, showing that FVS provides a much stronger constraint on the possible VS models. Examples demonstrate that the FVS inversion based on the pseudo-3D model outperforms the modal summation approach in both accuracy and generalization. The proposed pseudo-3D solution is quite general. It takes into account the source-to-receiver geometry and deals with special layer profiles where Love-type wave does not exist.

Full wavefield inversion with multiples: Nonlinear Bayesian inverse multiple scattering theory beyond the Born approximation

Imaging earth’s structures is fundamental to the earth’s interior, yet how to reconstruct earth’s heterogeneities using full-waveform inversion of full wavefield data that includes primary reflections and multiples remains enigmatic. I develop a nonlinear Bayesian approach for full-waveform inversion method with multiple scattering. Instead of using single scattering Born approximation to formulate the sensitivity kernels, I develop multiple scattering sensitivity kernels using multiple scattering-based Green’s functions. It is based on the Lippmann-Schwinger integral and Marchenko methods, for which the Green’s functions are retrieved from reflection data by solving a Marchenko equation. To estimate the uncertainty of velocities, I apply a Bayesian framework to the inverse problem. Our results indicate that the method does not depend on the earth’s scattering potential and the full-waveform inversion method with multiple scattering is a good alternative approach to image the earth’s structures.

Multiphase wavefield inversion methodology for seismic analysis of soil-structure interaction systems

Currently available inversion methods for providing seismic excitation for soil–structure interaction (SSI) systems regard all ground motions as the body wave component and invert only the body wavefields. However, the ground motions are dominated by body waves and surface waves, and ignorance of the latter has been demonstrated to be conservative for structural responses. To provide more accurate wavefields for the seismic input of SSI systems located on the half-space of rock mediums, a multiphase wavefield inversion (MPWI) methodology considering both body waves and Rayleigh surface waves is proposed in this study. The methodology applies forward modeling and inversion theory of body waves and Snell's law for complex angles to determine the exact Rayleigh wave components and construct the Rayleigh wavefields. The residual body waves are used to invert the body wavefields, focusing on optimizing the determination of incident angles by a least-squares iteration approach. Rayleigh and body wavefields are finally combined to construct the total wavefields. The efficiency of the proposed methodology is verified and validated with analytical solutions and real downhole recordings, and the applicability is examined by response comparisons with the traditional method in the free field and an urban complex building. Simulation results demonstrate that due to the consideration of the Rayleigh waves, the MPWI methodology results in higher free-field stresses and accordingly induces more intense seismic excitation. Correspondingly, the structural responses present an amplification effect.

ОТДЕЛЬНЫЕ ВОПРОСЫ ДИНАМИЧЕСКОЙ ИНВЕРСИИ ВОЛНОВОГО ПОЛЯ

Currently, reservoir parameter prediction methods based on the amplitude wave field inversion play an important role in solving geological problems in the joint interpretation of seismic and well data. From a formal point of view, well data are used to obtain additional conditions for solving inverse problems of seismic. But the formal description of solution is conditional, there is rather an adjustment of results obtained independently from seismic and well data. The paper considers the following issues: stability of the simultaneous inversion parameter estimation; calculation features of background model and coordination of background and seismic solution components; compliance with restrictions on the maximum sourcereceiver distances by kinematic muting and the range of reflection angles during AVO analysis. The AVO effect is analyzed, it displays itself in a change of the reflection coefficient sign and, correspondently, phase inversion of reflected wave.

Detecting sub-basalt Mesozoic sediments and active tectonics in the Narmada-Tapti Rift Zone, central India

To obtain structural information below basalt cover using conventional seismic reflection has always been a challenge due to the high impedance of the basaltic layer. This study enumerates P-wave refraction tomography to image the shallow structure along three long offset profiles in the Deccan Volcanic Province, one of the world's largest flood basalt volcanic regions. The travel time inversion is performed to obtain a starting model for the wavefield inversion, and synthetic tests are used to estimate the resolution. Our results show an abrupt increase of crystalline basement depth from 1.5 to 3 km across the Narmada South Fault. The shallow basement depth coincides with a 70-km-wide sub-basalt (>1.5 km deep) seismic shadow zone between the Narmada and Tapti rivers, associated with the sub-basalt graben caused by a crustal extension that contains sediments or a combination of basalt and sediments. The basaltic layer appears to be highly heterogeneous in velocity and thickness, and the degree of heterogeneity increases laterally and vertically with depth within the layer. It is quite likely that these sub-basalt sediments could be the potential zone for hydrocarbon, similar to the exposed Vindhyan in the north and Gondwana sediments in the south of our study area. Another intriguing feature is the Barwani Sukta Fault, which controls the tectonics of the region by dividing the basement configuration. We also compare our tomographic model with those determined from previously obtained seismic, gravity, and surface mapping. The tomographic image clearly shows that numerous faults are reaching up to the basement and extending laterally. We suggest that these neo-tectonic faults may be capable of generating large-magnitude earthquakes, including the 21 May 1997 (mb 6.0) Jabalpur earthquake.

Reconstruction of shear wave speed in tissue-mimicking phantoms from aliased pulse-echo imaging of high-frequency wavefields

Quantitative elasticity estimation in medical and industrial applications may benefit from advancements in reconstruction of shear wave speed with enhanced resolution. Here, shear wave speed is reconstructed from pulse-echo ultrasound imaging of elastic waves induced by high-frequency (>400 Hz), time-harmonic mechanical excitation. Particle displacement in shear wavefields is mapped from measured interframe phase differences with compensation for timing of multiple scan lines, then processed by spatial Fourier analysis to estimate the predominant wave speed and analyzed by algebraic wavefield inversion to reconstruct wave speed maps. Reconstructions of shear wave speed from simulated wavefields illustrate the accuracy and spatial resolution available with both methods, as functions of signal-to-noise ratio and sizes of windows used for Fourier analysis or wavefield smoothing. The methods are applied to shear wavefields with frequencies up to six times the Nyquist rate, thus extending the frequency range measurable by a given imaging system. Wave speed measurements in tissue-mimicking phantoms are compared with supersonic shear imaging and mechanical tensile testing, demonstrating feasibility of the wavefield measurement and wave speed reconstruction methods employed.

Simultaneous joint migration inversion as a high‐resolution time‐lapse imaging method: Feasibility and robustness study

ABSTRACTThe conventional time‐lapse processing workflow is usually sensitive to the non‐repeatable uncertainties between different vintages caused by noise, acquisition designs and independent processing. Therefore, in order to reduce these non‐repeatable uncertainties, all the datasets are usually acquired from well‐sampled and well‐repeated acquisition surveys, and the independent processing is always carefully tailored to maximally reduce the non‐repeatable uncertainties during processing. Moreover, the conventional time‐lapse analysis method, based on a time‐shift map, is not always a good indicator of the actual velocity differences due to its local one‐dimensional subsurface assumption. In order to relax these rigid requirements and have a better velocity change indicator, a robust high‐resolution simultaneous joint migration inversion was proposed as an effective time‐lapse tool for reservoir monitoring. The method combines a simultaneous data‐processing strategy with the joint migration inversion method. Joint migration inversion is a full wavefield inversion method with a parameterization in terms of reflectivity and propagation velocity. The simultaneous strategy allows the baseline and monitor parameters to communicate and compensate with each other dynamically during inversion, thus, suppressing the non‐repeatable uncertainties during the time‐lapse processing. To investigate the feasibility of using high‐resolution simultaneous joint migration inversion in practice, some numerical experiments are conducted to test the dependence of high‐resolution simultaneous joint migration inversion on the quality of the time‐lapse datasets including the following aspects: random noise; sparse surveys; ocean bottom node versus streamer (different types of monitoring surveys); non‐repeated sources, including source positioning errors and non‐repeated source wavelets; spatial weighting operators in the L2‐norm penalty terms; and sensitivity to weak time‐lapse effects. All the experiments are carried on the basis of a realistic synthetic time‐lapse model based on the Grane field offshore Norway. These experiments show that high‐resolution simultaneous joint migration inversion is robust to random noise, survey sparsity, survey non‐repeatability, source positioning errors and source wavelet discrepancies. Furthermore, high‐resolution simultaneous joint migration inversion remains effective when the spatial weighting operators in the L2‐norm penalty terms are largely relaxed, and high‐resolution simultaneous joint migration inversion is capable of detecting weak time‐lapse changes (e.g. velocity changes down to 35 m/s).

A reflection-based efficient wavefield inversion

Full-waveform inversion (FWI) is popularly used to obtain a high-resolution subsurface velocity model. However, it requires either a good initial velocity model or low-frequency data to mitigate the cycle-skipping issue. Reflection-waveform inversion (RWI) uses a migration/demigration process to retrieve a background model that can be used as a good initial velocity in FWI. The drawback of conventional RWI is that it requires the use of least-squares migration, which is often computationally expensive, and it is still prone to cycle skipping at far offsets. To improve the computational efficiency and overcome cycle skipping in the original RWI, we have incorporated it into a recently introduced method called efficient wavefield inversion (EWI) by inverting for the Born-scattered wavefield instead of the wavefield itself. In this case, we use perturbation-related secondary sources in the modified source function. Unlike conventional RWI, the perturbations are calculated naturally as part of the calculation of the scattered wavefield in an efficient way. Because the sources in the reflection-based EWI (REWI) are located in the subsurface, we are able to update the background model along the reflection wavepath. In the background velocity inversion, we calculate the background perturbation by a deconvolution process at each frequency. After obtaining the REWI inverted velocity model, a sequential FWI or EWI is needed to obtain a high-resolution model. We determine the validity of our approach using synthetic data generated from a section of the Sigsbee2A model. To further demonstrate the effectiveness of our approach, we test it on an ocean-bottom cable data set from the North Sea. We find that our methodology leads to improved velocity models as evidenced by flatter angle gathers.

A sequential inversion with outer iterations for the velocity and the intrinsic attenuation using an efficient wavefield inversion

Full-waveform inversion (FWI) has become a popular method to retrieve high-resolution subsurface model parameters. It is a highly nonlinear optimization problem based on minimizing the misfit between the observed and predicted data. For intrinsically attenuating media, wave propagation experiences significant loss of energy. Thus, for better data fitting, it is sometimes crucial to consider attenuation in FWI. Viscoacoustic FWI aims at achieving a joint inversion of the velocity and attenuation models. However, multiparameter FWI imposes additional challenges including expanding the null space and facing parameter trade-off issues. Theoretically, an ideal way to mitigate the trade-off issue in multiparameter FWI is to apply the inverse Hessian operator to the parameter gradients. However, it is often not practical to calculate the full Hessian and its matrix inverse because this will be extremely expensive. To improve the computational efficiency and mitigate the trade-off issue, we have used an efficient wavefield inversion (EWI) method to invert for the velocity and the intrinsic attenuation. This approach is implemented in the frequency domain, and the velocity, in this case, is complex-valued in the viscoacoustic EWI. We evaluate a sequential update strategy for the velocity and the intrinsic attenuation, and we repeat the separate optimizations, which we refer to as outer iterations, until the convergence is achieved. Because viscoacoustic EWI is able to recover an accurate velocity model, the velocity update leakage to the [Formula: see text] model is largely reduced. We determine the effectiveness of this approach using synthetic data generated for the viscoacoustic Marmousi and Overthrust models. To further demonstrate the validity of our approach, we generate data in the time domain using a viscoelastic wave equation solver and obtain reasonable inversion results in the frequency domain using the viscoacoustic approximation.

Efficient Wavefield Inversion With Outer Iterations and Total Variation Constraint

Full-waveform inversion (FWI) is popularly used to retrieve a high-resolution velocity model that maximizes the data fitting directly. It is a highly nonlinear optimization problem, and thus, FWI can easily fall into a local minimum. Wavefield reconstruction inversion (WRI) allows us to relax the wave equation constraint to provide a larger search space. However, it requires a high computational cost to update the velocity in each selected frequency through many expensive iterations. By recasting a linear optimization problem in terms of a modified source function (which includes the original source and secondary sources) and relying on the background velocity model, we end up with cheap inner iterations for inverting the wavefield. We refer to this setup as an efficient wavefield inversion (EWI). However, like WRI, EWI cannot mitigate the cycle-skipping problem completely when the background velocity model is far from the true one and low-frequency components in the data are missing. In this case, we propose to use additional outer iterations to better recover the velocity model. In the salt body inversion, we utilize a total variation (TV) regularization to constrain the inverted velocity model at each outer iteration. We demonstrate these features on a modified Marmousi model and a central part of the BP salt model. The application on a 2-D real data set also demonstrates the effectiveness of the proposed method.

Multiple joint wavefield inversions: Theory and field data implementations

Accurate velocity models for the near surface and overburden are needed for seismic processing and reliable depth imaging. Seismic with multiphysics data, well logs, and geology information need to be quantitatively integrated to obtain high-resolution velocity models. We detail our development and application of the joint wavefield inversion software platform, which enables flexible algorithmic schemes for the integration of multiparameter data and constraints. Inversion is performed in cascade or simultaneously using a variety of input data to constrain the velocity field reconstruction at multiple scales. Coupling mechanisms based on structure similarity together with rock-physics relations are optimally combined to boost resolution and enhance accuracy of the inverted velocity models. Ill-posed inversion problems are then solved using extensive geologic and rock-physics regularization instead of relying on smoothness constraints alone. We detail workflows and algorithms to guide the application of multiparameter joint inversion for velocity model building whether the input data are seismic traveltimes, electromagnetics (time/frequency domains), gravity, and/or surface waves. Extensive applications of multiparameter joint inversion are presented for a variety of complex geologic scenarios in which various multiparameter coupling strategies are illustrated. Robust velocity modeling and enhanced seismic imaging in time and depth domains are obtained as a result, proving the importance of multiphysics integration for reliable earth model parameter estimation.

Source-independent efficient wavefield inversion

SUMMARYFull-waveform inversion (FWI) is an effective tool to retrieve a high-resolution subsurface velocity model. The source wavelet accuracy plays an important role in reaching that goal. So we often need to estimate the source function before or within the inversion process. Source estimation requires additional computational cost, and an inaccurate source estimation can hamper the convergence of FWI. We develop a source-independent waveform inversion utilizing a recently introduced wavefield reconstruction based method, which we refer to as efficient wavefield inversion (EWI). In EWI, we essentially reconstruct the wavefield by fitting it to the observed data as well as a wave equation based on iterative Born scattering. However, a wrong source wavelet will induce errors in the reconstructed wavefield, which may lead to a divergence of this optimization problem. We use a convolution-based source-independent misfit function to replace the conventional data fitting term in EWI to formulate a source-independent EWI (SIEWI) objective function. By convolving the observed data with a reference trace from the predicted data and convolving the predicted data with a reference trace from the observed data, the influence of the source wavelet on the optimization is mitigated. In SIEWI, this new formulation is able to mitigate the cycle-skipping issue and the source wavelet uncertainty simultaneously. We demonstrate those features on the Overthrust model and a modified Marmousi model. Application on a 2-D real data set also shows the effectiveness of the proposed method.

An efficient wavefield inversion for transversely isotropic media with a vertical axis of symmetry

Conventional full-waveform inversion (FWI) aims at retrieving a high-resolution velocity model directly from the wavefields measured at the sensor locations resulting in a highly nonlinear optimization problem. Due to the high nonlinearity of FWI (manifested in one form in the cycle-skipping problem), it is easy to fall into local minima. Considering that the earth is truly anisotropic, a multiparameter inversion imposes additional challenges in exacerbating the null-space problem and the parameter trade-off issue. We have formulated an optimization problem to reconstruct the wavefield in an efficient matter with background models by using an enhanced source function (which includes secondary sources) in combination with fitting the data. In this two-term optimization problem to fit the wavefield to the data and to the background wave equation, the inversion for the wavefield is linear. Because we keep the modeling operator stationary within each frequency, we only need one matrix inversion per frequency. The inversion for the anisotropic parameters is handled in a separate optimization using the wavefield and the enhanced source function. Because the velocity is the dominant parameter controlling the wave propagation, it is updated first. Thus, this reduces undesired updates for anisotropic parameters due to the velocity update leakage. We find the effectiveness of this approach in reducing parameter trade-off with a distinct Gaussian anomaly model. We find that in using the parameterization [Formula: see text], and [Formula: see text] to describe the transversely isotropic media with a vertical axis of symmetry model in the inversion, we end up with high resolution and minimal trade-off compared to conventional parameterizations for the anisotropic Marmousi model. Application on 2D real data also indicates the validity of our method.

Robust wavefield inversion via phase retrieval

SUMMARY Extended formulation of full waveform inversion (FWI), called wavefield reconstruction inversion (WRI), offers potential benefits of decreasing the non-linearity of the inverse problem by replacing the explicit inverse of the wave-equation operator of classical FWI (the oscillating Green functions) with a suitably defined data-driven regularized inverse. This regularization relaxes the wave-equation constraint to reconstruct wavefields that match the data, hence mitigating the risk of cycle skipping. The subsurface model parameters are then updated in a direction that reduces these constraint violations. However, in the case of a rough initial model, the phase errors in the reconstructed wavefields may trap the waveform inversion in a local minimum leading to inaccurate subsurface models. In this paper, in order to avoid matching such incorrect phase information during the early WRI iterations, we design a new cost function based upon phase retrieval, namely a process which seeks to reconstruct a signal from the amplitude of linear measurements. This new formulation, called wavefield inversion with phase retrieval (WIPR), further improves the robustness of the parameter estimation subproblem by a suitable phase correction. We implement the resulting WIPR problem with an alternating-direction approach, which combines the majorization-minimization (MM) algorithm to linearise the phase-retrieval term and a variable splitting technique based upon the alternating direction method of multipliers (ADMM). This new workflow equipped with Tikhonov-Total variation (TT) regularization, which is the combination of second-order Tikhonov and total variation regularizations and bound constraints, successfully reconstructs the 2004 BP salt model from a sparse fixed-spread acquisition using a 3 Hz starting frequency and a homogeneous initial velocity model.

Microseismic Event Estimation Based on an Efficient Wavefield Inversion

Full-waveform inversion (FWI) has shown its potentials in active seismic scenario in extracting a high-resolution velocity model of the subsurface. In the microseismic scenario, the source function is unknown, and FWI can be applied to optimize the source image and the velocity model, simultaneously. However, FWI is a highly nonlinear optimization problem, and it causes a bigger challenge when the source location and origin time are unknown. To mitigate these issues, we propose a two-stage scheme to invert for the source function and the velocity using an efficient wavefield inversion (EWI). We use outer-loop iterations to repeat the process until we achieve convergence. We specifically formulate an optimization problem to linearly reconstruct the wavefield that tries to fit both the data, as well as the wave equation corresponding to the background model. In the first stage, the reconstructed wavefield is used to calculate a source function using the background wave equation modeling operator without any inversion or update process. In the second stage, we use the computed source function to represent the true source to update the velocity model in the same way we use EWI in the active seismic case. Applications on data generated from a modified Marmousi model with a single microseismic event and multiple simultaneous events demonstrate the ability of the proposed method. An application to field dataset also demonstrates that the proposed method is effective in locating the microseismic event and inverting for a reasonably good velocity model, sequentially.

An efficient wavefield inversion: Using a modified source function in the wave equation

The wavefield is often reconstructed through solving a wave equation corresponding to an active source and using our best knowledge of the medium to reproduce the data that we seek to fit the observed data as part of a process we call full-waveform inversion (FWI). Alternatively, the wavefield can be inverted and used to invert for the velocity model, in an extended optimization problem, in which we can relax the requirement that the wavefield satisfies the wave equation. In this case, the wavefield calculation, as in FWI, requires a matrix inversion (which depends on the velocity) at practically every iteration. Thus, we formulate a bilinear optimization problem with respect to the wavefield and a modified source function, as independent variables. We specifically recast the wave equation so that velocity perturbations are included in this modified source function (which includes secondary or contrast sources); thus, it represents the velocity perturbations implicitly. The optimization includes a measure of the wavefield’s fit to the data at the sensor locations and the wavefield, as well as the modified source function, compliance with a wave equation corresponding to the background model. This problem is, however, complex with an extended model space that is ill-posed, so we use an alternating-direction method to reduce the inversion to two subproblems for inverting each of the wavefields and extended source. On the other hand, the velocity perturbations can be extracted in a separate step via direct division (deconvolution). Because we avoid using gradient methods in extracting the velocity perturbations, we are less prone to crosstalk artifacts when we use simultaneous sources. We evaluate these features on a simple two-anomalies model and the modified Marmousi model.

A robust source-independent misfit function for time domain waveform inversion based on normalized convolved wavefield

It is usually necessary to provide a source wavelet before the waveform inversion, and accuracy of the wavelet determines whether the synthetic data matches the observed record. In addition to directly estimating a wavelet, another method is to construct a source-independent objective function. The source difference disappears in the convolved wavefield waveform inversion through the convolution of one data set and the reference trace selected from the other data set, because two different wavelets are already present in the two convolution terms. However, the convolution wavefield inversion is also seriously affected by the incorrect amplitude information of the seismic waves. The attenuation of seismic waves in underground media is quite common in practice. In contrast, the method based on the global normalized wavefield is less sensitive to the amplitude loss because it compares the phase information of the two data sets. The approach we present in this paper is a combination of two methods, that is to construct the normalized wavefield on the basis of the convolution wavefield. In this way, we alleviate the problem of the traditional convolution wavefield inversion caused by amplitude mismatch, and further extend the applicability of this method. The new normalized convolution wavefield inversion combines the advantages of the two methods, which are independence on the source wavelet and being insensitive to amplitude loss, we give a multi-scale and multi-stage inversion strategy for the new objective function, which can improve the implementation of the multi-scale strategy and effectively deal with missing low frequencies.

Full-waveform inversion for imaging and geologic interpretation: A deepwater Gulf of Mexico case study

Full-waveform inversion (FWI) is commonly used in model-building workflows to improve the resolution of the shallow velocity model and thus has a potentially positive impact on the imaging of deeper targets. This type of inversion commonly makes use of first arrivals from the longest offsets. However, signal from smaller offsets and later times can extend the depth range of the FWI-derived velocity model. Waveform inversion methods that use reflections have been shown to provide greater details and accuracy when deriving velocity models for deepwater exploration and production. The derived velocity sometimes provides an improved migrated image useful for interpretation in complex geology and enhances geologic features such as subsalt sediments, faults, and channels. We have used combination of FWI and a wavefield inversion approach known as reconstructed wavefield inversion (RWI) that makes use of diving waves and reflections to derive a velocity model for a deepwater survey off the coast of Veracruz in the Gulf of Mexico. The velocity model we derived from this approach produces an improved image of the target reservoir, and furthermore contains enough geologic details for direct interpretation. We enhanced the resolution of the velocity model further by performing a poststack amplitude inversion with the FWI + RWI derived velocity used as the input low-frequency model. The resulting high-resolution velocity provides an excellent product for detecting shallow gas anomalies, delineating a gas reservoir in an anticline structure as well as a system of deep, sand-filled channels. The inverted velocity also indicates a better correlation with sonic velocity measured from two blind wells than the initial tomography velocity, indicating the benefits of FWI approaches for quantitative reservoir characterization in deepwater environments.

A tool for designing digital filters for the Hankel and Fourier transforms in potential, diffusive, and wavefield modeling

The open-source code fdesign makes it possible to design digital linear filters for the Hankel and Fourier transforms used in potential, diffusive, and wavefield modeling. Digital filters can be derived for any electromagnetic (EM) method, such as methods in the diffusive limits (direct current, controlled-source EM [CSEM]) as well as methods using higher frequency content (ground-penetrating radar [GPR], acoustic and elastic wavefields). The direct matrix inversion method is used for the derivation of the filter values, and a brute-force minimization search is carried out over the defined spacing and shifting values of the filter basis. Included or user-provided theoretical transform pairs are used for the inversion. Alternatively, one can provide layered subsurface models that will be computed with a precise quadrature method using the EM modeler empymod to generate numerical transform pairs. The comparison of the presented 201 pt filter with previously presented filters indicates that it performs better for some standard CSEM cases. The derivation of a longer 2001 pt filter for a GPR example with a 250 MHz center frequency proves that the filter method works not only for diffusive EM fields but also for wave phenomena. The presented algorithm provides a tool to create problem specific digital filters. Such purpose-built filters can be made shorter and can speed up consecutive potential, diffusive, and wavefield inversions.