Full Waveform Inversion

Full Waveform Inversion (FWI) is a methodology that seeks to find a high-resolution, high-fidelity velocity model of the subsurface capable of matching individual synthetic seismic waveforms with an original raw field dataset. This is achieved iteratively by determining and minimizing a residual; the difference between modeled and recorded data.

The PGS refraction based FWI utilizes diving waves; wavefronts continuously refracted upwards through the earth due to the presence of a vertical velocity gradient. FWI is successful in resolving small scale velocity features; in particular, in shallow-water environments where reflection based methods are limited.

By making use of refractions and diving waves the restrictions posed by conventional reflection tomography are overcome, leading to highly accurate, high-resolution shallow velocity models. A benefit is that minimum pre-processing is required and free-surface effects can be left in the data.

The method begins from an initial starting model which is then iteratively improved using a sequence of linearized local inversions, to solve a fully non-linear problem. 3D FWI is most commonly, but not solely, used to recover high-resolution P-wave velocity models.

 

FWI workflow

The resulting FWI model is used in conjunction with conventional Pre-Stack Depth Migration (PSDM) to improve the imaging of the underlying reservoir using sub-critical reflection data. The spatial resolution and complexity of the FWI model may require a high-fidelity PSDM scheme for the migration such as Reverse Time Migration (RTM) which is based on the full two-way wave equation. Unlike conventional reflection tomography, FWI typically uses wide-angle refracted arrivals to build its model. 

A requirement of FWI is that the initial model allows matching of the observed travel times with an error less than half of the period. If not, cycle skipping artifacts will lead to convergence toward a local minimum not to the desired global minima, resulting in an erroneous model.

FWI modeling

Low frequencies in the field data are essential for robust and effective inversion without cycle skipping issues. GeoStreamer® dual-sensor acquisition provides these crucial low frequencies from the deep tow of the streamer. To ensure convergence of the model and avoid cycle skipping, FWI starts with the lowest frequencies in the data which contain coherent energy. The frequency content may subsequently be increased to add spatial resolution to the updates.

An accurate convergence of an FWI model phase is measured at each iterative stage using an integrated quality control procedure. Metrics demonstrating an improvement in the correlation of modeled and field data are used alongside data observations in both data and image space.

PGS offers both refraction and reflection based FWI. To avoid the aforementioned cycle skip phenomenon it is evident that FWI is ideally suited to broadband seismic data particularly rich in low frequency information. Technically the data should be rich in low wavenumber information provided by long offset acquisition.

The PGS reflection based FWI is designed for use with backscattered arrivals i.e. reflections. A benefit is that much deeper velocity model updates are possible for standard streamer lengths but the input data should have sea-surface effects removed. PGS' FWI is a time domain solution that utilizes an impedance image rather than a reflectivity image in order to extract spatial variations in velocity and density.

Data example3D View of SWIM image at 250 m depth with FWI velocity model overlaid.