Computers & Geosciences 31 (2
m
ou
ue
a˜o P
orm 1
Trend-surface analysis is the mathematical method
traps, geographical features, or to recognize structural
‘‘breaks’’ between successive units (Merriam and
1999; Hiruma et al., 1999).
This work presents trend-surface analysis of the
ARTICLE IN PRESS

Tel.: +55 11 30914216; fax: +55 11 30914258.
morphometric parameters, hydraulic gradient (Rodriguez,
1993) and isobase (Filosofov, 1960 cited in Jain, 1984;
0098-3004/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cageo.2005.02.011
E-mail addresses: guano@usp.br, carlos_grohmann@
yahoo.com.br.used to separate map data into components of regional
nature from local fluctuations (Agterberg, 1974; Davis,
1986). Regional trends are computed as polynomial
surfaces of successive powers; residual values, corre-
sponding to local fluctuations, are the arithmetic
difference between original data and trend surface.
Residuals maps play an important role in trend-surface
analysis given that they can favour on identify or
accentuate features of interest. This technique has
been widely used by petroleum geologists, to predict
Harbaugh, 1963; Merriam and Lippert, 1966; Sutterlin
and Hastings, 1986; Davis, 1986).
Morphometric maps are important tools in studies
related to neotectonics and geomorphology, where the
answers of natural landscapes to planet’s interior
dynamics are often masked by fast action of weathering,
and the presence of drainage network anomalies and
relief pattern discontinuities may be related with recent
terrain movements (Zuchiewicz, 1991; Rodriguez, 1993;
Salvador and Riccomini, 1995; Hiruma and Riccomini,study area, located in the eastern border of Quadrila´tero Ferrı´fero, southeastern Brazil, presents four main
geomorphological units, one characterized by fluvial dissection, two of mountainous relief, with a scarp of hundreds of
meters of fall between them, and a flat plateau in the central portion of the fluvially dissected terrains. Morphometric
maps were evaluated in GRASS-GIS and statistics were made on R statistical language, using the spatial package.
Analysis of variance (ANOVA) was made to test the significance of each surface and the significance of increasing
polynomial degree. The best results were achieved with sixth-order surface for isobase and second-order surface for
hydraulic gradient. Shape and orientation of residual maps contours for selected trends were compared with structures
inferred from several morphometric maps, and a good correlation is present.
r 2005 Elsevier Ltd. All rights reserved.
Keywords: Trend-surface analysis; Morphometric analysis; Geographic information systems; GRASS-GIS; R statistical language;
Analysis of variance
1. Introduction structural behaviour of stratigraphic units in search forTrend-surface analysis was carried out on data from morphometric parameters isobase and hydraulic gradient. TheTrend-surface analysis of
A case study in s
Carlos Henriq
Po´s-Graduac- a˜o, Instituto de Geocieˆncias, Universidade de S
Received 14 March 2004; received in revised f
Abstract005) 1007–1014
orphometric parameters:
theastern Brazil
Grohmann

aulo, Rua do Lago 562, 05508-080 Sao Paulo, SP, Brasil
6 February 2005; accepted 24 February 2005
www.elsevier.com/locate/cageo

Golts and Rosenthal, 1993), with integrated utilization
of free software GRASS-GIS (US Army CERL, 1993)
and R statistical language (Ihaka and Gentleman, 1996),
in the Serra do Carac-a region, eastern border of
Quadrila´tero Ferrı´fero, southeastern Brazil.
2. Geological and geomorphological context
The Quadrila´tero Ferrı´fero region, south Sa˜o Francisco
Craton, is characterized by Archaean granite-gneiss
domed complexes coeval to Rio das Velhas greenstone
belt (Machado et al., 1992), engaged to south and east in
a Paleoproterozoic metamorphic belt (Mineiro belt,
Teixeira and Figueiredo, 1991) defined as an acre-
scionary orogen of ca. 2.1Ga (Fig. 1).
The study area presents four main geomorphological
units (Fig. 2): Serra do Carac-a Range, with average
altitudes of 1400–1600m and maximum at 2064m; Serra
do Pinho Range, in the eastern side of the area, with N–S
trend; Chapada de Canga Plateau, in the central region
of the study area, leveled at ca. 900m; Minas Gerais
center-south and east Highlands, characterized by fluvial
responsible for present-day altimetric differences (King,
1956; Barbosa, 1980).
Evidences of Cenozoic tectonics in the Quadrila´tero
Ferrı´fero are observed in several sedimentary deposits
ARTICLE IN PRESS
ton (m
nas S
ntiqu
Catas Altas
Morro da
Água Quente
Fonseca
Santa Rita Durão
Bento Rodrigues
1 2 3 4 5
Fig. 2. Main geomorphological units in study area. (1) Serra do
Carac-a Range; (2) Chapada de Canga Plateau; (3) Serra do
Pinho Range; (4) Minas Gerais center-south and east High-
lands; and (5) Cities.
C.H. Grohmann / Computers & Geosciences 31 (2005) 1007–10141008Fig. 1. Simplified geological map of southeast Sa˜o Francisco cra
de Canga and Fonseca Fms.; (2) Itacolomi/Espinhac-o Gr.; (3) Mi
(5) SE Sa˜o Francisco craton gneiss; (6) Dom Silve´rio Gr.; (7) Ma
granulites; and (9) Study area.dissection. The scarp that limits the Serra do Carac-a
from the other units has hundreds of meters of fall, and
leads to believe that not only erosional processes, but
also post-Cretaceous tectonic movements contributed in
the morphological evolution.
According to Varaja˜o (1991), remains of planation
surfaces in the Quadrila´tero Ferrı´fero have close
relations with lithostructural domains. Reactivations
with vertical displacement of ancient faults would beodified from Campos Neto et al., 2004). (1) Cenozoic Chapada
upergroup; (4) Rio das Velhas Supergroup (40 – komatiitic unit);
eira gneisses (70 – amphibolite, 700 – granulite); (8) Juiz de Fora