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Summary When calculating horizontal and vertical gradients using filtration in the wave-number domain the condition that the input data should be defined on a horizontal plane is generally not satisfied on continents, namely in the areas with uneven topography. If we ignore this we can be confronted with incorrect outputs of our transformations. On the other hand, the differences among the heights of the measuring points can be utilized for direct detecting of the gradient-equivalent quantities which we call linear tendencies that can be contained in the Bouguer anomalies. To achieve this we should consider the gravity anomaly as a 3D function. As a by-product, except of the linear tendencies, the proposed straightforward method enables us to calculate also the local and regional anomalies which are associated to the linear tendencies intrinsic to the Bouguer anomalies in case that the topography is not flat.
SUMMARY To perform linearised inversion on seismic exploration scale datasets we are continually looking for methods to accelerate computation and reduce data handling overhead. One option to accelerate time reversal imaging is to use random domain boundaries for the source wavefield computation, alleviating much of the required IO in favour of some additional computation. The advantage of such a scheme is particularly noticeable when using GPUs as IO from disk is compounded. Additionally, data handling problems can be addressed by phase encoding data (weighting, shifting, summing) and then inverting for a common model between realisations. This reduces the quantity of data being imaged and modelled with respect to the original data set. Both random boundary and phase encoding methods rely on wavefield incoherency during correlation and stacking to build a clean image. Here we investigate if these can be effectively used together, or if these techniques combined create wavefields that are too incoherent, mutually slowing convergence as a function of cost when compared to linearised inversion without phase encoding. We show that this can be case when doing a single super shot realisation per iteration, but by using multiple realisations and shot subsets we can improve convergence and create cleaner reflectivity images.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (0.69)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (0.47)
SUMMARY We propose a new method to perform wave-equation migration velocity analysis by maximizing the flatness of the angle-domain common image gathers. Instead of maximizing the image-stack-power objective function directly with respect to the slowness, we link the objective function to the slowness indirectly through an intermediate moveout parameter. This approach is immune to the cycle-skipping problem, and it produces high-quality gradients. In addition, the proposed method does not require explicit picking of the moveout parameters. Our numerical examples demonstrate the great potential of this method: in the first example where there is a Gaussian-shaped anomaly slowness error, our method produces well-behaved gradient; from our test on the Marmousi models, the proposed method converges to a high-quality model that uniformly flattens the angle-domain common image gathers.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (1.00)
SUMMARY We present a seismic waveform inversion using a weighting function. With the assumption that the source wavelet can be sufficiently estimated, we define the objective function as the L2-norm of the difference between the Greenโs functions. We show the spectral analysis of the scaled gradient and use numerical examples to show that weighting can improve the inversion result.
Meantime a new Conversional formulation of the gradient based on the formula of objective functional with respect to Lamรฉ cross-correlation of the derivatives of forward and constants and density is also proposed. Using dimensional backward particle displacement wavefield is derived from analysis (Baumstein et al., 2009), the gradient of the the second-order wave equations. During the process of objective functional computed by the new adjoint wave back-propagation of the data residuals, the adjoint wave equations and the corresponding formulation of gradient is equations are just the same as the forward ones. Without tested to be perfectly right, and it is no need to preprocess preprocessing the data residuals before back-propagation, the data residuals any more. Moreover, we need not convert one cannot obtain a properly scaled gradient when applying particle velocity to particle displacement, and the new the first-order velocity-stress differential equations. In this formulation of gradient reduces the calculation of spatial paper, based on the first-order elastic system in time derivatives of the adjoint wavefield, which improves the domain, we propose a new form of adjoint wave equations, computational efficiency to a certain extent.
The objective of the present work is to evolve a We present a new interpretation technique for potential unified approach of quantitative interpretation of potential field i.e. gravity magnetic and self potential based on the fields (viz., gravity, magnetic; and SP) satisfying Laplaceโs inversion of total gradient (TG) derived from horizontal equation based on inversion of total gradient over complex and vertical derivatives of the anomaly. TG is calculated by geometries. Taking inspiration from the behavior of ants, the horizontal and vertical derivatives and is approximated Ants Colony Optimization (ACO) technique is attempted to by a bell shaped function, the inversion of which give the invert bell shaped TG in terms of horizontal location and position, depth and geometry of the source. The inversion depth and decay rate of the causative source for interfering process has been carried out by Ant Colony Optimization and complex geometries. We have compared the ACO (ACO), a technique inspired by the behavior of ant results with ELW and EULER techniques through three colonies. Using this approach we have disposed off the field examples, one each from magnetic, gravity, and SP singularity in Euler technique in case of a faulted thick slab adapted from published literature.
- Geophysics > Magnetic Surveying (1.00)
- Geophysics > Gravity Surveying (1.00)
- Materials > Metals & Mining (0.72)
- Energy > Oil & Gas > Upstream (0.70)
Summary Numerical implementation of the gradient of the cost function in a gradient-based full waveform inversion (FWI) is a migration operator used in wave equation migration. In FWI, minimizing different data residual norms results in different weighting strategies of data residuals at receiver locations prior to back propagation into the medium. In this paper, we propose different scaling methods to the receiver wavefield and compare their performances. Using time domain reverse time migration (RTM), we show that this type of scaling is able to significantly suppress outliers compared to conventional algorithms. Our tests also show that scaling by its absolute norm produces better results than other approaches.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.50)
SUMMARY The term of "Waveform inversion" (WFI) refers to a collection of techniques that use the information from seismic data to derive high-fidelity earth models for seismic imaging. The attractiveness of WFI lies mainly in its lack of approximations, at least in a theoretical sense, in contrast to other model determination techniques such as semblance or tomography. However, a whole raft of approximations must be made to make the technique viable with today's computing technology and restrictions of seismic acquisition. These are collectively referred to as "waveform inversion strategies" and in this paper we mainly discuss regularization and preconditioning strategies. WFI is a highly nonlinear, ill-posed problem. As such regularization techniques from optimization theory are beneficial for its solution. Regularization involves introducing additional constraints on the problem usually by restricting smoothness or sharpness of model parameters. These restrictions are driven by a priori geophysical information. In this paper, we apply total variation regularization (TV), a popular method which involves l1-norm of the model derivatives. Real data examples show that edge locations of velocity anomalies tend to be preserved using TV regularization. Compared to inverting the Helmholtz operator, time domain implementation is straightforward and relatively fast. Therefore we present the methodology, strategies, and 3D data examples for time domain WFI with TV regularization. We pursue a vertical transverse isotropic (VTI) acoustic formulation which accounts for the effects of anisotropy. Our WFI is a joint inversion for model parameter and source delay time. Model can be parametrized by P-wave velocity and/or anisotropy parameters, e and d. Various preconditioning strategies are also discussed in order to increase the convergence rate for this iterative scheme and reduce the risk of converging to local minima. This paper presents the time domain acoustic VTI WFI implementation. It also discusses practical strategies for regularization and preconditioning and their influences on the models that are obtained from WFI. These approaches will be illustrated on 3D marine data from the Green Canyon area of the Gulf of Mexico.
- North America > United States (0.36)
- North America > Mexico (0.25)
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.95)
SUMMARY In this paper I introduce two different model-space parametrizations for early-arrival waveform inversion of velocity and anisotropic parameter. More specifically, I jointly invert for vertical velocity and e parameter, while keeping the d parameter fixed. A model space parametrized by the squares of vertical and horizontal velocity results in vertical velocity and e updates with opposite signs. On the other hand, a model space parametrized by the logarithm of the vertical velocity squared and epsilon has more reasonable updates. However, ambiguity does exist in the inversion results between vertical velocity and e. I demonstrate these using a synthetic example.
Summary We propose to use wave-equation tomography (WET) method to build long-wavelength velocity structure for full waveform inversion (FWI). In WET, full wavefield modeling is performed and cross-correlation time delay between the arrivals from synthetic and real waveforms is used as objective function. Adjoint method is used to calculate the gradient in each iteration efficiently. Since WET and FWI share similar inversion structure, we use a hybrid misfit function to combine the two methods as an integrated workflow that is able to estimate high-resolution structure from poor starting model. To stabilize WET and make it converge to global minimum, we precondition the time delay measures with maximum cross-correlation coefficients and perform adaptive scale smoothing to the gradients. By exploring the band-limited feature of seismic wavefield, WET can provide better resolution than ray-based travel time tomography, which is under high frequency approximation. To illustrate the advantage of wave-equation tomography, we show in a 2D synthetic test that WET provides subsurface information that is critical for successful FWI. We also test 2D Marmousi model and satisfactory inversion results are achieved without much manual manipulating.