Re: Gravfft - Parker expansion

Dear all,

I think the question and answers so far have conflated and confused some things.

1, Parker DID explicitly consider the case of variable density. See Equation 5 in his original paper, which you can download from
http://topex.ucsd.edu/geodynamics/parker.pdf

2, Even so, what we can do with an FFT is limited to those aspects of the mathematics that are linear and spatially invariant (like the impulse response of the flexural isostasy force balance, or the impulse response of gravity anomaly due to a point mass). Therfore the right way to handle variable density and topography is to multiply them together first with grdmath and then use grdfft on the resulting product.

3, The flexural isostatic response, for sufficiently larger than zero elastic thickness, is a low-pass smoothing filter, and usually the transition wavelength will be so long that the higher-order terms in Parker's calculation for the gravitational effect of the isostatic compensation will be negligible.

4, In my experience calculating gravity anomalies due to sea floor topography, the higher-order terms become important only over tall seamounts whose summits come near to sea level. See for example DOI:10.1029/2006GL028857   Thus I would suggest that the higher-order terms are needed to calculate the attraction of the topography, but not its compensation.

5, I agree with Joaquim: it is always instructive to read the original papers carefully.

Walter

On Feb 10, 2014, at 1:48 PM, Paul Wessel <[email protected]> wrote:

> While Parker did not allow variable density, the method can accommodate it.  For instance, see http://dx.doi.org/10.1016/0012-821X(90)90078-C
> We might want to deal with this at some point.
> 
> -p
> 
> On Feb 10, 2014, at 8:31 AM, J. Luis <[email protected]> wrote:
> 
>> On 10-02-2014 14:32, Lester Anderson wrote:
>>> Hello,
>>>  
>>> Quick query. When calculating the flexural "Moho" there does not seem to be a way of applying anything but the default first term in Parker's expansion, so anything beyond that (eg -E4) will generate a warning message as below and the program continues with E1:
>>>  
>>> c:\SS20-work>gravfft black1-topo.grd -Gblack1-topo_flex25km.grd -T25000/2670/3330/1030 -Z32000 -V -fg -E3 -Q 
>>> gravfft: Warning: Due to a bug, or a method limitation (I didn't figure that yet) with the selected options, the number of terms in Parker expansion is reset to one
>>> See examples in the manual if you want to compute with higher order expansion
>>> *****
>>>  
>>> This error/warning is mentioned in the documentation, but I was wondering if there is a workaround if one needed to use higher terms of the Parker expansion in flexural studies, or is the first term sufficient? 
>> 
>> First, let me state that those are old notes that I wrote at the time of first versions of gravfft and they are not so ... fresh now, but I note that the same doc that you refer also say
>> 
>> "...For higher powers of bathymetry in Parker expansion, only the above example seams to give the correct result."
>> 
>> 
>>>  As with all these things, setting the mean Moho depth and a constant density contrast is a big oversimplification.
>>>  
>>> Is it feasible to compile a variable density grid for flexural studies?
>> 
>> It's always educative to read the original papers. 
>> No, Parker method does not allow a variable density across the interface.
>> 
>> Joaquim
>> 
>> To unsubscribe, send the message "signoff gmt-help" to [email protected]
> 
> To unsubscribe, send the message "signoff gmt-help" to [email protected]

To unsubscribe, send the message "signoff gmt-help" to [email protected]