Generally, when you want to reach a GPS-Leveling geoid surface (Geometric geoid) from the gravity values (or may be gravity model), you may have to use a corrector surface to deal with the biases between these two surfaces (between geometric and gravimetric geoid surface), but some papers were published where the researchers didn't use corrector surface between aforementioned surfaces, so the main question is: How can you trust your gravity values, or computation from gravity values to geoid or especially to your gravity model? How do you know that your gravity model is correct or not? Because you can assume that your gravity model works properly and correct the gravimetric geoid surfaces to the geometric geoid by corrector surface, while this assumption may be wrong.
If there is a difference between the GPS/levelling and the gravimetrically determined surface it is normally due to the constraints caused by the levelling adjustment. The error of the gravimetric surface may be estimated using e.g. the error estimation capability of least-squares collocation. It will typically be a few cm, while the GPS/levelling may have an offset of several decimeters, see e.g. the description of the UK/Irish geoid computation. Another good example is the determination of the N0 offset of the levelling datum in Pakistan, see the paper by Sadiq et al, a few years ago. see the papers on my home-page http://cct.gfy.ku.dk/publ_cct/cct_publ.htm
Do not hesitate to further questions,
kind regards
Christian
Dear Ismael! Why do you consider GPS-levelling geoid as geometric geoid? Levelling is not geometric measurement means. It is related to a plumb line.
Dear Prof. Tscherning
First thank you for your valuable response,
I will read these two papers of your suggestion, and i have question about them i will ask you,
Again thank you,
Ismael,
Dear Dr. Kaftan,
Thank you for your precise advice,
In fact, in comparison to gravimetric geoid method that uses gravity data, i used this phrase for geoid from GPS-Leveling method that uses leveling measurements on the geometric surface of the Earth, let me know if this phrase may be confused with another geoid determination method?
Regards,
Ismael,
Dear Ismael, in addition to your comment, GPS can be called like geometric method. But in my opinion "geometric geoid" will not be a correct therm. I think that every geoid is a physical model of an equipotential surface. It is better when a therm is clearly reflect the essence. I do not argue with you if you do not wish to use your therm officially.
Dear Dr. Kaftan
Thank you so much for your notices,
Yes may be this phrase make misunderstanding to some one else,
It is better to use other term,
Regards,
Ismael,
I would like to tell about some curious situation. As you know it is necessary to use gravity data for classical reference ellipsoid determination. But now it is possible to determine this shape by the use just rectangular 3D coordinates of global reference frame sites without gravity data. It will another type of ellipsoid. My student has been approximating the Earth geometry surface described by ITRF coordinates like rotation ellipsoid form. It is clearly geometric task. He called that shape like "geometric ellipsoid" and immediately suffered from critic of several old professors. They said that every ellipsoid is geometrical figure. They were right in general especially for mathematical terminology. Then the student has abandoned that not successful term. "Geometric ellipsoid " sounds funny.