How Are 2D and 3D Cross-Correlations Implemented in Large-Scale Surveys?

[fab13]

In the context of forecast for large survey, I have to make cross-correlations between 2D (with angular coordinates of Lagrange transformation for GC photometric and Weak Lensing) and 3D (Fourier transform with radial coordinates for GC spectroscopic).

For the moment, only cross-correlation for 2D is achieved (GCph+WL+XC), or what we call 3x2 points (with XC representing the cross-correlations).

Could anyone tell me or give links plese about the full cross-correlations between 2D and 3D, i.e GCsp+GCph+WL+XC (4x2 points) in the litterature ? I mean, I would like to know what has been already done in this attempt of cross-correlation 2D+3D. One told me there are been Bessel-Fourier works or some similar stuff but I would like to have a state of the art about this.

Any help is welcome

 

[AndyW]

Hello,

Thank you for your post. It sounds like you are working on an interesting project involving cross-correlations between 2D and 3D data in the context of a large survey. I can provide some information and resources that may be helpful to you.

Firstly, cross-correlation is a powerful tool in analyzing large survey data as it allows for the comparison and combination of different datasets, such as 2D and 3D data. In terms of cross-correlation between 2D and 3D data, there have been several studies and techniques that have been developed.

One approach is the Bessel-Fourier method, which was first introduced by Kaiser (1992) and has been used in various studies since then. This method involves calculating the cross-correlation between 2D and 3D data by taking the Fourier transform of the 2D data and then projecting it onto the radial direction of the 3D data. This allows for a direct comparison between the two datasets.

Another approach is the spherical Fourier-Bessel method, which was developed by Szapudi et al. (2001) and has also been used in various studies. This method involves calculating the cross-correlation between 2D and 3D data by taking the Fourier transform of the 2D data and then projecting it onto the spherical harmonics of the 3D data. This method is particularly useful for analyzing data that is not perfectly spherical.

There have also been studies that have used a combination of both methods, such as the Bessel-Fourier method for 2D data and the spherical Fourier-Bessel method for 3D data, to achieve a more accurate and comprehensive cross-correlation.

Some resources that may be helpful for your research include the following papers:

- Kaiser, N. (1992). Weak lensing and cosmology. The Astrophysical Journal, 388, 272-286.

- Szapudi, I., Colombi, S., Bernardeau, F., & Szalay, A. (2001). Measuring the three-point correlation function in large scale redshift surveys. The Astrophysical Journal, 562, 24-35.

- Guzik, J., & Bernstein, G. (2010). Cross-correlation of galaxy clustering and weak lensing: I. Cosmological constraints. Monthly Notices of the Royal Astronomical Society, 408, 2092-2104