We demonstrate that near-surface heterogeneities can be imaged by natural migration of backscattered surface waves in common shot gathers. No velocity model is required because the data are migrated onto surface points with the virtual Green's functions computed from the shot gathers. Migrating shot gathers recorded by 2D and 3D land surveys validates the effectiveness of detecting nearsurface heterogeneities by natural migration. The implication is that more accurate hazard maps can be created by migrating surface waves in land surveys.

Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the background model using a single scattered wavefield from an inverted perturbation. However, current RWI methods are mostly based on isotropic media assumption. We extend the idea of the combining inversion for the background model and perturbations to address transversely isotropic with a vertical axis of symmetry (VTI) media taking into consideration of the optimal parameter sensitivity information. As a result, we apply Born modeling corresponding to perturbations in only for the variable e to derive the relative reflected waveform inversion formulation. To reduce the number of parameters, we assume the background part of η = ε and work with a single variable to describe the anisotropic part of the wave propagation. Thus, the optimization variables are the horizontal velocity v, η = ε and the e perturbation. Application to the anisotropic version of Marmousi model with a single frequency of 2.5 Hz shows that this method can converge to the accurate result starting from a linearly increasing isotropic initial velocity. Application to a real dataset demonstrates the versatility of the approach.

Multi parameter full waveform inversion (FWI) usually suffers from the inherent tradeoffin the multi parameter nature of the model space. In orthorhombic anisotropy, such tradeoffis magnified by the large number of parameters involved in representing the elastic or even the acoustic approximation of such a medium. However, using a new parameterization with distinctive scattering features, we can condition FWI to invert for the parameters the data are sensitive to at different stages, scales, and locations in the model. Specifically, with a combination made up of a velocity and particular dimensionless ratios of the elastic coefficients, the scattering potential of the anisotropic parameters have stationary scattering radiation patterns as a function of the type of anisotropy. With our new parametrization, the data is mainly sensitive to the scattering potential of 4 parameters: the horizontal velocity in the x direction, x, which provides scattering mainly near zero offset in the x vertical plane, εd, which is the ratio of the horizontal velocity squared in the x and x direction, and δ3 describing the anellipticity in the horizontal plane. Since, with this parametrization, the radiation pattern for the horizontal velocity and ε is azimuth independent, we can perform an initial VTI inversion for these two parameters, and then use the other two parameters to fit the azimuth variation in the data. This can be done at the reservoir level or any region of the model. Including the transmission from reflections, the migration velocity analysis (MVA) component, into the picture, the multi azimuth surface seismic data are mainly sensitive to the long wavelength components of uh, δ3, and εd through the diving waves, and η1, ηd, and δ3, in the transmission to or from reflectors (especially, in the presence of large offsets). They are also sensitive to the short wavelength component of uh and ε.

Addressing anisotropy in full wavenumber inversion (FWI) is crucial to obtaining credible models, and it is extremely challenging considering the multi parameter nature of the inversion. A successful FWI in anisotropic media takes into account the sensitivity of the data (or the wave) to the long and short wavelength components of the anisotropic parameters. Considering the low sensitivity of FWI to the anellipticity parameter ? when parametrizing the acoustic transversely isotropic model with the horizontal velocity, η and ε, we develop a combined FWI and reflection waveform inversion (RWI) to invert for the anisotropic parameters that influence surface seismic data. This practical waveform inversion (PWI) separates the parameters to their resolvable scales, with information accessed from the data fitting (FWI) and the image focusing (RWI) objectives. With this parametrization, the RWI role is to obtain a smooth ηmodel, as well as velocity, while FWI focusses on the scattering potential of the horizontal velocity. The parameter η is used to produce the Born scattered wavefield for the RWI part and eventually fit the amplitude for the imperfect physics in the FWI part.

For the purpose of extracting higher resolution information from a 3D field data set, we apply a 3D elastic orthorhombic (ORT) anisotropic full waveform inversion (FWI) to hopefully better represent the physics of the Earth. We utilize what we consider as the optimal parameterization for surface acquired seismic data over a potentially orthorhombic media. This parameterization admits the possibility of incorporating a hierarchical implementation moving from higher anisotropy symmetry to lower ones. From the analysis of the radiation pattern of this new parameterization, we focus the inversion of the 3D data on the parameters that may have imprint on the data with minimal tradeoff, and as a result we invert for the horizontal P-wave velocity model, an ε1 model, its orthorhombic deviation, and the shear wave velocity. The inverted higher resolution models provide reasonable insights of the medium.

The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially performed using the wave-equation traveltime inversion (WT) method. The WT tomograms are then used as starting background models for VTI full waveform inversion. Preliminary numerical tests on synthetic data demonstrate the feasibility of this method for multi-parameter inversion.

Full waveform inversion (FWI) is an iterative method of data-fitting, aiming at high resolution recovery of the unknown model parameters. However, it is a cumbersome process, requiring a long computational time and large memory space/disc storage. One of the reasons for this computational limitation is the gradient calculation step. Based on the adjoint state method, it involves the temporal cross-correlation of the forward propagated source wavefield with the backward propagated residuals, in which we usually need to store the source wavefield, or include an extra extrapolation step to propagate the source wavefield from its storage at the boundary. We propose, alternatively, an amplitude excitation gradient calculation based on the excitation imaging condition concept that represents the source wavefield history by a single, specifically the most energetic arrival. An excitation based Born modeling allows us to derive the adjoint operation. In this case, the source wavelet is injected by a cross-correlation step applied to the data residual directly. Representing the source wavefield through the excitation amplitude and time, we reduce the large requirements for both storage and the computational time. We demonstrate the application of this approach on a 2-layer model with an anomaly and the Marmousi II model.

The lack of low frequency components in seismic data usually leads full waveform inversion into the local minima of its objective function. An exponential damping of the data, on the other hand, generates artificial low frequencies, which can be used to admit long wavelength updates for waveform inversion. Another feature of exponential damping is that the energy of each trace also exponentially decreases with source-receiver offset, where the leastsquare misfit function does not work well. Thus, we propose a deconvolution-based objective function for waveform inversion with an exponential damping. Since the deconvolution filter includes a division process, it can properly address the unbalanced energy levels of the individual traces of the damped wavefield. Numerical examples demonstrate that our proposed FWI based on the deconvolution filter can generate a convergent long wavelength structure from the artificial low frequency components coming from an exponential damping.

Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of microseismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the velocity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.

We present an acoustic eikonal equation governing the complex-valued travel time of P-waves in attenuating, transversely isotropic media with a vertical symmetry axis (VTI). This equation is based on the assumption that the Pwave complex-valued travel time is independent of the Swave velocity parameter v in Thomsen's notation and the attenuation coefficient A in the Thomsen-type notation for attenuating VTI media. We combine perturbation theory and Shanks transform to develop practical approximations to the attenuating acoustic eikonal equation, capable of admitting analytical description of the attenuation in homogeneous media. For a horizontal, attenuating VTI layer, we also derive non-hyperbolic approximations for the real and imaginary parts of the complex-valued reflection travel time.