Francesco Perrone

Wavefield tomography based on local image correlations

The estimation of a velocity model from seismic data is a crucial step for obtaining a high-quality image of the subsurface. Velocity estimation is usually formulated as an optimization problem where an objective function measures the mismatch between synthetic and recorded wavefields and its gradient is used to update the model. The objective function can be defined in the data-space (as in full-waveform inversion) or in the image space (as in migration velocity analysis). In general, the latter leads to smooth objective functions, which are monomodal in a wider basin about the global minimum compared to the objective functions defined in the data-space. Nonetheless, migration velocity analysis requires construction of common-image gathers at fixed spatial locations and subsampling of the image in order to assess the consistency between the trial velocity model and the observed data. We present an objective function that extracts the velocity error information directly in the image domain without analysing the information in common-image gathers. In order to include the full complexity of the wavefield in the velocity estimation algorithm, we consider a two-way (as opposed to one-way) wave operator, we do not linearize the imaging operator with respect to the model parameters (as in linearized wave-equation migration velocity analysis) and compute the gradient of the objective function using the adjoint-state method. We illustrate our methodology with a few synthetic examples and test it on a real 2D marine streamer data set.

Comparison of Shot Encoding Functions For Reverse-time Migration

Reverse-time migration (RTM) represents one of the most accurate, but also one of the costliest algorithms available for imaging in complex media. The RTM computational cost can be reduced by shot encoding, i.e. by imaging simultaneously a large number of shots. This approach reduces computational cost if the number of encoded seismic experiments is smaller than the number of shots. Different encoding strategies are possible, including linear and random encoding which represent end-members of a more general family of encodings. For a fixed maximum delay (i.e., computational cost), we can trade spatial bandwidth for cross-talk noise. Linear encoding is characterized by low bandwidth and high signal-to-noise ratio, while random encoding is characterized by high bandwidth and low signal-to-noise ratio. Mixed encodings allows us to calibrate the amount of resolution desired in the migrated image, given an acceptable level of noise in the image.

Image-warping waveform tomography

Imaging the change in physical parameters in the subsurface requires an estimate of the long wavelength components of the same parameters in order to reconstruct the kinematics of the waves propagating in the subsurface. One can reconstruct the model by matching the recorded data with modeled waveforms extrapolated in a trial model of the medium. Alternatively, assuming a trial model, one can obtain a set of images of the reflectors from a number of seismic experiments and match the locations of the imaged interfaces. Apparent displacements between migrated images contain information about the velocity model and can be used for velocity analysis. A number of methods are available to characterize the displacement between images; in this paper, we compare shot-domain differential semblance (image difference), penalized local correlations, and image-warping.We show that the image-warping vector field is a more reliable tool for estimating displacements between migrated images and leads to a more robust velocity analysis procedure. By using image-warping, we can redefine the differential semblance optimization problem with an objective function that is more robust against cycle-skipping than the direct image difference. We propose an approach that has straightforward implementation and reduced computational cost compared with the conventional adjoint-state method calculations. We also discuss the weakness of migration velocity analysis in the migrated-shot domain in the case of highly refractive media, when the Born modelling operator is far from being unitary and thus its adjoint (migration) operator poorly approximates the inverse.

Wavefield Tomography Based on Local Image Correlations

Seismic imaging includes the estimation of both the position of the structures that generate the data recorded at the surface and a model that describes the propagation in the subsurface. The waves recorded at the surface are extrapolated in the model by solving a wave equation, and they are crosscorrelated with a synthetic source wavefield simulated in the same model. Reflectors are located where the source and receiver wavefields match in time and space. If the velocity model is inaccurate, the reflectors are positioned at incorrect locations. We propose an objective function in the image space that does not require common-image gathers (CIGs). We consider pairs of images from adjacent experiments and reformulate the semblance principle in the physical space, instead of the extended space at selected CIGs. We use penalized local correlations of two images to estimate shifts in the image space.

Wave-equation Migration with Dithered Plane Waves

Wave-equation migration algorithms, such as downward continuation and reverse-time migration (RTM), represent accurate but costly tools for imaging complex media. The intrinsic computational cost of these techniques can be reduced by shot-encoding, i.e. by imaging simultaneously a large number of shots. The encoding strategy is effective if the number of encoded seismic experiments is smaller than he number of original shots. Nonetheless, because of the nonlinearity of the imaging condition, simultaneous imaging of several experiments introduces artifacts, usually referred to as crosstalk. Different encoding schemes have different drawbacks: linear shot-encoding limits the spatial bandwidth of the final image, but it is free of crosstalk, while random shot-encoding produces random-like artifacts but preserves the spatial resolution. It is possible to combine these two approaches and design a more robust encoding scheme; mixed shot-encoding supplies a well spatially resolved image, given an acceptable level of crosstalk noise. In RTM, where the computational cost depends linearly on the maximum delay in the data, fixed the computational cost, mixed shot-encoding achieves a better imaging result with respect to both linear and random shot-encoding.