how to synthesize spherical harmonic coefficients into geoid

[Lydia823]

what formula to use to synthesize spherical harmonic coefficients of density anomaly contribution or surface dynamic topography contribution or CMB dynamic topography contribution computed from aspect , parameters set according to manual of page 368-369?

[gassmoeller]

@Shangxin-Liu you can probably answer this best. Is there a good paper that contains the equations?

Apart from that Lydia if you are looking for a spatial visualization of the geoid you can use the visualization/geoid postprocessor (as opposed to the normal geoid postprocessor) to output the geoid in the same dataset as the rest of the solution (and visualize with Paraview or however you currently visualize the rest of your data). The Geoid::evaluate function in source/postprocess/geoid.cc should also give you a point to start looking for how to convert the coefficients to spatial values.

[Shangxin-Liu]

Hi Lydia, @Lydia823

The geoid code output spherical harmonics of density, surface topography, and CMB topography contribution in dimensional form with 4piG/(surface gravity) prefactor. One of documents clearly shows this equation is equation (7) in the paper http://www.sciencedirect.com/science/article/pii/S0031920113002057

[Lydia823]

Dear Shangxin, Thanks for your advice of the paper, i have downloaded it and will read it carefully.

-----原始邮件----- 发件人: "Shangxin Liu" notifications@github.com 发送时间: 2017年7月7日 星期五 收件人: geodynamics/aspect aspect@noreply.github.com 抄送: Lydia823 rhcui@asch.whigg.ac.cn, Author author@noreply.github.com 主题: Re: [geodynamics/aspect] how to synthesize spherical harmonic coefficients into geoid (#1836)

Hi Lydia,

The geoid code output spherical harmonics of density, surface topography, and CMB topography contribution in dimensional form with 4piG/(surface gravity) prefactor. One of documents clearly shows this equation is equation (7) in the paper http://www.sciencedirect.com/science/article/pii/S0031920113002057

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[ian-r-rose]

@gassmoeller You are right about the execute() function. I think that the synthesis step should still be clearly documented in the manual, since there are an unfortunate number of spherical harmonics normalizations in the literature.

[Lydia823]

@gassmoeller Thanks for your good advice, i will look carefully of that in geoid.cc.

[Shangxin-Liu]

As we discussed in the hackathon, it would be better to put the spherical harmonic synthesis (back and forth) into utilities.cc because in the future we may need to enable ASPECT to transfer other variables like velocity etc to spherical harmonic domain in the post processing. But we need to choose a universal format for this. I think the current format of normalization is a pretty commonly used one in geophysics. Other details that may also need to be taken care of includes the input spherical function's format etc. I'd like to make this change later. @gassmoeller @ian-r-rose

[ian-r-rose]

Unfortunately, at least three conventions are commonly used (geodetic, Schmidt, and fully normalized). The one we are using (fully normalized) is the best, I think.

I agree that it should probably be in utilities.cc, ultimately.

[Shangxin-Liu]

Yeah, the fully normalized one we use is very common in seismology (except S40RTS:-))

I personally think this should be the future universal format in ASPECT. @gassmoeller @ian-r-rose

[gassmoeller]

I am fine with that, and would support the move. Anyone interested in going forward with a pull request?