st thickness. Moreover, the selection of a single reference depth
depends largely on the seismic information and personal experience of the researcher, and this
would enhance the uncertainty in the inversion result. Based on the existing gravity inversion
methods and the gravitational isostasy hypothesis, in inverting the gravity observations this study
adds a topography correction term to the expression of the crust reference depth. In this paper we
used the Bouguer gravity anomaly data in the region of (70°E~140°E, 15°N~50°N) and calculated
the crust thickness, and studied the correlation between the crust thickness variation and the topography
fluctuation.
Since this method directly uses the gravity and topography data and gives the crust thickness
determination independent of seismic observations, we can compare the results obtained from different
analysis method and different data source. When various methods have been used for a single
study region, we can obtain a more realistic result of the crust thickness and crust velocity
structure for this region.
1 Iterative inversion and analysis procedure
The procedure of the traditional FFT analysis is as follows: At first we transfer the Bouguer
gravity data in the time domain to that in frequency domain, and extend them down to the next
reference depth D. Then the data in the frequency domain is transferred back to the time domain
with inverse FFT (IFFT). Further we use the formula
Δg(x, y, D) = 2πGσ (x, y, D) (1)
to calculate the surface density σ at the reference depth D. Then we use the relation between the
volumetric density ρ and surface density σ
σ (x, y, D) = ρH(x, y) (2)
to deduce the fluctuation H(x, y) of the Moho discontinuity. Cubic formula is used to calculate the
surface gravity anomaly generated by the variation of Moho discontinuity. Then the residuals between
the observed gravity anomaly and the calculated anomaly are found and inverted again to
find the Moho fluctuation correction. Doing so iteratively until the residual is smaller than the error
threshold, we can find the final Moho fluctuation. The coordinate system used is a rectangular
system o−x1x2x3, with the ground surface being taken as the coordinate plane o−x1x2, and the
gravitational downward direction being the vertical axis o−x3. To facilitate the calculation the
horizontal axis o−x1 and o−x2 are set to be parallel to the two horizontal edges of the density
anomaly cube (Figure 1).
266 ACTA SEISMOLOGICA SINICA Vol.19
Figure 1 A density anomaly cube for calculating gravity anomaly at the coordinate origin (a); Flowchart
of inverting gravity and topography data to obtain crust thickness (b)
The gravity anomaly at the coordinate origin generated by a homogeneous cube of density ρ
at (x1, x2, x3) is
A
E
A
D
A
B
r x
g o G x r x x r x x x x
⎭ ⎬ ⎫
⎩ ⎨ ⎧
′′ ′
′ ′
Δ = − ′ ′ + ′ + ′ ′ + ′ − ′
3
1 2
1 2 2 1 3 ( ) ρ ln( ) ln( ) arctan (3)
where 2
3
2
2
2
1
r′2 = x′ + x′ + x′ . Figure 1b gives the flowchart of processing the gravity and topography
data to obtain the crust thickness. Finally the crust thickness can be expressed as
crust thickness = Moho depth fluctuation + corrected reference depth + topography variation.
2 Gravity isostasy and correction to the reference depth D
2.1 Data and its processing
This study used the 2′×2′ Bouguer gravity anomaly data provided by the CAS Geodesy and
Geodynamics Laboratory (in Wuhan, China) for the region of (70°E~140°E, 15°N~50°N). In order