S U M M A R YOngoing works on full waveform inversion (FWI) are yielding an increasing number of objective functions as alternative to the traditional L2-waveform. These studies aim at designing more robust functions and inversion strategies to reduce the intrinsic dependence of the FWI results on (1) the initial model and (2) the lowest frequency present in field data. In this work, we perform a comparative study of five objective functions in time domain under a common 2-D-acoustic FWI scheme using the Marmousi model as benchmark. In particular, we compare results obtained with L2-based functions that consider the minimization of different wave attributes; the waveform-based, non-integration-method; instantaneous envelope; a modified version of the wrapped instantaneous phase and an improved version of the crosscorrelation travel time (CCTT) method; and hybrid strategies combining some of them. We evaluate the robustness of these functionals as a function of their performance with and without low frequencies in the data and the presence of random white Gaussian noise. Our results reveal promising strategies to invert noisy data with limited low-frequency content (≥4 Hz), which is the single strategy using the instantaneous phase objective function followed by the hybrid strategies using the instantaneous phase or CCTT as initial models, in particular the combinations [I. Phase + Waveform], [CCTT + Waveform] and [CCTT + I. Phase].

Abstract. We present the implementation of Thomsen's weak anisotropy approximation for vertical transverse isotropy (VTI) media within TOMO3D, our code for 2-D and 3-D joint refraction and reflection travel-time tomographic inversion. In addition to the inversion of seismic P-wave velocity and reflector depth, the code can now retrieve models of Thomsen's parameters (δ and ε). Here, we test this new implementation following four different strategies on a canonical synthetic experiment in ideal conditions with the purpose of estimating the maximum capabilities and potential weak points of our modeling tool and strategies. First, we study the sensitivity of travel times to the presence of a 25 % anomaly in each of the parameters. Next, we invert for two combinations of parameters (v, δ, ε and v, δ, v⊥), following two inversion strategies, simultaneous and sequential, and compare the results to study their performance and discuss their advantages and disadvantages. Simultaneous inversion is the preferred strategy and the parameter combination (v, δ, ε) produces the best overall results. The only advantage of the parameter combination (v, δ, v⊥) is a better recovery of the magnitude of v. In each case, we derive the fourth parameter from the equation relating ε, v⊥ and v. Recovery of v, ε and v⊥ is satisfactory, whereas δ proves to be impossible to recover even in the most favorable scenario. However, this does not hinder the recovery of the other parameters, and we show that it is still possible to obtain a rough approximation of the δ distribution in the medium by sampling a reasonable range of homogeneous initial δ models and averaging the final δ models that are satisfactory in terms of data fit.

Complex signal analysis allows separation of instantaneous envelope and phase of seismic waveforms. Seismic attributes have long routinely been used in geological interpretation and signal processing of seismic data as robust tools to highlight relevant characteristics of seismic waveforms. In the context of adjoint waveform inversion (AWI), it is crucial choosing an efficient parameter to describe the seismic data. The most straightforward option is using whole waveforms but the mixing of amplitude and phase parameters increases the nonlinearity inherent to the methodology. Several studies support the good functioning of the instantaneous phase (IP), a more linear parameter to measure the misfit between synthetic and recorded data. The IP is calculated using the inverse of the tangent function, where its principal value can be defined either wrapped in between different limits or also unwrapped. The wrapped phase presents phase jumps that reflect as noise in the inversion results. The conditioning of these discontinuities solves the problem partially and the continuous unwrapped IP is not a good descriptor of the waveform. For this reason, it is worth to explore beyond the traditional description of the IP parameter. Two alternative functions have been studied: 1) a revision of the triangular IP and 2) the first implementation of the normalized signal. The main objective of this paper is therefore, to review the fundamentals of the IP attribute in order to design robust IP-based objective functions which allow mitigating the inherent nonlinearity in the AWI method.

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Abstract. We present a high-resolution P-wave velocity model of the sedimentary cover and the uppermost basement until ~ 3 km depth obtained by full-waveform inversion of multichannel seismic data acquired with a 6 km-long streamer in the Alboran Sea (SE Iberia). The inherent non-linearity of the method, especially for short-offset, band-limited seismic data as this one, is circumvented by applying a data processing/modeling sequence consisting of three steps: (1) data re-datuming by back-propagation of the recorded seismograms to the seafloor; (2) joint refraction and reflection travel-time tomography combining the original and the re-datumed shot gathers; and (3) FWI of the original shot gathers using the model obtained by travel-time tomography as initial reference. The final velocity model shows a number of geological structures that cannot be identified in the travel-time tomography models or easily interpreted from seismic reflection images alone. A sharp strong velocity contrast accurately defines the geometry of the top of the basement. Several low-velocity zones that may correspond to the abrupt velocity change across steeply dipping normal faults are observed at the flanks of the basin. A 200–300 m thick, high-velocity layer embedded within lower velocity sediment may correspond to evaporites deposited during the Messinian crisis. The results confirm that the combination of data re-datuming and joint refraction and reflection travel-time inversion provides reference models that are accurate enough to apply full-waveform inversion to relatively short offset streamer data in deep water settings starting at field-data standard low frequency content of 6 Hz.