Adaptive Waveform Inversion

Salt is the biproduct of evaporation in basins and forms horizontal layers like sedimentary rocks. However, salt is geologically unique because of its (1) low density, (2) low permeability and (3) low viscosity. When compressed, salt flows upwards over geologically rapid timescales of kilometres per thousand years.

Upwards salt flow fractures and faults the overlying rock, and salt is impermeable to fluid migration. Therefore, salt flow creates structural traps for fluids, influencing the shape of oil and gas reservoirs. As such the identification of salt boundaries and geometries is of vital importance in natural resource exploration.

The goal of a seismic survey is to acquire a dataset of sub-surface seismic velocities, and the goal of a seismic waveform inversion is to gradually make changes and improvements to an initial model until a subsurface model is reached which accurately reproduces the observed dataset when a synthetic seismic wave is passed through the model.

An accurate sub-surface model in a salt-affected region like the Gulf of Mexico will have well resolved salt boundaries, show variations within the salt, and show variations below the salt. However, in conventional seismic exploration methods, the identification of salt boundaries is limited in three main ways.

Firstly, historical data acquisition in offshore salt affected regions (e.g., the Gulf of Mexico) uses short offsets between seismic sources and receivers, and receivers which cannot capture long wavelength seismic signals below frequencies of 3 Hz.  This is a problem in simple implementations of Full Waveform Inversion, where a phenomenon known as ‘cycle skipping’ occurs. If a velocity model prediction differs from the true model by more than half a seismic wave cycle, successive algorithmic predictions of improved models will tend be incorrect.

Secondly, the conventional workflow for constructing a model requires subjective human choices about whether a prediction of the salt geometry is correct. This human intervention introduces time delays which means it can take years for industrial geophysicists to finalise a sub-surface model.

Thirdly, these subjective choices are frequently demonstrated to be incorrect as (i) more data becomes available and (ii) algorithms which model more precise seismic waveform physics are applied.

To circumvent these three principal issues, geophysicists at S-Cube have developed an automated workflow utilising algorithms which circumvent these limitations.

The inversion’s initial model uses a local 1-Dimensional relationship (Figure 1, Top) describing the physics of sedimentary rock compaction with increasing depth. Firstly, an instance of adaptive waveform inversion (AWI) is applied to drive this basic model towards a model of salt geometries, where wave speed through impermeable salt is faster than adjacent sedimentary rock (Figure 1, Bottom). This method has good immunity to cycle skipping, as the inversion attempts to minimise differences between the observed model and predictions in time rather than in space.

Good detail like deep incisions in the red, fast salt portion are resolved by AWI. Yellow higher velocities show separation between salt and slow porous sediment or the approximate ‘top-salt’ and the transition from red to green shows the approximate ‘bottom-salt’.

Once a representative starting model from AWI is produced, the inversion proceeds by updating successive model predictions with combinations of Reflection Waveform Inversion (RWI) and Constrained Waveform Inversion algorithm (CWI). RWI is a recent algorithm development which models the physics of reflected seismic waves and their multiples. Seismic waves reflect when they cross from one rock type to another, much like how light reflects off a mirror, and multiples describe seismic waveforms reflecting off multiple surfaces, like light in a room of mirrors. RWI in a salt affected region is like using lights in a dark room to predict where the mirrors are, where the mirrors in the subsurface are boundaries between different sub-surface materials like the top and bottom salt.

CWI is another recent advanced algorithm which makes use of known geological constraints to drive accurate model predictions. For example, between the top salt and bottom salt, the velocities should be salt like, and below the bottom salt, the velocities should be sediment like, and the regional 1D compaction trend should still be true.

The combined use of AWI, RWI and CWI in S-Cube’s new automated workflow does not require any human intervention and yet by incorporating known waveform physics and geology, produces an accurate model of the sub-surface (Figure 2, Top). This model has more detail than a model produced in a conventional workflow (Figure 2, Bottom).

S-Cube’s automated model has the same broad scale geometry, but with fine scale details within the salt and below the salt, and thus yields much more information about the resource reservoirs.

Additionally, S-Cube’s model takes only weeks to produce from raw field data, and requires no modification to convert 40 years of seismic survey data into up to date models of salt and sub-salt geology.

Useful Link:

@theLeadingEdge,Warner_etal2023 (https://library.seg.org/doi/full/10.1190/tle42030196.1 )

Keywords: 

Full Waveform Inversion, Adaptative Waveform Inversion, Cycle Skipping, Gulf of Mexico, Salt, Top-salt, Bottom-salt, AWI, CWI