Re: About isostatic computation and -N+l (gravfft)

Gabriel,

Gravity computations by FFT method are defined to less than one 
constant. It doesn't matter if anomalies span -30 +30 mGal or 0 60. 
Neither is correct in the absolute sense because we lost the mean layer 
thickness. If you want an absolute value you need to use grdgravmag.
When comparing with measured values you want to look at the RMS that are 
insensitive to a constant shift. See the paper referenced at the bottom 
of the gravfft man page.
Ah, and don't know why we made the -E1 by default (number of terms in 
Parker expansion). You want more, -E3 at least, and that grdfft cannot 
do that. What you want is gravfft.

Cumprimentos

Joaquim

> Hi Joaquim,
>
> I have run a test here and confirmed that what I am seeking with 
> "gravfft" is the old "grdfft" answer, which implicitly had -L set when 
> doing the isostatic computation.
>
> The command lines that I used are written bellow, and also the 
> z[min,max] answers from grdinfo:
>
> ---------------
> # under gmt4.5.11
> grdfft topo.grd -Gtmp.flex4.grd -T0/2900/3300/1030/2900 -M
> grdmath tmp.flex4.grd -35000 ADD = flex4.grd
>
> # under gmt5.1.1
> gmt gravfft topo.grd -Gflex5.grd -T0/2900/3300/1030 -Q -fg -Z35000
> ---------------
> # grdinfo:
> # topo.grd z=[62,2545]
> # flex4.grd z=[-46.5,-35]
> # flex5.grd z=[-43,-31.5]
>
> Both give me an Airy root that reaches 11.5 km, and since the "grdfft" 
> output is absolute, by adding the reference depth I am able to obtain 
> a grid of the "isostatic Moho", which remains close to -35 km where 
> the topography is near 0, and reaches -46.5 km where the topography is 
> higher (this is exactly what I am looking for). The "gravfft" output, 
> in the other hand, spans from -31.5 km to -43 km.
>
> My objective here is to compare "isostatic Mohos" (using different 
> Te's) and their respective gravity effects with observed data, thus my 
> interest in keeping the absolute values (not those about a mean) and 
> in the gravfft tool, otherwise I could remain with the old grdfft.
>
> But again, if I compute the gravity effect from flex5.grd, the output 
> will be something like [-30,30 mGal] (of course!), while the answer 
> that I am seeking, which would be directly comparable to observed 
> data, is that from flex4.grd (all negative gravity values).
>
> I hope that I made myself clear this time.
>
> Thank you (e muito obrigado pela atenção),
> Gabriel
>
>
> Em Quinta-feira, 14 de Novembro de 2013 23:09, Joaquim Luis 
> <[email protected]> escreveu:
> Gabriel,
>
> Yes I say your 'avoid demeaning' question but don't understand it. Why 
> would you want it? Anyway we can't because it's inherent to  FFT to 
> remove the so called DC component (the mean) before applying the 
> transform. Sorry if I'm not really answering your question but I'm 
> afraid I didn't quite understand what you are expecting to obtain.
>
>> Yes Joaquim, I'm getting exactly that, but I would like to set -N+l. 
>> I don't know what happened to the second part of my first e-mail, so 
>> I will quote it: "Is there a way to avoid the demeaning? Setting -N+l 
>> does nothing, so I don't know whether this is a bug or if -N+a is 
>> really needed."
>>
>> Thank you
>> Gabriel
>>
>>
>> Em Quinta-feira, 14 de Novembro de 2013 16:46, J. Luis 
>> <[email protected]> <mailto:[email protected]> escreveu:
>> On 14-11-2013 18:26, Gabriel Dragone wrote:
>>> Hello,
>>>
>>> I have a doubt concerning the isostatic calculation done by gravfft 
>>> (-T). Using, for example, Te=0 and a compensation depth (-Z) of 
>>> 35000 m, I would expect that all topography had its root bellow 
>>> 35000. Nevertheless, since -N+a is set, the response is a 
>>> fluctuation around it.
>>
>> The FFT method (Parker's), after detrending,  implies that the 
>> solution is 'waves' about zero but there is one term in the equation 
>> that represents the average compensation depth (that's what -Z does). 
>> So naturally your solution should be about the 35 km depth (parts 
>> above and others bellow). Isn't that what you get?
>>
>>
>>
>>> Is there a way to avoid the demeaning? Setting -N+l does nothing, so 
>>> I don't know whether this is a bug or if -N+a is really needed.
>>>
>>
>> The man says "-T implicitly sets -N+a". This is for better 
>> convergence of the Parker's method'
>>
>> Joaquim
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>>
>>
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