A stochastic simulation technique analyzes the effectiveness of sparse Fourier reconstruction methods for multidimensional sampling functions. A regular 2D sampling pattern, called a weave pattern, is a suitable sampling scenario for sparse Fourier recovery. The simplicity of a weave sampling pattern provides a good alternative to replace random sampling patterns in compressive sensing applications. A double-weave 3D seismic acquisition design has been developed by using the weave sampling pattern for the shot and receiver distributions. Besides its homogeneous spatial coverage in the shot-receiver and offset-azimuth coordinates, double-weave 3D acquisition is a compatible survey design for alias-free 5D sparse Fourier interpolation in the shot and receiver domains. Zigzag and orthogonal double-weave acquisition layouts were proposed for land seismic surveys considering the economic and environmental parameters. The effectiveness of 5D interpolation for double-weave 3D acquisition were tested using synthetic planar 5D seismic events.