Velocity model building from seismic reflection data by full‐waveform inversion

Full‐waveform inversion is re‐emerging as a powerful data‐fitting procedure for quantitative seismic imaging of the subsurface from wide‐azimuth seismic data. This method is suitable to build high‐resolution velocity models provided that the targeted area is sampled by both diving waves and reflected waves. However, the conventional formulation of full‐waveform inversion prevents the reconstruction of the small wavenumber components of the velocity model when the subsurface is sampled by reflected waves only. This typically occurs as the depth becomes significant with respect to the length of the receiver array. This study first aims to highlight the limits of the conventional form of full‐waveform inversion when applied to seismic reflection data, through a simple canonical example of seismic imaging and to propose a new inversion workflow that overcomes these limitations. The governing idea is to decompose the subsurface model as a background part, which we seek to update and a singular part that corresponds to some prior knowledge of the reflectivity. Forcing this scale uncoupling in the full‐waveform inversion formalism brings out the transmitted wavepaths that connect the sources and receivers to the reflectors in the sensitivity kernel of the full‐waveform inversion, which is otherwise dominated by the migration impulse responses formed by the correlation of the downgoing direct wavefields coming from the shot and receiver positions. This transmission regime makes full‐waveform inversion amenable to the update of the long‐to‐intermediate wavelengths of the background model from the wide scattering‐angle information. However, we show that this prior knowledge of the reflectivity does not prevent the use of a suitable misfit measurement based on cross‐correlation, to avoid cycle‐skipping issues as well as a suitable inversion domain as the pseudo‐depth domain that allows us to preserve the invariant property of the zero‐offset time. This latter feature is useful to avoid updating the reflectivity information at each non‐linear iteration of the full‐waveform inversion, hence considerably reducing the computational cost of the entire workflow. Prior information of the reflectivity in the full‐waveform inversion formalism, a robust misfit function that prevents cycle‐skipping issues and a suitable inversion domain that preserves the seismic invariant are the three key ingredients that should ensure well‐posedness and computational efficiency of full‐waveform inversion algorithms for seismic reflection data.     

Correlation‐based reflection waveform inversion by one‐way wave equations

Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.     

Elastic full waveform inversion of multi‐component OBC seismic data

Elastic full waveform inversion of seismic reflection data represents a data‐driven form of analysis leading to quantification of sub‐surface parameters in depth. In previous studies attention has been given to P‐wave data recorded in the marine environment, using either acoustic or elastic inversion schemes. In this paper we exploit both P‐waves and mode‐converted S‐waves in the marine environment in the inversion for both P‐ and S‐wave velocities by using wide‐angle, multi‐component, ocean‐bottom cable seismic data. An elastic waveform inversion scheme operating in the time domain was used, allowing accurate modelling of the full wavefield, including the elastic amplitude variation with offset response of reflected arrivals and mode‐converted events. A series of one‐ and two‐dimensional synthetic examples are presented, demonstrating the ability to invert for and thereby to quantify both P‐ and S‐wave velocities for different velocity models. In particular, for more realistic low velocity models, including a typically soft seabed, an effective strategy for inversion is proposed to exploit both P‐ and mode‐converted PS‐waves. Whilst P‐wave events are exploited for inversion for P‐wave velocity, examples show the contribution of both P‐ and PS‐waves to the successful recovery of S‐wave velocity.     

Full waveform inversion using oriented time‐domain imaging method for vertical transverse isotropic media

Full waveform inversion for reflection events is limited by its linearised update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model and, thus, use a gradient given by the oriented time‐domain imaging method. Specifically, we apply the oriented time‐domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to two‐dimensional or three‐dimensional velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearised representations of the reflection response. To eliminate the crosstalk artifacts between different parameters, we utilise what we consider being an optimal parametrisation for this step. To do so, we extend the prestack time‐domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high‐wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.     

Full waveform inversion of SH‐ and Love‐wave data in near‐surface prospecting

We develop a two‐dimensional full waveform inversion approach for the simultaneous determination of S‐wave velocity and density models from SH ‐ and Love‐wave data. We illustrate the advantages of the SH/Love full waveform inversion with a simple synthetic example and demonstrate the method's applicability to a near‐surface dataset, recorded in the village ?achtice in Northwestern Slovakia. Goal of the survey was to map remains of historical building foundations in a highly heterogeneous subsurface. The seismic survey comprises two parallel SH‐profiles with maximum offsets of 24 m and covers a frequency range from 5 Hz to 80 Hz with high signal‐to‐noise ratio well suited for full waveform inversion. Using the Wiechert–Herglotz method, we determined a one‐dimensional gradient velocity model as a starting model for full waveform inversion. The two‐dimensional waveform inversion approach uses the global correlation norm as objective function in combination with a sequential inversion of low‐pass filtered field data. This mitigates the non‐linearity of the multi‐parameter inverse problem. Test computations show that the influence of visco‐elastic effects on the waveform inversion result is rather small. Further tests using a mono‐parameter shear modulus inversion reveal that the inversion of the density model has no significant impact on the final data fit. The final full waveform inversion S‐wave velocity and density models show a prominent low‐velocity weathering layer. Below this layer, the subsurface is highly heterogeneous. Minimum anomaly sizes correspond to approximately half of the dominant Love‐wavelength. The results demonstrate the ability of two‐dimensional SH waveform inversion to image shallow small‐scale soil structure. However, they do not show any evidence of foundation walls.     

Quantitative estimation of water storage and residence time in the epikarst with time‐lapse refraction seismic

The hydrodynamic characterization of the epikarst, the shallow part of the unsaturated zone in karstic systems, has always been challenging for geophysical methods. This work investigates the feasibility of coupling time‐lapse refraction seismic data with petrophysical and hydrologic models for the quantitative determination of water storage and residence time at shallow depth in carbonate rocks. The Biot–Gassmann fluid substitution model describing the seismic velocity variations with water saturation at low frequencies needs to be modified for this lithology. I propose to include a saturation‐dependent rock‐frame weakening to take into account water–rock interactions. A Bayesian inversion workflow is presented to estimate the water content from seismic velocities measured at variable saturations. The procedure is tested first with already published laboratory measurements on core samples, and the results show that it is possible to estimate the water content and its uncertainty. The validated procedure is then applied to a time‐lapse seismic study to locate and quantify seasonal water storage at shallow depth along a seismic profile. The residence time of the water in the shallow layers is estimated by coupling the time‐lapse seismic measurements with rainfall chronicles, simple flow equations, and the petrophysical model. The daily water input computed from the chronicles is used to constraint the inversion of seismic velocities for the daily saturation state and the hydrodynamic parameters of the flow model. The workflow is applied to a real monitoring case, and the results show that the average residence time of the water in the epikarst is generally around three months, but it is only 18 days near an infiltration pathway. During the winter season, the residence times are three times shorter in response to the increase in the effective rainfall.     

汶川地震断裂带东北端浅部结构的人工地震探测

结合汶川地震断裂带动态监测,利用快速响应探测系统,开展了断层带浅部结构人工地震探测.针对地震断裂带动态监测条件下的复杂波场和低信噪比的情况,在f-k波场分离的基础上,分别利用了折射波共中心点成像、面波速度反演、反射波叠加成像方法,进行了浅层断层和构造成像处理,并对处理结果进行了综合解释,给出了断裂带浅部断层分布和速度特征.为汶川地震龙门山断裂带东北端动态监测提供了基础结构信息,所发展的断裂带快速响应探测技术对于地震应急动态监测具有重要意义.     

Analysis of time‐lapse travel‐time and amplitude changes to assess reservoir compartmentalization

Fluid depletion within a compacting reservoir can lead to significant stress and strain changes and potentially severe geomechanical issues, both inside and outside the reservoir. We extend previous research of time‐lapse seismic interpretation by incorporating synthetic near‐offset and full‐offset common‐midpoint reflection data using anisotropic ray tracing to investigate uncertainties in time‐lapse seismic observations. The time‐lapse seismic simulations use dynamic elasticity models built from hydro‐geomechanical simulation output and a stress‐dependent rock physics model. The reservoir model is a conceptual two‐fault graben reservoir, where we allow the fault fluid‐flow transmissibility to vary from high to low to simulate non‐compartmentalized and compartmentalized reservoirs, respectively. The results indicate time‐lapse seismic amplitude changes and travel‐time shifts can be used to qualitatively identify reservoir compartmentalization. Due to the high repeatability and good quality of the time‐lapse synthetic dataset, the estimated travel‐time shifts and amplitude changes for near‐offset data match the true model subsurface changes with minimal errors. A 1D velocity–strain relation was used to estimate the vertical velocity change for the reservoir bottom interface by applying zero‐offset time shifts from both the near‐offset and full‐offset measurements. For near‐offset data, the estimated P‐wave velocity changes were within 10% of the true value. However, for full‐offset data, time‐lapse attributes are quantitatively reliable using standard time‐lapse seismic methods when an updated velocity model is used rather than the baseline model.     

Anisotropic elastic full‐waveform inversion of walkaway vertical seismic profiling data from the Arabian Gulf

Borehole seismic addresses the need for high‐resolution images and elastic parameters of the subsurface. Full‐waveform inversion of vertical seismic profile data is a promising technology with the potential to recover quantitative information about elastic properties of the medium. Full‐waveform inversion has the capability to process the entire wavefield and to address the wave propagation effects contained in the borehole data—multi‐component measurements; anisotropic effects; compressional and shear waves; and transmitted, converted, and reflected waves and multiples. Full‐waveform inversion, therefore, has the potential to provide a more accurate result compared with conventional processing methods. We present a feasibility study with results of the application of high‐frequency (up to 60 Hz) anisotropic elastic full‐waveform inversion to a walkaway vertical seismic profile data from the Arabian Gulf. Full‐waveform inversion has reproduced the majority of the wave events and recovered a geologically plausible layered model with physically meaningful values of the medium.     

Reflection multi‐scale envelope inversion

Sufficient low‐frequency information is essential for full‐waveform inversion to get the global optimal solution. Multi‐scale envelope inversion was proposed using a new Fréchet derivative to invert the long‐wavelength component of the model by directly using the low‐frequency components contained in an envelope of seismic data. Although the new method can recover the main structure of the model, the inversion quality of the model bottom still needs to be improved. Reflection waveform inversion reduces the dependence of inversion on low‐frequency and long‐offset data by using travel‐time information in reflected waves. However, when the underground medium contains strong contrast or the initial model is far away from the true model, it is hard to get reliable reference reflectors for the generation of reflected waves. Here, we propose a combination inversion algorithm, i.e., reflection multi‐scale envelope inversion, to overcome the limitations of multi‐scale envelope inversion and reflection waveform inversion. First, wavefield decomposition was introduced into the multi‐scale envelope inversion to improve the inversion quality of the long‐wavelength components of the model. Then, after the initial model had been established to be accurate enough, migration and de‐migration were introduced to achieve multi‐scale reflection waveform inversion. The numerical results of the salt‐layer model and the SEG/EAGE salt model verified the validity of the proposed approach and its potential.     

The use of low frequencies in a full‐waveform inversion and impedance inversion land seismic case study

Velocity model building and impedance inversion generally suffer from a lack of intermediate wavenumber content in seismic data. Intermediate wavenumbers may be retrieved directly from seismic data sets if enough low frequencies are recorded. Over the past years, improvements in acquisition have allowed us to obtain seismic data with a broader frequency spectrum. To illustrate the benefits of broadband acquisition, notably the recording of low frequencies, we discuss the inversion of land seismic data acquired in Inner Mongolia, China. This data set contains frequencies from 1.5–80 Hz. We show that the velocity estimate based on an acoustic full‐waveform inversion approach is superior to one obtained from reflection traveltime inversion because after full‐waveform inversion the background velocity conforms to geology. We also illustrate the added value of low frequencies in an impedance estimate.     

多主频波场的时间阻尼全波形反演

低频成分缺失和地下速度强烈变化会导致严重的周期跳现象,是地震数据全波形反演的难题.通过对地震数据加时间阻尼和时间积分降主频处理,提出了一种可有效去除周期跳现象的多主频波场时间阻尼全波形反演方法.由浅到深的速度不准确会造成波形走时失配和走时失配的累积.浅部速度的准确反演可有效地减小深部波形走时失配与周期跳现象.对地震数据施加时间阻尼得到时间阻尼数据,利用不同阻尼值的时间阻尼地震数据实现由浅到深的全波形反演.低主频波场的周期跳现象相对高主频波场的要弱.对地震波场进行不同阶的时间积分以得到不同主频的波场,把低主频波场的全波形反演结果作为高主频波场全波形反演的初始模型.应用缺失4 Hz以下频谱成分的二维盐丘模型合成数据验证所提出的全波形反演方法的正确性和有效性,数值试验结果显示多主频波场的时间阻尼全波形反演方法对缺失低频成分地震数据和地下速度强烈变化具有很好的适应性.     

The near-surface information gap for time and depth imaging

The shallowest few hundred metres of the earth cannot be adequately imaged by conventional seismic when tuned for deeper targets. Adding independent measurements (such as uphole or shallow refraction surveys) reduces this information gap, but in some arid areas (such as Saudi Arabia) the near‐surface complexities are not well resolved, even in this way. The joint tomographic inversion of different wave types can contribute to reducing these ambiguities further, by complementing the different penetration ranges and propagation directions of reflected, refracted and diving waves. Here, we demonstrate the weakness of diving waves when used alone, and the value of complementing them by available reflected and refracted arrivals.     

2D inversion of refraction traveltime curves using homogeneous functions

A method using simple inversion of refraction traveltimes for the determination of 2D velocity and interface structure is presented. The method is applicable to data obtained from engineering seismics and from deep seismic investigations. The advantage of simple inversion, as opposed to ray‐tracing methods, is that it enables direct calculation of a 2D velocity distribution, including information about interfaces, thus eliminating the calculation of seismic rays at every step of the iteration process. The inversion method is based on a local approximation of the real velocity cross‐section by homogeneous functions of two coordinates. Homogeneous functions are very useful for the approximation of real geological media. Homogeneous velocity functions can include straight‐line seismic boundaries. The contour lines of homogeneous functions are arbitrary curves that are similar to one another. The traveltime curves recorded at the surface of media with homogeneous velocity functions are also similar to one another. This is true for both refraction and reflection traveltime curves. For two reverse traveltime curves, non‐linear transformations exist which continuously convert the direct traveltime curve to the reverse one and vice versa. This fact has enabled us to develop an automatic procedure for the identification of waves refracted at different seismic boundaries using reverse traveltime curves. Homogeneous functions of two coordinates can describe media where the velocity depends significantly on two coordinates. However, the rays and the traveltime fields corresponding to these velocity functions can be transformed to those for media where the velocity depends on one coordinate. The 2D inverse kinematic problem, i.e. the computation of an approximate homogeneous velocity function using the data from two reverse traveltime curves of the refracted first arrival, is thus resolved. Since the solution algorithm is stable, in the case of complex shooting geometry, the common‐velocity cross‐section can be constructed by applying a local approximation. This method enables the reconstruction of practically any arbitrary velocity function of two coordinates. The computer program, known as godograf , which is based on this theory, is a universal program for the interpretation of any system of refraction traveltime curves for any refraction method for both shallow and deep seismic studies of crust and mantle. Examples using synthetic data demonstrate the accuracy of the algorithm and its sensitivity to realistic noise levels. Inversions of the refraction traveltimes from the Salair ore deposit, the Moscow region and the Kamchatka volcano seismic profiles illustrate the methodology, practical considerations and capability of seismic imaging with the inversion method.     

Full waveform inversion in the time lapse mode applied to CO2 storage at Sleipner

Carbon capture and storage is a viable greenhouse gas mitigation technology and the Sleipner CO₂ sequestration site in the North Sea is an excellent example. Storage of CO₂ at the Sleipner site requires monitoring over large areas, which can successfully be accomplished with time lapse seismic imaging. One of the main goals of CO₂ storage monitoring is to be able to estimate the volume of the stored CO₂ in the reservoir. This requires a parametrization of the subsurface as exact as possible. Here we use elastic 2D time‐domain full waveform inversion in a time lapse manner to obtain a P‐wave velocity constrain directly in the depth domain for a base line survey in 1994 and two post‐injection surveys in 1999 and 2006. By relating velocity change to free CO₂ saturation, using a rock physics model, we find that at the considered location the aquifer may have been fully saturated in some places in 1999 and 2006.     

Misfit functionals in Laplace‐Fourier domain waveform inversion,with application to wide‐angle ocean bottom seismograph data

In seismic waveform inversion, non‐linearity and non‐uniqueness require appropriate strategies. We formulate four types of L2 normed misfit functionals for Laplace‐Fourier domain waveform inversion: i) subtraction of complex‐valued observed data from complex‐valued predicted data (the ‘conventional phase‐amplitude’ residual), ii) a ‘conventional phase‐only’ residual in which amplitude variations are normalized, iii) a ‘logarithmic phase‐amplitude’ residual and finally iv) a ‘logarithmic phase‐only’ residual in which the only imaginary part of the logarithmic residual is used. We evaluate these misfit functionals by using a wide‐angle field Ocean Bottom Seismograph (OBS) data set with a maximum offset of 55 km. The conventional phase‐amplitude approach is restricted in illumination and delineates only shallow velocity structures. In contrast, the other three misfit functionals retrieve detailed velocity structures with clear lithological boundaries down to the deeper part of the model. We also test the performance of additional phase‐amplitude inversions starting from the logarithmic phase‐only inversion result. The resulting velocity updates are prominent only in the high‐wavenumber components, sharpening the lithological boundaries. We argue that the discrepancies in the behaviours of the misfit functionals are primarily caused by the sensitivities of the model gradient to strong amplitude variations in the data. As the observed data amplitudes are dominated by the near‐offset traces, the conventional phase‐amplitude inversion primarily updates the shallow structures as a result. In contrast, the other three misfit functionals eliminate the strong dependence on amplitude variation naturally and enhance the depth of illumination. We further suggest that the phase‐only inversions are sufficient to obtain robust and reliable velocity structures and the amplitude information is of secondary importance in constraining subsurface velocity models.     

基于交叉梯度约束的地震初至纵波与瑞雷面波联合反演

本文提出了一种初至纵波(P波)与瑞雷面波的交叉梯度联合反演策略.通过对初至P波进行全波形反演可以获得近地表P波速度结构;通过对仅含瑞雷面波信息的地震数据转换到频率-波数域进行加窗振幅波形反演(Windowed-Amplitude Waveform Inversion,w-AWI)可获得近地表横波(S波)速度结构.在二者反演的目标函数中均加入P波速度和S波速度的交叉梯度作为正则化约束项,使得在反演过程中P波速度和S波速度相互制约,相互约束,从而实现对地震初至P波与瑞雷面波的联合反演.数值模拟结果表明交叉梯度联合反演可以提高S波速度反演分辨率,而P波速度反演结果并没有得到提高.实际资料的反演结果表明,交叉梯度联合反演能够获得更加可信的近地表速度结构.     

Exploring some issues in acoustic full waveform inversion

The least‐squares error measures the difference between observed and modelled seismic data. Because it suffers from local minima, a good initial velocity model is required to avoid convergence to the wrong model when using a gradient‐based minimization method. If a data set mainly contains reflection events, it is difficult to update the velocity model with the least‐squares error because the minimization method easily ends up in the nearest local minimum without ever reaching the global minimum. Several authors observed that the model could be updated by diving waves, requiring a wide‐angle or large‐offset data set. This full waveform tomography is limited to a maximum depth. Here, we use a linear velocity model to obtain estimates for the maximum depth. In addition, we investigate how frequencies should be selected if the seismic data are modelled in the frequency domain. In the presence of noise, the condition to avoid local minima requires more frequencies than needed for sufficient spectral coverage. We also considered acoustic inversion of a synthetic marine data set created by an elastic time‐domain finite‐difference code. This allowed us to validate the estimates made for the linear velocity model. The acoustic approximation leads to a number of problems when using long‐offset data. Nevertheless, we obtained reasonable results. The use of a variable density in the acoustic inversion helped to match the data at the expense of accuracy in the inversion result for the density.     

Image‐domain wavefield tomography with extended common‐image‐point gathers

Waveform inversion is a velocity‐model‐building technique based on full waveforms as the input and seismic wavefields as the information carrier. Conventional waveform inversion is implemented in the data domain. However, similar techniques referred to as image‐domain wavefield tomography can be formulated in the image domain and use a seismic image as the input and seismic wavefields as the information carrier. The objective function for the image‐domain approach is designed to optimize the coherency of reflections in extended common‐image gathers. The function applies a penalty operator to the gathers, thus highlighting image inaccuracies arising from the velocity model error. Minimizing the objective function optimizes the model and improves the image quality. The gradient of the objective function is computed using the adjoint state method in a way similar to that in the analogous data‐domain implementation. We propose an image‐domain velocity‐model building method using extended common‐image‐point space‐ and time‐lag gathers constructed sparsely at reflections in the image. The gathers are effective in reconstructing the velocity model in complex geologic environments and can be used as an economical replacement for conventional common‐image gathers in wave‐equation tomography. A test on the Marmousi model illustrates successful updating of the velocity model using common‐image‐point gathers and resulting improved image quality.     

Offset‐variable density improves acoustic full‐waveform inversion: a shallow marine case study

We have previously applied three‐dimensional acoustic, anisotropic, full‐waveform inversion to a shallow‐water, wide‐angle, ocean‐bottom‐cable dataset to obtain a high‐resolution velocity model. This velocity model produced an improved match between synthetic and field data, better flattening of common‐image gathers, a closer fit to well logs, and an improvement in the pre‐stack depth‐migrated image. Nevertheless, close examination reveals that there is a systematic mismatch between the observed and predicted data from this full‐waveform inversion model, with the predicted data being consistently delayed in time. We demonstrate that this mismatch cannot be produced by systematic errors in the starting model, by errors in the assumed source wavelet, by incomplete convergence, or by the use of an insufficiently fine finite‐difference mesh. Throughout these tests, the mismatch is remarkably robust with the significant exception that we do not see an analogous mismatch when inverting synthetic acoustic data. We suspect therefore that the mismatch arises because of inadequacies in the physics that are used during inversion. For ocean‐bottom‐cable data in shallow water at low frequency, apparent observed arrival times, in wide‐angle turning‐ray data, result from the characteristics of the detailed interference pattern between primary refractions, surface ghosts, and a large suite of wide‐angle multiple reflected and/or multiple refracted arrivals. In these circumstances, the dynamics of individual arrivals can strongly influence the apparent arrival times of the resultant compound waveforms. In acoustic full‐waveform inversion, we do not normally know the density of the seabed, and we do not properly account for finite shear velocity, finite attenuation, and fine‐scale anisotropy variation, all of which can influence the relative amplitudes of different interfering arrivals, which in their turn influence the apparent kinematics. Here, we demonstrate that the introduction of a non‐physical offset‐variable water density during acoustic full‐waveform inversion of this ocean‐bottom‐cable field dataset can compensate efficiently and heuristically for these inaccuracies. This approach improves the travel‐time match and consequently increases both the accuracy and resolution of the final velocity model that is obtained using purely acoustic full‐waveform inversion at minimal additional cost.