Journal of Applied Mathematics and Physics, 2013, 1, 63-67

http://dx.doi.org/10.4236/jamp.2013.14012 Published Online October 2013 (http://www.scirp.org/journal/jamp)

Copyright © 2013 SciRes. JAMP

Kriging of Airborne Gravity Dat a in the

Coastal Ar e as of th e Gulf of Mexi co

Hongzhi Song, Alexey L. Sadovski, Gary Jeffress

Conrad Blucher Institute, Texas A&M University-Corpus Christi, Corpus Christi, USA

Email: Alexey.sadovski@tamucc.edu

Received July 2013

ABSTRACT

This paper deals with the application of kriging technique to find the continuous map of gravity on the geoid in the

coastal areas and to evaluate its precision.

Keywords: Gravity; Kriging; Geoid; Map; Statistics

1. Introduction

By using satellites, scientists discovered the long wave

(large scale) geoid for the Earth (Seeber, 2003; Drink-

water et al., 2003) [1], but its resolution is not sufficient

for orthometric height determination from GPS when it

comes to the relatively small scale and/or local events

such as flooding. This was the case after flooding created

by storm surges fr om hurri can es Katri na, R ita (2 005), a nd

Ike (2008) in the coastal areas of the Gulf of Mexico. So,

there is a need to develop method(s) and model(s) of the

geoid determination at the local level, based on local

observations of gravity, and complemented by observa-

tions of gravity from the air and space.

In principle, there is a need for gravity g at every point

of the Earth’s surface. Gravity is continuously changing,

and it reflects the results of Earth’s phenomena, such as

tropic storm, hurricane, earthquake, early tides, variation

in the atmosphere density, etc. Gravity also alters when

only a small change happened in the constructions and

the density of materials beneath the constructions. But

having gravity data provided everywhere on the Earth is

totally impossible in reality. To predict values of a ran-

dom unsampled area from a set of observations is needed.

It is well known that the kriging method is not the best

approach to predict free-air gravity anomalies, but in this

paper, we assume that the kriging method is a better ap-

proach than other methods for prediction of gravity based

on the airborne data provided by National Geodetic Sur-

vey (NGS). The result we still have a confidence in the

kriging method is that the kriging method can estimate

the prediction error to assess the quality of a prediction.

This function makes the kriging method with a big dif-

ference from other methods.

2. Data

Data used in this chapter is airborne gravity data of the

Gravity for the Redefinition of the American Vertical

Datum (GRAV-D) project which was released by NGS

[2]. Table 1 lists the nominal block characteristics, and

details can be founded in GRAV-D General Airborne

Gravity Data User Manual. Four blocks (Block CS01,

CS02, CS03 and CS04) data (Figure 1) were chosen to

be interpolated.

The total sample size (four blocks together) is 389578,

and the gravity values range between 975480 mGal and

977490 mGal. Keep in mind, the standard gravity is

980665 mGal. The airborne gravity data was fixed by

using free-air reduction and by the international gravity

formula [3].

3. Kriging of Gravity on the Geoid

The kriging method here was conducted by using Arc-

GIS 10.1—Spatial Analyst and Geostatistical Analyst.

There are six different types of kriging in Geostatistical

Analyst tools. The most common types are ordinary

kriging and universal kriging, which were chosen to be

used in this study. The simple kriging method is also

Table 1. Nominal data characteristics.

Characteristic Nominal Value

Altitude 20, 000 ft (~ 6.3 km)

Ground speed250 knots (250 nautical miles/hr)

Along-track gravimeter sampling1 sample per second = 128.6 m (at nominal ground speed)

Data Line Spacing10 km

Data Line length400 km

Cross Line Spacing40-80 km

Cross Line Length500 km

Data Minimum Resolution20 km