Compressive Seismic Survey Design: Three Approaches

A candid discussion of the different design options for Compressive Seismic Acquisition:

The central motivation behind Compressive Seismic is that by making your survey non-uniform, you can acquire fewer traces and get the same end result using an appropriate solver. There is a ton of math to support this theory, and much of the groundwork was done in medical imaging and optics, where Compressive Sensing is the norm.

When this technology was adapted for the seismic industry, there were three main philosophies regarding how it should be applied.

Pure Random

With this approach, shot and receiver points are randomized arbitrarily with constraints or based on a regular sub-grid with constraints. The advantage of this method is that it is computationally inexpensive. The problem is that there is no guarantee that the solver will produce an optimal reconstruction, especially around obstacles. The efficacy of randomness relies on the law of large numbers, so in regions of a limited size with significant or frequent obstacles (and therefore with a very low trace density), it may be difficult for a random design to reconstruct adequately. For the same reason, random designs may not be able to safely reduce the number of acquired traces to the same degree as an optimized design.

Optimally Adjusted

The optimally adjusted design takes a conventional design, applies random shifts with constraints, and further optimizes the design using some objective function or solver. The advantage here is that because the design is tuned to the solver, you are nearly guaranteed a better result than pure random. However, converging to an ideal solution can be computationally expensive since the shifts are random with potentially infinite possible variations (depending on the applied constraints). There are also practical repercussions in the field due to the irregularity of shot and receiver points.

An example survey design using the optimally adjusted approach. Grey squares/cyan circles are the original shot/receiver points. Red squares/blue circles are the CS shot/receiver points. The CS design has small random shifts along the line direction.

Regularly Indexed

This design starts with a regularly-indexed base grid and removes points, so the CS design is a subset of the original design with shot/receiver points still on the base grid, just with redundant points removed. This approach is easier to implement in the field than a random or optimally adjusted/moved design, as acquisition crews do not need to keep track of changing distance intervals between nodes. The crew only needs to know which points will be skipped/removed; otherwise, acquire them as usual. As with the optimally adjusted/moved design, the regular indexed design is optimized using a solver. However, since a finite number of grid nodes and regular grids are easier to handle computationally (e.g., FFT vs. DFT), this approach can reliably converge to an optimal design without great computational expense.

An example survey design using the regularly indexed approach. Note that the original grid (grey, cyan) is half as dense as the CS grid, which uses the same number of shot/receiver points but can be reconstructed to a 50% smaller bin size (or 4x fold).

Conclusion

Whichever design you choose, the benefits of CS are undeniable, whether it be an MRI, seismic survey, or picture on your mobile phone. The option of reducing acquisition costs without compromising quality or the alternative of keeping costs constant but enhancing imaging through dense irregular spacing are both highly compelling use cases with significant benefits, no matter the approach.

We at In-Depth strongly advocate for a regularly-indexed design, which we apply in our Compressive Seismic Acquisition workflows (U.S. Patent Nos. 10,156,648 & 10,317,512). To see the power of this approach applied in action, see Fairfield’s recent IMAGE publication assessing our regularly-indexed CS design and reconstruction technology in the Permian Basin, where we produced nearly identical seismic imaging using only 70% of the original shots and receivers.

If you ever have to spend twenty minutes in an MRI machine, thank CS for not taking two hours!