Abstract：Hartley Transform(HT)is an integral transform similar to Fourier Transform(FT)and it inherits most FT properties. Fast Hartley Transform(FHT) can be achieved by using the structures similar to that in Fast Fourier Transform (FFT). However, HT has two advantages over FT: (1)the same forward and inverse transforms, and (2)real number transform. As a result, HT is faster than FT because the internal storage needed in real number operation is half as mush as that in complex number operation. Hence, in many data processings with FT, such as filtering, forward modeling, migration and so on, HT results in faster operation and less internal storage than FT does. HT original formulae are derived from FT circular function expressions. The relationship between HT and FT or Hilbert transform is analysed in detail. HT properties are summed by comparing with FT, and they are extended to discrete HT and multidimensional HT. HT and FT have similar or same properties, so that widely used FT program can be easy converted into HT program, resulting in faster seismic data processing.
