Accelerating seismic computations using customized number representations on FPGAs

Brief Introduction

The code above is the computationally intensive portion of the FK step in a downward continuation based migration. The governing equation for the FK step is the Double Square Root Equation (DSR) (, ). The DSR equation describes how to downward continue a wavefield $U$ one depth $\Delta z$ step. The equation is valid for a constant velocity medium $v$ and is based on the wave number of the source $k_s$ and receiver $k_g$. The DSR equation can be written as,

$$U(\omega,k_s,k_g,z+\Delta z) ={\rm exp}\left[-i \omega v \le... ...{1 - \frac{k_s v}{\omega}}\right) \right] U(\omega,k_s,k_g,z),$$ (3)

where $\omega$ is frequency. The code takes the approach of building a priori a relatively small table of the possible values of $\frac{v k}{\omega}$. The code then performs a table lookup that converts a given $\frac{v k}{\omega}$ value to an approximate value of the square root.

In practical applications wfld contains millions of elements. The computation pattern of this function makes it an ideal target to map to a streaming hardware circuit on an FPGA.

Accelerating seismic computations using customized number representations on FPGAs