New heat flow data and recent relative Vs (ΔVs/Vs) studies suggest differential crustal warming from prolonged intrusions in the Socorro magma body area. Heat flow above the Socorro magma body, relative to the adjacent Colorado Plateau and Datil-Mogollon region, indicates that ∼8 times more heat has been introduced into the crust than contained in a basaltic Socorro magma body. A combination of relative Vs contours and heat flow data suggests this differential is less, a factor ∼4.5. From relative Vs contours, depth of Socorro magma body, and conduction time constants, the minimum time required to increase heat flow resulting from midcrustal intrusions is ∼1–3 m.y. Recent models indicate that observed historic uplift at the Socorro magma body is explained by viscoelastic response of crustal material surrounding the Socorro magma body. Our estimates suggest that a long time scale (∼106 yr) for emplacement of basaltic magma sill(s) and surface uplift need not be directly related. Based on heat flow, we estimate >600 m of basaltic intrusion during Pliocene–Pleistocene time. Compared with adjacent rift basins, the Socorro magma body area shows anomalous landscape instability but no significant uplift of stream terraces across the magma body. Contiguous areas in the Rio Grande Rift have high heat flow but no present magma layer, no historic uplift, and little seismicity. Elliptical relative Vs crustal contours for the area suggest conductive heat transfer. The relative Vs model implies that the Socorro magma body is fed by narrow conduits (dikes) from the upper mantle and that the depth of the sill-like Socorro magma body is primarily controlled by rheology.
New heat flow data, recent relative shear wave velocity models (relative Vs = ΔVs/Vs), historical locale uplift, differential uplift within the Socorro magma body region, limited uplift with respect to other nearby regions of the Rio Grande Rift during Pleistocene–Pliocene time, and high heat flow in neighboring areas of the Rio Grande Rift all relate to the development and thermal antiquity of the Socorro magma body area. The Socorro magma body is the first and possibly the most uniquely seismically defined midcrustal sill-like magma body on Earth (Fig. 1A), and it is notably lacking recent volcanism. Both the observed heat flow above the Socorro magma body (Fig. 1A expanded view) and the relative Vs cross section along La Ristra in juxtaposition to the Socorro magma body (Figs. 1A and 1B) indicate crustal heating above that of nearby areas just outside the Rio Grande Rift. The heat flow data allow us to separate the effects of elevated temperatures from the effects of partial melting and fluids in the anomalous relative Vs crustal regions. From these data, we estimate additional past heat input (magma intrusions) into the crust, compare this estimate with the heat likely contained in the presently observed Socorro magma body, and better appreciate the thermal evolution of the area.
Relative Vs contours from recent studies and previous seismic-reflection studies determining the depth of the Socorro magma body allow estimates of probable depths for past magma intrusions (Fig. 1B). From these depth estimates, we calculate the minimum times required to obtain the increase in observed heat flow above the Socorro magma body as conduction time constants. Comparing the proposed Pliocene–Pleistocene thermal development of the Socorro magma body area with heat flow and seismic data from nearby areas within the Rio Grande Rift, we find that the present or historic uplift related to the observed Socorro magma body does not directly extrapolate to geomorphic studies. This comparison allows us to consider the complex relation between midcrustal intrusion activity and long-term surface uplift over time scales on the order of 106 yr. Relative Vs contours are also interpreted to suggest mechanisms associated with magma emplacement in the crust and the controlling depth factors of midcrustal sill-like intrusions.
The Socorro magma body (Fig. 1A) was reported by Sanford et al. (1977). Continued study has revealed its extent (∼3400 km2), thickness (∼130 m), depth (∼18.75 km), and possible change in areal extent with time (Reinhart and Sanford, 1981; Ake and Sanford, 1988; Balch et al., 1997). A potential root of the Socorro magma body was discussed by Schlue et al. (1996), and across the northern part of the Socorro magma body, seismic-reflection lines also indicate the existence of a sill-like midcrustal magma body (Brown et al., 1980; De Voogd et al., 1988).
Leveling and satellite interferometry data indicate recent and historic uplift over the Socorro magma body. Leveling surveys indicate an average uplift over the Socorro magma body of ∼1.8 mm yr−1 from 1951 to 1980 and ∼3.4 mm yr−1 from 1912 to 1951 (Larsen et al., 1986). Satellite interferometry data indicate a similar uplift rate (2.5–4 mm yr−1) for 1992–2000 and 1992–2006 (Fialko and Simons, 2001; Finnegan and Pritchard, 2009; Pearse and Fialko, 2010). These studies suggest active magma inflation. Early geomorphic studies suggested similar uplift rates over the past 105–106 yr (Bachman and Mehnert, 1978), thus tempting speculation relating the intrusion of the Socorro magma body directly to uplift rate. However, magma solidification rates for sills would not allow magma to be intruded at observed uplift rates (Pearse and Fialko, 2010; Turcotte and Schubert, 2002, p. 166–168). The recent model studies by Pearse and Fialko (2010) show that the observed present uplift is related mainly to the thermal-mechanical viscoelastic response of material surrounding the Socorro magma body on a time scale of 103 yr.
Finnegan and Pritchard (2009) conducted a geomorphic examination of three rivers and two terraces crossing the Socorro magma body and concluded that these features indicate no more than 25–50 m of cumulative differential surface uplift, referenced to nearby basins north and south, since middle Pleistocene. Love et al. (2009) interpreted geological maps of both the top(s) of aggraded ancestral Rio Grande basin fill (ca. 850 ka), and two terraces in the same reach to show no more than 10–15 m of variation in elevation above the modern gradient of the Rio Grande; much of this variation can be explained by modes of terrace preservation. However, compared to basins north and south, the margins of the Socorro Basin, where coincident with present-day uplift above the Socorro magma body, appear to be distinctly dissected and deeply eroded (Love et al., 2009; Fig. 2), which implies considerable uplift and landscape instability on the margins of the Socorro Basin. In total, these studies suggest a potential disconnect between historical magma emplacement and geodetic uplift versus Pliocene–Pleistocene magma emplacement and geologic uplift.
THERMAL CONSIDERATIONS AND POSSIBLE INTRUSION RATES
Basaltic sills of the order of 100 m thick (as the Socorro magma body is observed) solidify in similar material in a few hundred years (Fialko and Simons, 2001; Turcotte and Schubert, 2002); so intrusion times should be less than solidification times. We can therefore make a first-order estimate of intrusion rate for the Socorro magma body. If the observed Socorro magma body (130 m thick) represents an initial basaltic intrusion (no secondary melts), intruded in 20–30 yr, its thickness would increase at an average rate of ∼6.5–4.3 m yr−1. The solidification time of a magma 6.5–4.3 m thick is ∼7–2 mo (after Turcotte and Schubert, 2002). Recognizing somewhat longer times will be required to solidify successive layers as the sill forms because of increased temperature of neighboring material, these intrusion and solidifications rates are in reasonable first-order agreement. The volume of the Socorro magma body is ∼4.4 × 1011 m3 (Balch et al., 1997); if intruded in 20–30 yr, the intrusion rate would be ∼730–490 m3 s−1. This appears not unreasonable in terms of maximum likely effusion rates for nearby Holocene basalt flows in New Mexico near Grants and Carrizozo (∼85 and 65 km from the Socorro magma body, respectively, 500 and 800 m3 s−1; Zimbelman and Johnston, 2002). These rates are approximately three orders of magnitude greater than volume increases derived from modeling interferometric synthetic aperture radar (InSAR) data or inferred from leveling data between 1911 and 1981 (e.g., Fialko and Simons, 2001; Fialko et al., 2001). Regardless of intrusion rate, the estimated volume of the Socorro magma body (440 km3) far exceeds any historic eruption of basaltic magmas (e.g., 12 km3 at Laki, Iceland).
POTENTIAL SECONDARY SILICIC MELTS
Secondary silicic melts for the Socorro magma body region can extend the time possible to seismically observe a melt layer associated with an initial basaltic intrusion. Seismic models indicate that the Socorro magma body sits at the interface between granitic (upper) crust and gabbroic (lower) crust (Hartse, 1991); this geometry suggests the potential for secondary melts to be introduced in the granitic crust. Pearse and Fialko (2010) suggested the presence of silicic partial melts for a Socorro magma body ∼103 yr old.
We can make first-order end-member calculations for the resulting silicic layer solidification times. Assuming the pre-Socorro magma body intrusion heat flow was as measured today (96 mW m−2, see following), because the heat from the Socorro magma body at 18.75 km depth has not yet reached near surface, the predicted temperature at 18.75 km depth is ∼560 °C (after Lachenbruch and Sass, 1978, their fig., 9–18). The basaltic magma intrudes at ∼1080–1250 °C, depending on how much water is present (Mysen, 1981); therefore, the difference between the in situ temperature and the basaltic magma temperature, ΔTb, is ∼605 ± 85 °C. A silicic partial melt can range between solidus and liquidus (at 19 km ∼665–940 °C, with water present; Mysen, 1981), and therefore the difference between in situ and silicic melt temperatures, ΔTg, can be ∼105–380 °C. If we consider the differential heat content between basaltic magma and silicic melt, we estimate 1 m3 of basalt magma can possibly generate ∼1.6–3.4 m3 of granitic magma: by equating (1 m3 × cb × ρb × ΔTb + 1 m3 × Lb × ρb) basalt magma = (z m3 × cg × ρg × ΔTg + z m3 × Lg × ρg) silicic melt, where from Annen and Sparks (2002, their table 1) cb and cg are specific heats (1.48 and 1.37 × 103 J kg–1 °C−1), ρb and ρg are densities (2.8 and 2.65 × 103 kg m−3), and Lb and Lg are heats of solidification or melting (4.0 and 2.7 × 105 J kg−1). If half of the heat from the basalt intrusion is transferred upward into the granitic crust and half downward into the basaltic crust, then a basaltic magma layer 100 m thick will contain in the upper 50 m enough heat to generate on the order of 80–180 m of silicic melt (partial melt) above. However this secondary melting occurs, a resulting silicic melt 80–180 m thick could require roughly a hundred to several thousand years to solidify, depending on the temperature difference between the magma and juxtaposed material and magma thickness (after Turcotte and Schubert, 2002; diffusivity = 0.6 × 10−6 m2 s−1; Whittington et al., 2009). This estimate is consistent with the model of Pearse and Fialko (2010).
NEW HEAT FLOW DATA AND RECENT SEISMIC STUDIES
Three new heat flow values have been estimated at sites near the Socorro magma body boundary (Fig. 1A expanded view; Table 1). These estimates were obtained from bottom-hole temperatures measured in relatively deep petroleum tests and thermal conductivity measurements from nearby heat flow sites. Although there are important uncertainties to be considered with such data, these deep temperature measurements are typically below the effects of groundwater flow, which often perturb shallower temperature measurements, and as a data group are statistically as good as groups of typical measurements in defining regions of different heat flow (Reiter et al., 1985). The three new values and the previously measured value of 92 mW m−2 (Reiter et al., 1975) yield a heat flow average of 96 mW m−2 for the Socorro magma body region. The two values close to the town of Socorro are influenced by groundwater flow; the value of 72 mW m−2 is also well beyond one standard deviation of the average when included in the data group.
Recent seismic studies are also available for the Socorro magma body region (Figs. 1A and 1B). Figure 1B shows an east-west projected cross section (A–A′; Fig. 1A expanded view) of relative Vs along La Ristra seismic line (after West et al., 2004; making horizontal and vertical scales the same). The negative relative Vs contours shown in Figure 1B indicate higher temperatures and/or more fluids present in the region relative to a standard model (see caption, Fig. 1B). The seismic model averages data from regions both to the north and south of La Ristra. Because the Socorro magma body to the south of La Ristra as well as the area to the north of La Ristra both have anomalously high heat flow, crustal thermal sources in both areas are likely. The relative Vs contours may be interpreted as relative isotherms, and the elliptical geometries of these contours are consistent with horizontal tabular magma intrusions (sills) at elevated temperatures diffusing or conducting heat into the surrounding rocks. The Socorro magma body is also projected onto the cross section in Figure 1B.
HEAT ADDED BY CRUSTAL SOURCES IN THE SOCORRO MAGMA BODY REGION
Heat Flow Data Considerations
In order to estimate the heat contribution of crustal heat sources as suggested by heat flow data (Fig. 1A expanded view), we consider data both inside and just outside or near of the Socorro magma body. Just west of the Socorro magma body and just outside the Rio Grande Rift boundary, five heat flow values average 80 mW m−2 (Reiter et al., 1975; Edwards et al., 1978; Fig. 1A). Just north of the Socorro magma body, on the western edge of the Rio Grande Rift, a heat flow value of 82 mW m−2 has been measured at a site on La Ristra (Edwards et al., 1978). This value is considered to be a good representation of the locale because of the deep (820 m) temperature measurements. Therefore, we suggest that the background heat flow near the Rio Grande Rift and the Socorro magma body is 80–82 mW m−2. The heat flow site on La Ristra at the western boundary of the Rio Grande Rift is above a Moho depth of ∼39.5 km; the Moho depth in the middle of the Rio Grande Rift at station 29 is ∼35.5 km (Fig. 1B). This difference in Moho depth can increase mantle heat flow, if Moho temperatures are maintained during crustal thinning. The additional mantle heat flow for such a Moho shallowing is ∼3 mW m−2 (Reiter et al., 1986). Therefore, additional intrusive crustal heat sources in the Rio Grande Rift and Socorro magma body are estimated as causing an increase in heat flow from ∼83–85 mW m−2 to ∼96 mW m−2.
To estimate the heat added to the crust by intrusions, we consider potential temperature-depth regimes of the Socorro magma body region. Figure 3 shows temperature-depth curves interpolated from Lachenbruch and Sass (1978, their fig., 9–18) for heat flows of 85 and 96 mW m−2. This model represents steady-state intrusion of the crust and stretching of the upper mantle and is the most appropriate representation of subsurface temperatures available for the Rio Grande Rift environment. By subtracting the integrals over depth of these two curves, we can estimate the crustal heat gain per horizontal square meter when heat flow increases from 85 to 96 mW m−2: ΔQ = Δ (integrals of Tdz, over a depth interval) × c × ρ (where c is specific heat and ρ is 2.68 × 103 kg m−3 for the upper crust and 2.77 kg m−3 for the lower crust; Hartse, 1991). If one considers the influence of crustal heat sources to extend only to the base of the outer relative Vs ellipse (24.5 km, Fig. 1B), then ΔQ ∼3.7 × 1012 J m−2.
We compare this added crustal heat to that introduced by a basaltic sill 130 m thick as suggested for the Socorro magma body (Ake and Sanford, 1988). The heat in the sill per meter length, and per meter depth into the cross section (Fig. 1B), relative to the in situ material is: c × ρ × 130 m × 1 m2 × ΔTb + L × ρ × 130 m × 1 m2, where c and L are specific heat and heat of solidification or melting, respectively, ρ = 2.8 kg m−3 for intrusive basalt (Annen and Sparks, 2002), and ΔTb is between ∼520 and 690 °C (as previously given). The resulting heat input is 4.3–4.9 × 1011 J m−2, a factor of ∼8 less than the additional crustal heat estimated from the heat flow increase suggested earlier. The extra heat contained in a unit cross-section depth for the Socorro magma body is calculated by multiplying these estimates by a 50-km-wide Socorro magma body; these are ∼2.15–2.45 × 1016 J.
Relative Vs and Heat Flow Considerations
From the relative Vs cross section (Fig. 1B), one could suggest the possibility of somewhat lower midcrustal temperatures approaching the boundary of the Socorro magma body (because of less anomalous relative Vs). The distribution of heat flow values does not constrain possible variation of heat flow across the Socorro magma body (Fig. 1A expanded view). Assuming the ellipses in Figure 1B reflect crustal heat sources as well as crustal fluids, we can estimate the crustal heat added above background per unit depth into the cross section as: ΔQ = ellipse area × 1 m × c × ρ × ΔT, where c and ρ are as defined previously and ΔT is the temperature difference between background heat flow (85 mW m−2) and present heat flow. Taking the heat flow above the inner ellipse (−7.7% relative Vs) to be 96 mW m−2, the difference of temperatures at 15 km (the middle of the ellipses) between 85 and 96 mW m−2 is ∼51 °C (Fig. 3). Approximating the differential temperatures in the middle and outer ellipses as linearly proportional to relative Vs, the differential temperatures would be: 6.5/7.7 × 51 °C = 43 °C and 5.5/7.7 × 51 °C = 36 °C. The net heat content increase is then ∼10.4 × 1016 J per meter into the cross section. A comparison of this estimate to the heat calculated in the Socorro magma body per meter depth into cross section (2.15–2.45 × 1016 J) suggests that the ellipses contain 4.8–4.2 times as much differential heat as the Socorro magma body.
Considering that the relative Vs contours in Figure 1B indicate relative temperature contours, several possible intrusion histories are possible. We can, however, make minimum estimates of the time required for crustal heat sources to increase the near-surface heat flow above background values by considering conduction time constants. Typical conduction time constants are calculated from the exponential decay expression e–z2/4kt and setting z2/4ktc = 1 (where z is depth, t is time, tc is the conduction time constant, and k is the thermal diffusivity, ∼0.9 × 10−6 m2 s−1 for the upper crust; Whittington et al., 2009). If we solve for tc and substitute into the series expression representing a continuous temperature increase at a given depth (z), we find resulting temperatures at 1 km depth are ∼83% of equilibrium. Because it is unlikely that intrusions would occur in a sequence sufficiently rapid to result in a constant temperature increase, the time constant may be considered as a minimum time required to produce a near-surface heat flow change from a temperature increase at a given depth. Considering the relative Vs −7.7% ellipse to be the most likely depth for thermal sources, time constants from the upper, middle, and lower depths of the −7.7% Vs anomaly to the surface (12, 15, and 19 km) are 1.3, 2.1, and 3.3 m.y., respectively. Therefore, a minimum time of 1–3 m.y. would be required to generate the observed heat flow increase in the Socorro magma body region.
This temporal estimate is based on the heat transfer process from the midcrust to near surface being dominated by conduction. There are several observations that support this idea and the suggestion that the heat flow data are not influenced by very recent (∼103 yr old) magma intrusions. First, the halo pattern observed in the relative Vs analysis resembles conduction from a higher-temperature sill-like body (Fig. 1B). We suggest that the observed elliptical relative Vs pattern in the crust is too large to be derived from a single Socorro magma body–like intrusion. The strongly dominant upward convective heat transfer necessary to bring heat quickly from the present Socorro magma body to near the surface (in ∼103 yr) should significantly skew the relative Vs contours toward the surface. Second, the heat flow value at the southern boundary of the Socorro magma body is in a location that has not experienced recent uplift, and the two heat flow sites near the northern boundary of the Socorro magma body have experienced modest recent uplift, and yet the heat flows are about the same (101, 98, and 93 mW m−2; Figs. 1A [expanded view] and 2). This observation suggests that the heat flow is not related to present uplift or the modern Socorro magma body. Third, two sites just south of the Socorro magma body along the Rio Grande, within the Rio Grande Rift, indicate high heat flow in an area having no magma body, no uplift, and low seismicity (138 and 97 mW m−2; Figs. 1A and 2). Two heat flow values ∼30 km north of the Socorro magma body along the Rio Grande, within the Rio Grande Rift (99 and 92 mW m−2), are in or near a region that has undergone historic uplift from 1909 to 1951 (Larsen et al., 1986); however, this area has no detectable crustal magma layer and relatively low seismicity. Similarly, high heat flow appears to be present in a broad region within the Rio Grande Rift north of the Socorro magma body that has no present magma body, low seismic activity, and no detectable recent uplift. These observations imply that outside the Socorro magma body, but within the Rio Grande Rift, the increase in heat flow has been derived from crustal magma sources that solidified more than ∼103 yr ago and are not producing historic uplift or anomalous seismicity; this is consistent with the suggestion that heat associated with the presently observed Socorro magma body has not affected the near-surface heat flow. If the present uplift is receiving a contribution related to ongoing magma intrusion close to the surface, e.g., perhaps the largest uplift locale near the center of the Socorro magma body (Fig. 2), there may be associated advection of fluids increasing local heat flow above present values. Heat flow measurements in the area of greatest uplift would be valuable.
We have shown from heat flow data and relative Vs anomalies that the extra crustal heat content present in the Socorro magma body region is ∼4.5–8 times greater than the heat contained in a basaltic Socorro magma body. This implies that additional basaltic intrusions of 585–1040 m have been emplaced into the crust to contribute to the present elevated heat flow and observed relative Vs anomalies. The minimum conduction time required for the corresponding heat flow increase is estimated to be 1–3 m.y. (temperature increase occurring at 12–19 km depth from the relative Vs anomalies). Sequential intrusions (50 m every 103–105 yr) accumulating over periods of 105–106 yr are justified, as modeled by Annen and Sparks (2002). Thus, we envision the Socorro magma body as the most recent manifestation of a long-term mafic sill complex fundamentally associated with crustal heating and extension focused along the Rio Grande Rift.
We can estimate an average order of magnitude intrusion rate from these approximations. If ∼800 m of basalts intrude over 1.6 m.y., an average intrusion rate will be on the order of 50 m per 100 k.y. At this intrusion rate, for dry basalt over 16 m.y., the model of Annen and Sparks (2002) would give a resulting temperature of ∼608 °C at 20 km depth. This temperature is similar to the temperature estimated for heat flow of 96 mW m−2 at 20 km depth (582 °C; Fig. 3). Wetter basaltic magmas as well as a number of other model parameters could contribute to the somewhat different temperature estimates. More frequent pulses of smaller volume are probably more consistent with active volcanic fields (e.g., 5 m per 104 yr).
The intense seismicity and surface uplift in the Socorro magma body locale compared to neighboring areas of New Mexico (Sanford et al., 2002; Pearse and Fialko, 2010) suggest that heightened tectonic activity logically relates to present magma intrusion. If the Socorro magma body is presently spreading (Balch et al., 1997), the implication is very recent or ongoing intrusion. The aseismic halo around the periphery of the Socorro magma body (Sanford et al., 2002) suggests compression, which might result from intrusion relating to greater uplift near the middle of the Socorro magma body. This would be consistent with the notion of magma spreading.
Margins of the Socorro Basin, centrally located above the Socorro magma body, are anomalously uplifted and dissected compared with basins to the north and south (Fig. 2); however, middle to late Quaternary Rio Grande terraces are unequivocally not deflected (Finnegan and Pritchard, 2009; Love et al., 2009). If our estimate of a few million years to introduce ∼800 m of intrusions and develop the high heat flow at the Socorro magma body is correct, then the relatively small differential uplift between the Socorro magma body and the region to the north is consistent with ongoing uplift (102–103 yr) at the Socorro magma body, because there is no present magma body in the region just north of the Socorro magma body. These results appear to imply that: (1) between intrusion episodes, subsequent to the intrusion uplift event, there is a relaxation and subsidence period (a possibility suggested by Finnegan and Pritchard, 2009; Pearse and Fialko, 2010); and/or (2) the net intrusion-uplift processes at the Socorro magma body and nearby regions of the Rio Grande Rift have been roughly equivalent over the past ∼106 yr. The closely spaced intrarift blocks above the Socorro magma body and adjacent to the modern Socorro Basin clearly record uplift and subsidence associated with longer-term rift development and movement along faults (Love et al., 2009).
From the contours shown in Figure 1B, we deduce several important ideas concerning the development of crustal intrusions and the emplacement of the Socorro magma body. The relative Vs contours shown in Figure 1B indicate that the relative velocity anomaly decreases downward from the −7.7% region in the crust to the Moho; the contours also show that the relative anomaly in the mantle decreases upward from the most anomalous zone to the Moho. From these observations, we infer that the crustal intrusions are derived from the most anomalous zone in the upper mantle and result from rapid transport along relatively narrow conduits (dikes) too narrow to be observed seismically. In contrast, a large, broad, slowly rising diapir would result in continued high temperatures and partial melts (large, bulbous, negative relative Vs anomaly) between the upper mantle and the most anomalous regions in the crust (Fig. 1B). Second, the Socorro magma body is at the base of the most anomalous zone in the crust (the hottest zone with the most partial melt). This depth is then most likely a trap for ascending magmas (cf. Parsons et al., 1992). The ductile material above the Socorro magma body is silicic, while the material below the Socorro magma body is gabbroic (Hartse, 1991). Consequently there is a density, compositional, and rheological discontinuity at this depth because the silicic material is much closer to its melting temperature than the underlying gabbroic material (even before crustal intrusion, 85 mW m−2; Fig. 1), and therefore it is much weaker. Isotropic stress conditions in the weak silicic material would require a horizontal stress increase, which cannot be supported, for basaltic dike intrusions; therefore, it is easier to intrude horizontally just below the silicic layer.
Phillip Miller drafted Figure 1, and Leo Galbadon drafted Figure 2. Allan Sanford and another reviewer provided many helpful comments on the study. Sigma Plot 8.0 was used to produce Figure 3, and Table Curve 5.01 was used to integrate the temperature-depth curves.