Downward continuation of heat flow density data and thermal regime in Eastern Canada

Tectonophvsics, 194 (1991) 349-356 Elsevier Science Publishers

349

B.V., Amsterdam

Downward

continuation of heat flow density data and thermal regime in Eastern Canada Jean-Claude

Mareschal

Dhpartment des Sciences de la Terre and GEOTOP, UniuersitP du Quebec a Montrkal, Mont&al, Que. H3C 3P8, Canada (Received

January

2, 1990; revised version

accepted

March

26, 1990)

ABSTRACT Mareschal, J.C., 1991. Downward continuation Cermak and J.H. Sass (Editors), Forward 349-356.

of heat flow density data and thermal and Inverse Techniques in Geothermal

regime in Eastern Canada. Modelling. Tectonophysics,

In: V. 194:

Heat flow density (HFD) data from Eastern Canada were analyzed by downward continuation. The data cover parts of the Superior and Grenville provinces of the Canadian Shield, and parts of the Appalachian orogen. The downward continuation eliminates the effect of shallow crustal radiogenic heat production and better reveals differences in the thermal regime of deeper origin. The analysis shows that the deep heat flow beneath the Superior and Grenville provinces is low and the temperature in the lower crust is also low. The thermal regime of the crust changes markedly across a boundary that follows the St Lawrence River. Surface heat flow and heat production are markedly higher in the Appalachian Province. With much higher temperature and heat flow, the thermal regime in the Appalachian lower crust is also distinctly different from that of the shield. Temperature and heat flow increase eastward toward the Atlantic margin.

have been proposed

Introduction

relationship, The thermal all the major

regime tectonic,

of the lithosphere volcanic

crement

affects

D is often preferred

relationship

and metamorphic

that are compatible

but an exponential unaffected

by

with this

decrease because

with de-

it leaves the

differential

erosion

processes. Heat flow density (HFD) data provide the main constraint on the present thermal struc-

(Lachenbruch, 1970). This understanding has been recently questioned. The significance of the rela-

ture

tionship

of the

portant and

clues

lithosphere; about

the evolution

they

also

the conditions of the continental

contain

im-

port is considered

of formation

surements

lithosphere.

q=q,+AD In this relationship, the slope D is related to the thickness of the surficial heat producing layer and AD is understood as the contribution of the surficial heat sources to the heat flow; the intercept q,,, is interpreted as the deep contribution to the heat flow. Several models of heat source distribution Publishers

(Jaupart,

1983). Also, the mea-

production

in the superdeep

decreases with the tectonic age of a province (Polyak and Smirnov, 1968; Vitorello and Pollack,

et al., 1968).

0 1991 - Elsevier Science

of heat

heat trans-

well of the Kola peninsula (Arshavskaya et al., 1986) did not support the exponential model. It has been suggested that the average heat flow

The understanding of continental heat flow is based mostly on the linear relationship between the heat flow, q, and the heat production, A, in the crystalline rocks exposed at the surface (Roy

0040-1951/91/$03.50

is not so clear when horizontal

1980). It has also been proposed

that, at the time

of crustal

flow is equal

stabilization,

the heat

to

the present heat flow in young provinces, such as the Basin and Range. Analysis of the continental heat flow data shows that the average heat flow does not vary significantly between late Paleozoic and early Proterozoic provinces (Sclater et al., 1980; Morgan, 1985). The heat flow is higher in B.V

J.-C. MARESCHAL

350

younger

that are still affected

by tran-

the deep heat flow were obtained

it is lower for the Archean

cratons.

continuation

provinces

sient effects;

The low Archean concerns could

the oldest preserved

indicate

elements,

crust.

or a primary

Alternately,

an increase

tion of the shallow

crust.

It

their

crust is depleted

Ballard

is the result of early

feature

of the Archean

et al. (1987)

observed

in heat flow from the craton

the surrounding that

it

but it does not establish

or not this depletion

stabilization

because

continental

that the Archean

in radiogenic whether

heat flow is intriguing

mobile

heat flow is the result

of

the formation of a thick lithospheric root beneath the craton. The Canadian Shield, where a variety of terranes with distinct ages are juxtaposed, is an ideal region to investigate the importance of the geothermal

characteristics

Unfortunately,

for crustal

the distribution

stabilization.

of HFD

the

depth HFD

heat sources

is proportional variations

Mareschal strates

et al.,

that

that

to the wavelength

1989a).

same in the Grenville

the contribu-

and assume

(Mareschal

the character

that it changes

from downward

that include

The

et

al.,

analysis

of

1985; demon-

of the heat flow is the

and Superior

markedly

provinces,

but

in the Appalachians.

toward

belts. They have suggested

the early Archean

operators

data is

Downward continuation

The

method

potential

fields

of

of heat flow

downward

in geophysics

continuation was introduced

of by

Tsuboi (1939).

and Fuchida (1937, 1938) and Tsuboi In was developed and used mostly for

gravity

and magnetic

data by many

workers

(e.g.,

extremely uneven within and between the different geologic provinces of Eastern Canada. Jessop

Bullard and Cooper, 1948; Kreisel, 1949; Peters, 1949; Bott, 1967; Bodvarsson, 1971, 1973, among

et al. (1984) compiled all the data collected in Canada prior to 1983; this report included 27 sites from the Superior Province, 17 in the Canadian

others). Huestis (1979, 1980, 1981) considered the more general problem of inversion of heat flow data; he applied the method of Backus and Gil-

Appalachians, and only 5 sites from the Grenville Province; in addition fifteen sites were reported in

bert (1968) temperature

the platform sediments lying on Grenville ment (Southern Ontario and St-Lawrence

data.

baselow-

lands). Most of the recent additions to these HFD data are located in the Superior (Drury and Taylor, 1987) and Churchill provinces (Drury, 1985) or the Appalachians (Drury et al., 1987). Twenty-five new HFD and heat generation measurements from sites located in Quebec are reported by Mareschal et al. (1989b)

and

Pinet

et al. (in press);

measurements include twelve new sites Grenville Province. The HFD measured

these in the in the

Grenville by Mareschal et al. (1989b) is extremely low (22-30 mW m-’ after adjustment for postglacial climatic variations). These data thus suggest that the Grenville HFD is comparable to that of Archean crust with lower radiogenic heat production. The purpose of this paper is to report on an analysis of the thermal regime of Eastern Canada by downward continuation of the heat flow density data. The Fourier spectrum of the HFD was evaluated from all the data available in Eastern Canada. The temperature in the lower crust and

to infer lower distributions

These

results

were

and upper compatible generalized

bounds with

on the

by Huestis

(1984) who considered the effect of thermal conductivity variations on the temperature estimates. Brott et al. (1981) presented a downward continuation technique based on image theory which yields subsurface sources are present,

temperatures when no heat or permits an interpretation of

the source configuration. The distribution of radiogenic heat sources with and the mantle heat flow are often esti-

depth

mated by analyzing the spatial variations of the heat flow data (Roy et al., 1968; Lachenbruch, 1970). Fourier

transform

techniques

are conveni-

ent to analyze spatial variations of data and to downward continue potential fields, but they have seldom been used for heat flow because the data are usually too sparse to provide a good estimate of the spectrum. Mareschal et al. (1985, 1989a) have thus generalized the technique of Bodvarsson (1973) for downward continuation of the heat flow. They determine the Fourier components of the HFD. Assuming that the depth of the sources for each component is proportional to its wave-

DOWNWARD

length,

CONTINUATION

OF HEAT

they infer source

with the surface

HFD

By convention, defined

FLOW

AND

distributions

directly

THERMAL

REGIME,

transforms

as follows (e.g., Sneddon,

351

CANADA

(2) The heat sources

compatible

between

from the spectrum.

the Fourier

EAST

pair is

When

the heat

are uniformly

sources

given by the following al., 1989a): J-

dx dy

Y) = &lr,l_m,%? xexp[

k,>)

-i(k,x

+ k,y)]

In Fourier

transform

domain,

heat equation 1959):

is given

the equilibrium and

Jaeger,

1 is

T(k,,

the

z)=

k,, thermal

-Sk, K k,, z)

temperature T(k,,

distribution k,,

conductivity,

are the surface

z = 0), assumed

HFD q0(k,, ky). If there were no heat sources, form of the temperature would be given by: T(k,

T(j$, z) =

q,(k). mslnh(

T(k,

-smh(cu)

z) =

et

Ikjz
lk Id

q,(k).

exp(ar-

IklK

q(k,

z) = q,,(k)

q(k,

z) = -q,(k)

z) = hqo(x)

If the heat between

and

S(k,r, k,, z) is the Fourier transform of the heat source density at depth z. In geophysical applications, the heat sources are not known, and the only constraints on the ture

(Mareschal

lklz) Iklz>a _ Iklz
dk, dk,

by (Carslaw

a2

K

and the heat flow are

expressions

cosh( lk I z) sinh(a)

exp(a-

IkIt) (klz>a

T-k:-k; aZ where

on a

CQJ-cc

xexp[i(k,x+k,Y)]

f(X?

are concentrated

plane layer, the temperature

1972):

distributed

and the layer z = a/ I k (

the surface

tempera-

to be zero, the Fourier

distribution

temperature T(k,

z)=

sources

the surface spectrum

are uniformly is obtained

distributed

z = cu/ I % 1, the

and the plane

as:

l~~~k’~~~~l[l-exp(-lklz) ex (Y -exp(

-a)

sinh( 1X I z)]

Iklz
and trans-

at depth

z

xexp(-lklz)[cosh(cw)-l] Ik)z>a

sinh{ lklz}

In general, this expression transform because the Fourier Bodvarsson (1973) converge.

is not a Fourier integral does not proposed a long

wavelength approximation to continue downward potential fields to arbitrary depth; only the wavenumbers smaller than l/z are retained in the spectrum; larger wave numbers are considered to be part of the noise and are filtered out. Mareschal et al. (1985) considered short wavelengths to be related to the shallow heat sources and included them in the downward continued temperature and heat flow spectra. They examined two heat source distributions: (1) The heat sources are concentrated on the layer z=a/Ikl.

and the heat flow spectrum

-exp(-cr)

is given by:

cosh( lklz)]

Ik(z
4%

z>=4ow ex;;$: Xexp(-

1

(1 - casha)

lklz)

Iklz>a For the two distributions considered, the heat sources vary horizontally like an harmonic function of given wavenumber and are positive as well as negative. The undesirable negative values can be eliminated by adding a constant to the harmonic source distribution so that the heat sources are

J.-C. MARESCHAL

352

positive

everywhere.

must be removed ponent

This

constant

contribution

from the zero wavenumber

quencies

that are not resolved;

Fourier

com-

spectrum

Figure Thermal

that has been determined

used to interpolate

of the heat flow spectrum.

tinued

regime of Eastern Canada

i.e. the part of the

between

3 shows the temperature

to a depth

on a map of Eastern include ported

Canada

all the HFD between

values

44” N and

60 o W and 80 ’ W (Jessop Taylor,

1987; Drury

in Fig. 1. The data that

have

been

50” N and

et al., 1984; Drury

et al., 1987, Mareschal

and

the HFD

data

are irregularly

uted, the usual FFT technique cannot to determine the spectrum. Interpolating on a regular

grid would

smooth

temperature. beneath

be applied the HFD

out the data and

Province.

of November

trum

and the “warmer” cides geographically

they can be resolved

from closely

burg, 1976). This inversion is an undetermined problem as the number of frequencies in the spectrum is much larger than the number

of data. The

the

also be noted

that

crust

implies

6.2 Saguenay

25 1988 (North

earth-

et al., 1989).

The Grenville front does not appear to coincide with any boundary between different thermal provinces.

although

is low

Shield, including

in the lower

for the magnitude

alter the spectrum, and thus effectively eliminate the short wavelength components from the specspaced data points. The Fourier spectrum was thus determined by direct inversion (e.g., Olden-

It should

of

rather than ductile behavior. This is conwith the 29 km focal depth that has been

determined quake

estimate

It shows that the temperature

the low temperature brittle sistent

of the main

a precise

the entire Canadians

Grenville

et al.,

distrib-

and does not provide

con-

conduc-

to be 2.4 W m-’

Such a map is only indicative

trends

re-

between

1989b; Pinet et al., 1991). Figure 2 shows a contoured heat flow map of Eastern Canada. Because

K-‘.

data used in the study are displayed

downward

of 20 km. The thermal

tivity of the crust was assumed The HFD

can be

the data.

The

southeast;

temperature

the boundary

increases between

Appalachian with the

to increase

Figure 4 shows the temperature to 20 km when

the heat

the shield

Province coinSaint-Lawrence

River. The temperature continues ward the Atlantic margin. tinued

toward

the “cold”

downward sources

tocon-

are de-

frequencies that are retained are those that are well resolved by the data. The implicit assumption

termined from surface heat production measurements. It shows the same trends as in the previous

is that the Fourier

map,

spectrum

vanishes

for the fre-

but

with

higher

temperatures.

This

is be-

60” W_

SUPERIOR

Fig. 1. Map of the study area. Dots indicate

the location

of HFD measurements

for Holocene

climatic

sites. The values posted

variations.

are HFD (mW/m’)

adjusted

DOWNWARD

CONTINUATION

OF HEAT

FLOW

Fig, 2. Contoured

often

the basement

5 shows the HFD

REGIME,

EAST

the

measurements,

outcroping metavolcanic rocks and not on basement

underestimate

tion. Figure

THERMAL

353

CANADA

heat flow map of the study area. Contour

cause most of the heat production performed on metasedimentary

AND

heat

downward

or rocks, produc-

continued

lines are 5 mW mm2 apart.

Grenville

metamorphic

Province events

was

between

affected

by several

late Archean

(2650

Ma) and Grenvillian (1000 Ma) time (e.g., Doig, 1977). In the parautochtonous belt south of Grenville front, the high-grade rocks exposed have Archean

metamorphic

ages; paleopressures

in the

to a depth of 20 km. This operation has removed the effect of the shallow sources from the HFD. The trend is similar to that exhibited by the tem-

range 600-800 MPa have been determined (Indares and Martignole, 1989). In this part of the Grenville Province, the shallow crust consists of

perature

Archean

entire

field. The heat flow density shield is low. Apparently,

beneath

the

there is no ther-

rocks that formed

at lower crustal

depth.

The low heat flow is thus the result of depletion

of

mal boundary between the Superior and the Grenville provinces. This absence of contrast in HFD

radiogenic elements of these rocks of lower crustal origin. One could also conjecture that, if indeed an

has several implications.

It is now established

Archean

Fig. 3. Subsurface

map at 20 km depth.

was assumed

temperature

to be 2.4 W m-l

K-l.

that

The contour

“ tectonosphere”

lines are 50 o C apart.

The thermal

The heat sources were assumed to vary as a harmonic plane z = 0.2/k, where k is the wave number.

function

formed

conductivity

under

the cra-

of the upper crust

and to be concentrated

on the

J.-C. MARESCHAL

354

Fig. 4. Subsurface was assumed

temperature

map at 20 km depth.

to be 2.4 W mm’ K-‘.

The contour

The heat sources

uniformly

ton,

it extended

far into

the Grenville

extended

Prosug-

as far as the

Conclusions Because of the limited HFD data available in Eastern Canada, the tectonic immplications of the thermal regime of the Canadian Shield have not yet been

fully explored.

Downward

The thermal

from available

conductivity

heat production

of the upper

measurements

crust

and extend

to 10 km.

is one technique

Province,

beyond the present boundary of the Superior vince (i.e. the Grenville front). This analysis gests that it could have Saint-Lawrence River.

lines are 50 o C apart.

were determined

information

that

may help

from the HFD

The major difficulty

to derive

useful

data.

in such studies is to extract

this information from unevenly distributed data. In this study, the data were inverted to determine their Fourier spectrum. This technique effectively selects the wavelengths of the Fourier spectrum that the data satisfactorily resolve and disregards all other wavelengths. Implicitly, it assumes that the HFD spectrum can be extrapolated where no data are available. The analysis

continuation

of the thermal

to regions

regime of the crust

60%‘_

Fig. 5. Heat flow at a depth harmonic

of 20 km after removal function

of shallow

and to be concentrated

sources

contribution.

on the plane z = 0.2/k,

The heat sources

were assumed

where k is the wave number.

to vary as a

DOWNWARD

CONTINUATION

in eastern

Canada

the Provinces Archean

OF HEAT

shows

ent boundary cluded Grenville

extended

part

contains

the pres-

Province

M.J. and Taylor,

Can. J. Earth Drury,

in-

nature

Also,

the

133: l-14. Huestis,

in radio-

and temperature partly

values in the

the result

but they are mostly

are probably

related

of localized

of deeper

to higher

flow and transient effects opening of the Atlantic.

Appalachian

S.P., 1979. Extremal

reduced

associated

heat

with

Huestis,

The author

gratefully Sciences

S.P.,

the

Huestis,

acknowledges

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