## 1. Introduction

[2] Crustal-scale seismic surveying at sea is most of the time carried out in two dimensions with an array of ocean bottom seismometers (OBS). Instruments are deployed in lines along which shots are fired. The length of the OBS profiles is defined so as to have sufficiently large source-receiver offsets to record turning waves whose refraction depth cover the zone of interest (the Moho, for example).

[3] For standard crustal surveying with large OBS spacings, the data are conventionally exploited through traveltime tomography. The most basic approach only uses first-arrival refraction traveltimes to derive a large-scale velocity model [e.g., *Toomey et al.*, 1994; *Zelt and Barton*, 1998]. The geometry of the main discontinuities can be inferred by combining refracted first arrivals and wide-angle reflections in the tomography [e.g., *Zelt and Smith*, 1992; *Korenaga et al.*, 2000; *Hobro et al.*, 2003]. However, highly heterogeneous structures may prevent the correlation of reflected phases from one OBS gather to the next one, specially when the OBS spacing is large. Without such correlation, the strong geological assumption of a layered velocity model is necessary to tentatively identify and pick phases. Expertise and extrapolation are needed to provide a qualitative interpretation of these coarse seismic profiles.

[4] The number of available instruments that can be deployed during a seismic experiment has recently dramatically increased from typically less than 10 to several tens of OBSs. Designing a multifold crustal-scale OBS experiment with a receiver spacing of 1–2 km while keeping sufficiently long profiles for imaging the lower crust is now possible. However, the receiver spacing remains significantly larger than the air gun shot spacing (50–200 m) and the seismic coverage of the medium, albeit strongly improved, is still weaker than that currently achieved in multichannel seismics. This new type of multifold wide-aperture data sets is suitable for waveform processings such as prestack depth migration which is the method of choice for multichannel seismic reflection data. However, in the wide-angle geometry, the full wavefield must be taken into account, including refracted, precritical and postcritical reflected waves; this introduces significant differences. In the following, we will define by full waveform tomography (FWT) any quantitative processing that is able to fit waveforms recorded over a broad range of apertures. Considering the whole wavefield is expected to provide a significant improvement in the resolution of tomographic models.

[5] Full waveform inversion was introduced by *Tarantola* [1984] and *Lailly* [1984] in the processing of seismic reflection data. The approach relies on linearized inverse theory [e.g., *Tarantola*, 1987] based on adjoint operators. A misfit norm is defined between observed seismograms and some computed in an initial medium. The optimization iteratively updates the model by minimizing this misfit. Waves are recomputed in the updated model and the procedure is repeated until the misfit function reduction is no more significant. Such linearized optimization will perform successfully if the starting model is close enough to reality. For wide-aperture data, the long-wavelength model can be reconstructed through first-arrival traveltime tomography (FATT). This model should be accurate enough to proceed with linearized FWT [*Pratt*, 1999].

[6] In the optimization procedure, the kernel for modeling the full wave field in heterogeneous media is critical. Among different methods, finite difference (FD) techniques provide a good compromise between accuracy, computational cost, simplicity of implementation and the ability to describe heterogenous models.

[7] Successful applications of FWT to real data remained rare until recently because of the computational cost of the forward problem (multisource full wavefield modeling) and the sensitivity of the method to different sources of error (ground-receiver coupling, source calibration, noise, accuracy of the starting model). More fundamentally, the method was mainly applied to multichannel seismic reflection data, [e.g., *Crase et al.*, 1990, 1992]. In this context, building an initial model of sufficient accuracy has always been a bottleneck since the reflection acquisition geometry is not suited to reconstruct the long wavelengths of a structure.

[8] Two-dimensional FWT based on FD wave modeling was originally developed in the time-space domain [e.g., *Tarantola*, 1984; *Gauthier et al.*, 1986; *Crase et al.*, 1990, 1992; *Pica et al.*, 1990; *Shipp and Singh*, 2002]. The overall computational effort is huge because the FD forward modeling must be fully completed twice per shot: once for a source position corresponding to the shot (forward problem) and once for a fictitious source consisting of a simultaneous excitation of data residuals at receiver positions, as we shall see for the inverse problem. On the other hand, the time domain makes it easier to time window seismic arrivals [*Kolb et al.*, 1986].

[9] To circumvent the limitations of time domain methods, *Pratt and Worthington* [1990] and *Pratt et al.* [1998] developed two-dimensional (2-D) full waveform modeling and tomography in the frequency domain for which the FD modeling of waves is very well adapted to multisource problems like in modern seismic acquisitions [*Pratt and Worthington*, 1990; *Stekl and Pratt*, 1998]. Moreover, attenuation can be easily implemented in frequency domain modeling algorithms using complex velocities. The inverse problem is also solved in the frequency domain by successively inverting one or several discrete frequencies, thus allowing a compact volume of data to be managed [*Pratt et al.*, 1998]. The inversion classically proceeds from low to higher frequencies to inject increasing wave numbers in the tomographic model. This multiscale approach helps to mitigate the nonlinearity of the inverse problem [*Pratt et al.*, 1996]. Moreover, wide-aperture acquisition geometries lead to a strong redundancy in the wave number domain [*Pratt and Worthington*, 1990], as a result of the combined influence of the source frequency and the diffraction angles on the intrinsic resolution of FWT. This redundancy allows decimation of data sets by inverting a selected subset of frequencies (see *Sirgue and Pratt* [2004] for a criterion to define an optimal frequency interval). This is another key point which, in addition to the efficiency of frequency domain wave modeling, makes 2-D frequency domain FWT significantly less computationally intensive than its time domain counterpart.

[10] The dramatic increase in achievable spatial resolution when using waveform tomography in addition to traveltime tomography for crustal experiments was already presented by *Pratt et al.* [1996] for synthetic data. This paper is devoted to the first application of frequency domain FWT to a real crustal-scale OBS data set. The target zone is the highly heterogeneous crustal structure of the eastern Nankai subduction zone (Tokai area). Results of FATT and asymptotic prestack depth migration were already presented by *Dessa et al.* [2004a]. Some preliminary results of FWT applied to this data set were also presented by *Dessa et al.* [2004b]. A smaller-scale application of frequency domain FWT to wide-aperture, on-land seismic data collected in a complex thrust belt in the southern Apennines (Italy) was also performed [*Ravaut et al.*, 2004; *Operto et al.*, 2004].

[11] The second part of the paper reviews the main theoretical principles of frequency domain FWT. Emphasis is then put on the numerical strategies that were specifically developed for acoustic FWT applied to a large OBS data set. We also present a theoretical sensitivity analysis of FWT with respect to FATT. In the third part, the results of FWT on the Nankai multifold OBS data set are shown. The main geological features of the velocity models are described and discussed based on several illustrations (traveltime and waveform modeling) of the data fit. The actual resolution of the FWT images is compared with theoretical predictions. The different sources of error affecting the velocity model are also discussed.