Deep Drilling Project Research Articles

Magma Intrusions and Earthquake Swarm Occurrence in the Western Part of the Bohemian Massif

We are proposing a hypothesis that earthquake swarms in the West Bohemia/Vogtland seismoactive region are generated by magmatic activity currently transported to the upper crustal layers. We assume that the injection of magma and/or related fluids and gases causes hydraulic fracturing which is manifested as an earthquake swarm at the surface. Our statements are supported by three spheres of evidence coming from the western part of the Bohemian Massif: characteristic manifestations of recent geodynamic activity, the information from the neighbouring KTB deep drilling project and from the 9HR seismic reflection profile, and the detailed analysis of local seismological data. (1) Recent manifestations of geodynamic activity include Quaternary volcanism, rich CO2emissions, anomalies of mantle-derived3He, mineral springs, moffets, etc. (2) The fluid injection experiment in the neighbouring KTB deep borehole at a depth of 9 km induced hundreds of micro-earthquakes. This indicates that the Earth's crust is near frictional failure in the western part of the Bohemian Massif and an addition of a small amount of energy to the tectonic stress is enough to induce an earthquake. Some pronounced reflections in the closely passing 9HR seismic reflection profile are interpreted as being caused by recent magmatic sills in the crust. (3) The local broadband seismological network WEBNET provides high quality data that enable precise localization of seismic events. The events of the January 1997 earthquake swarm are confined to an extremely narrow volume at depths of about 9 km. Their seismograms display pronounced reflections of P- and S-waves in the upper crust. The analysis of the process of faulting has disclosed a considerable variability of the source mechanism during the swarm.

On the origin of saline fluids in the KTB (Continental Deep Drilling Project of Germany)

Highly saline fluids were encountered during the German Continental Deep Drilling Project (KTB) from depths ranging between 2 and 3 km to about 9 km. The most reliable data were obtained from samples extracted during a long-term pumping test in the 4000-m deep KTB pilot hole. Some 460 m 3 Ca–Na–Cl brines with about 68 g l −1 total dissolved solids (TDS) and some 270 m 3 associated gases, mainly N 2 and CH 4 were pumped to the surface from the main fracture system situated near the bottom of the pilot hole. Geochemical and isotopic data support the hydraulic tests which suggest the presence of an open and large fluid reservoir at depth. The pumped fluids from this main fracture system were released from a deep reservoir situated at more than 5500 m depth which is hydraulically connected with the 9101 m deep KTB main hole, drilled some 250 m to the northeast of the pilot hole. While Ca and Sr contents of the extracted brines may be the result of water–rock interaction, Cl is most likely of external origin. The Cl is hypothesized to derive from geotectonic processes rather than to descending infiltration of paleo-seawater (evaporitic brines). The sampled fluids have probably migrated from a deeper reservoir to their present position since the Cretaceous–Tertiary period due to tectonic activity. However, several isotopic studies have identified an admixture of descending paleowaters down to more than 4000 m depth. The high 36Cl/Cl ratio of the fluids sampled during the long-term pumping test point to a host rock highly enriched in U–Th, unlike the sampled KTB country rocks. The fluid reservoir is believed to be in contact with the Falkenberg granite massif situated about 2 km to the E of the KTB holes, capable of supplying sufficient neutron flux for considerable subsurface production of 36Cl. The Na–Cl–(K-, SO 4) precursor fluids of the Ca–Na–Cl brines were produced in the course of extensive tectonic processes since the Late Caledonian within the Bohemian Massif.

Palaeoclimatic temperature signals — can they be washed out?

The present paper investigates the hydraulic conditions which could perturb a palaeoclimatically induced temperature signal in the underground. By a series of forward model analysis the behaviour of a Pleistocene Ice-Age-induced surface temperature change is analysed. It is shown that even at high Darcy fluid velocities of 5 × 10 −8 m s −1 the transient temperature wave remains preserved although altering its shape with depth and amplitude. The forward results were later on analysed by a backward process which inverts the temperature signal and ideally should reproduce the given temperature history. Since the inversion routine assumes pure diffusive conditions in a 1-D horizontally layered medium, large deviations did show up in the case of an advectively influenced subsurface. A proposed correction strategy, reducing the borehole temperature logs first for their steady-state advective component before applying the inversion process yields much smaller deviations and reasonable climatic signals even for Darcy fluid velocities of 10 −8 m s −1. Knowing that a palaeoclimatic temperature signal must be visible in subsurface, an earlier steady-state thermal study of the German Continental Deep Drilling Project has been improved. The actual successful forward fitting process accounts for advection, topography, lithological heterogeneities and a transient temperature signal induced by surface temperature changes. The last temperature log could be excellently fitted with a maximum temperature difference of only 0.3 K between 300 m and 3000 m. The model assumptions required a realistic distribution of the main lithologies. In the considered depth range the temperature field at KTB is strongly dominated by palaeoclimatic effects and by lithological heterogeneities. Thermal advection seems to be visible but of secondary importance only.

Thermobarometry and P–T path of garnet–aluminosilicate-bearing gneisses from the KTB drill core (Continental Deep-Drilling Project, Germany)

Thermobarometry and P–T path of garnet–aluminosilicate-bearing gneisses from the KTB drill core (Continental Deep-Drilling Project, Germany)

Ion Probe Oxygen Isotope Analysis of Quartz and Magnetite from the Biwabik Iron Formation, Minnesota

The oxygen isotopic compositions of coexisting quartz and magnetite have previously been measured, using conventional fluorination techniques, in samples from a number of Precambrian iron formations (e.g. Perry and Bonnischen, 1966; Perry et al., 1973). Their aim was to utilize equilibrium mineral pair geothermometry to infer temperatures of metamorphism and diagenesis of both recrystallized and relatively unaltered Precambrian chemical sediments. The present study has acquired in situ, high spatial resolution, ion probe oxygen isotope measurements of samples from the relatively undeformed Biwabik Iron Formation, Minnesota, in conjunction with detailed petrographic observation. This had the aim of testing the extent of isotopic equilibrium between this mineral pair to investigate the interplay of depositional signatures and modifications due to diagenetic recrystallization of initial precipitates. Methods . Detailed petrographic observation and compositional analyses were obtained of seven samples from cores 2, 5 and 7 from the Biwabik Iron Formation of the Mesabi Deep Drilling Project (details in Pfleider et al., 1968). Oxygen isotope analyses of these samples were then obtained using the Isolab 54 ion microprobe at the University of Manchester, UK (Saxton et al., 1996). The 1So/160 ratios were determined by secondary ionization mass spectrometry using a Cs + primary beam and the 81SOsMow values determined by calibration with standard materials (Lyon et al., 1995). Analysis transects of between 11 and 19 spots were made across quartz and magnetite in the selected areas within the chosen samples with crater sizes ranging from 20 to 60 Ixm in diameter and a few gm in depth. Results and discussion. Petrographic observation at high resolution identified magnetite as a late stage mineral, generally with a subhedral to euhedral crystal habit from 10 to 100 gm, which exhibited a cross-cutting relationship with all the other constituent phases. It was present in a number of textural associations including granule rims, replaced granules, disseminated crystals and crystalline aggregates. Quartz was present as a microcrystalline matrix mineral between the disseminated and aggregated magnetite crystals. Mean values for quartz and magnetite within each sample were calculated to enable the determination of the oxygen isotopic fractionation (AQM) between this coexisting mineral pair. These values are shown in Table 1. Mean quartz values range from 18.3 to 24.2 %0 and mean magnetite values range from -10.7 to -3 .6 %0. The calculated isotopic fractionations range from 25.6 to 33.6 %0. Our data have been plotted in Fig. 1 in conjunction with previously published oxygen isotope analyses of the quartz-magnetite mineral pair from the Biwabik Iron Formation (Perry and Bonnischen, 1966; Perry et al, 1973). Oxygen isotope ratios of quartz and magnetite from the metamorphosed Duluth contact zone and the transition zone between this and the relatively undeformed iron formation are shown by open circles (Perry and Bonnischen, 1966). Data from samples taken from the same cores as the present study (Perry et al., 1973) are plotted as solid diamonds and lie in a steeply dipping array towards lower quartz and higher magnetite values than the present results. An average fractionation of 24%0 was determined from this data. This is almost 10%o lower than the highest fractionation shown by the present study (open diamonds). This can be explained by a comparison of ion microprobe analysis and the conventional fluorination techniques that were used to generate the other data sets. Firstly, ion probe analysis eliminates the effects of contamination of

In-situ electrical conductivity and permeability of mid-crustal rocks from the KTB drilling : Consequences for high conductive layers in the earth crust

Freshly cored samples from a microprofile (7011–7013m in depth) of the German Continental Deep Drilling Project (KTB) were taken to measure the complex electrical conductivity σ (1 kHz up to 1 MHz), porosity, BET-surface, permeability and density. The porosity ranged about 1 vol%, while the permeability k varied from 16.05 µD to > 0.01 µD for in-situ pressure conditions. The permeability decreased about 2 orders in magnitude up to pressures of 200 MPa. Conductivity σ was measured in the same pressure range on 1 M NaCl saturated samples. Thin sections and SEM analysis revealed an enrichment of carbon and ilmenite (about 1 vol%) on inner cleavage cracks of mica, thus causing an unusual high σ (ranging from 4.2 × 10-3 S/m to 67 × 10-3 S/m) being orders of magnitude higher than normally measured on such types of rocks (about 300 × 10-6 S/m). An inverse pressure dependence of σ was detected on some of the samples. Electronic conduction was confirmed by least-squares-fits of model data to the frequency dispersion of the conductivity and by measuring the time dependence of the volume conductivity and its frequency dispersion. Thus the dominating role of the reconnected network of carbon and ilmenite on the enhanced volume conductivity was proved. An increase of the conductivity due to hydrofracturing by high pore fluid pressures plays a less important role.

On the origin of saline fluids in the KTB (continental deep drilling project of Germany)

Highly saline fluids were encountered during the German Continental Deep Drilling Project (KTB) from depths ranging between 2 and 3 km to about 9 km. The most reliable data were obtained from samples extracted during a long-term pumping test in the 4000-m deep KTB pilot hole. Some 460 m 3 Ca Na Cl brines with about 68 g l −1 total dissolved solids (TDS) and some 270 m 3 associated gases, mainly N 2 and CH 4 were pumped to the surface from the main fracture system situated near the bottom of the pilot hole. Geochemical and isotopic data support the hydraulic tests which suggest the presence of an open and large fluid reservoir at depth. The pumped fluids from this main fracture system were released from a deep reservoir situated at more than 5500 m depth which is hydraulically connected with the 9101 m deep KTB main hole, drilled some 250 m to the northeast of the pilot hole. While Ca and Sr contents of the extracted brines may be the result of water-rock interaction, Cl is most likely of external origin. The Cl is hypothesized to derive from geotectonic processes rather than to descending infiltration of paleo-seawater (evaporitic brines). The sampled fluids have probably migrated from a deeper reservoir to their present position since the Cretaceous-Tertiary period due to tectonic activity. However, several isotopic studies have identified an admixture of descending paleowaters down to more than 4000 m depth. The high 36ClCl ratio of the fluids sampled during the long-term pumping test point to a host rock highly enriched in U Th, unlike the sampled KTB country rocks. The fluid reservoir is believed to be in contact with the Falkenberg granite massif situated about 2 km to the E of the KTB holes capable of supplying sufficient neutron flux for considerable subsurface production of 36C1. The Na Cl (K , SO 4) precursor fluids of the Ca Na CI brines were produced in the course of extensive tectonic processes since the Late Caledonian within the Bohemian Massif.

Borehole instabilities in the KTB main borehole

Borehole instability has been a central problem for drilling operations and borehole measurements within the German Continental Deep Drilling Project (KTB) main borehole, which has been drilled entirely through crystalline rocks, mostly paragneisses and metabasites. The types of borehole instabilities observed were drilling‐induced tensile fractures, breakouts, and convergence zones. These were strongly dominated by foliate, graphitic gneisses with sometimes very low and anisotropic rock strength, unfavorably high and nonuniform horizontal stresses, and the effects of hydraulic interactions of the drill mud and formation fluids. The instability problems encountered in the KTB main borehole have clearly demonstrated that undergauge sections, which first appeared at depths below 7500 m and probably resulted from time‐dependent convergence of wet crystalline rocks, had a much greater impact on the drilling operations than all the breakouts or drilling‐induced tensile fractures.

Formation of ore minerals in metamorphic rocks of the German continental deep drilling site (KTB)

The German Continental Deep Drilling Program (KTB) drilled a 9.1 km deep profile through amphibolite facies metamorphic rocks and reached in situ temperatures of 265°C. Each lithologic unit is characterized by typical ore mineral assemblages related to the regional metamorphic conditions. Paragneisses contain pyrrhotite + rutile + ilmenite ± graphite, metabasic units bear ilmenite + rutile + pyrrhotite ± pyrite, and additionally, the so‐called variegated units yield pyrrhotite + titanite assemblages. In the latter unit, magnetite + ilmenite + rutile + titanite assemblages related to the lower amphibolite facies breakdown of ilmenite‐hematite solid solution also occur locally. Retrograde hydrothermal mineralization which commenced during Upper Carboniferous times is characterized by the following geochemical conditions: (1) low saline Na‐K‐Mg‐Cl fluids with sulfur and oxygen fugacities at the pyrite‐pyrrhotite buffer and temperatures of 400–500°C, (2) fluids with CO2, CH4±N2, andpH, Eh, sulfur, and oxygen fugacity in the stability field of graphite + pyrite at temperatures of 280–350° and (3) moderate to high saline Ca‐Na‐Cl fluids with CH4+ N2; sulfur and oxygen fugacity are in the stability field of pyrrhotite at temperatures <300°C. The latter environment is confirmed by in situ conditions found at the bottom of the deep drilling. Monoclinic, ferrimagnetic pyrrhotite is the main carrier of magnetization which disappears below about 8.6 km, corresponding to in situ temperatures of about 250°C. Below this depth, hexagonal antiferromagnetic pyrrhotite with a Curie temperature of 260°C is the stable phase. Temperature‐dependent transformation of pyrrhotite and the reaching of its Curie isotherm within the Earth crust are one of the striking results of the KTB deep drilling project.

A magnetotelluric investigation of the San Andreas Fault at Carrizo Plain, California

High quality, wide‐band magnetotelluric data were collected along two profiles crossing the San Andreas fault at Carrizo Plain, California for crustal imaging as part of the San Andreas Deep Drilling Project. Two‐dimensional inversions of the data indicate that the upper crustal part of the San Andreas fault does not appear here as an anomalously conductive zone. Additionally, a broad resistive zone under the Temblor Mountains (east of the fault) suggests resistive crystalline or metamorphic rocks may be present here as opposed to the more conducting Franciscan assemblage, contradicting the generally‐accepted geologic model.

Comparative K–Ar and Rb–Sr age determinations of retrograde processes on rocks from the KTB deep drilling project

Conventional K–Ar and Rb–Sr age determinations were carried out on fine mineral fractions of the KTB rocks and of rocks from the surrounding area in order to get an idea of the timing of retrograde processes which the rocks had suffered in the Late Variscan and afterwards. Coarse-grained mica minerals were used as reference minerals. It can be demonstrated that conventional K–Ar dating on fine mineral fractions is a useful tool to date retrograde processes in crystalline rocks. For methodical reasons the Rb–Sr method is less suitable. A complex age pattern was found which could be divided into different age groups representing different periods of either penetrative retrograde overprint or formation and reactivation of distinct cataclastic fault zones. Whereas the rocks of the KTB have undergone a penetrative retrograde overprint during the Permo-Triassic without any visible deformation, the Jurassic brought a first reactivation of cataclastic fault zones. In Cretaceous time an overprint led to a pronounced second reactivation of cataclastic fault zones. This latter process turned out to be the important one for the stacking and a repetition of the drilled profile in the KTB. The data and interpretations obtained on the fine mineral fractions coincide excellently with fission track data on sphene from the drill site, with sedimentological records concerning a larger regional scale and with hydrothermal alterations and ore-forming events in mid-Europe.

Thermobarometry and P–T path of garnet–aluminosilicate-bearing gneisses from the KTB drill core (Continental Deep-Drilling Project, Germany)

Garnet zoning characteristics, reaction microstructures, and thermobarometric studies document a multistage P–T evolution for the paragneisses of the KTB drill core. The prograde heating and burial path led through the sillimanite stability field before it entered the kyanite field close to the P–T peak. The uppermost paragneiss–amphibolite unit (0–560 m) reached peak conditions at 650–670 °C and 7–8 kbar. The units below (560–3574 m) show higher peak temperatures of 680–720 °C, with maximum pressures between 8 and 9 kbar. This P–T discontinuity implies a tectonic contact, but otherwise, the two sections of the drill core do not show evidence for a separate metamorphic history and probably lay on a common crustal paleogeotherm at peak conditions. Homogenization of Mg, Fe, and Mn in garnet at or near peak conditions points to a significant time interval between burial and subsequent decompression. Accordingly, the prograde metamorphic episode must be significantly older than the 380–370 Ma decompression and cooling period, possibly mid-Ordovician. Following nearisothermal decompression with partial breakdown of garnet and growth of sillimanite, a second, previously unrecognized pressure peak was reached at 5.7– 6.7 kbar and temperatures of around 590 °C. A late low-pressure imprint is documented by the local presence of andalusite. The lack of a continuous metamorphic P–T gradient in the drilled crustal section either requires strong postmetamorphic tilting of isograds and/or small-scale intraformational stacking of crustal slices of similar metamorphic grade.

Using borehole breakouts to constrain the complete stress tensor: Results from the Sijan Deep Drilling Project and offshore Santa Maria Basin, California

We use borehole breakouts in nonvertical drill holes to constrain the directions of the three principal stresses and their relative magnitudes. In this paper we start by modifying previously published breakout selection criteria to work with highly deviated borehole data. We present a forward modeling technique using genetic algorithms and a nongradient N‐dimensional optimizer to find the best fitting stress state for a set of breakout data. The stress state is parameterized by three Euler angles and the stress state ratio ϕ. A technique is developed to determine the 95% confidence weighted misfit between a model and the data. We then map out the 95% misfit confidence limits on the best fitting stress state. This technique is applied to data published by Qian and Pedersen [1991]. Removing their constraint of a vertical principal stress direction reduces the misfit between the stress state and the breakout data. We find that the best fitting stress state they report with a vertical principal stress direction lies outside our 95% confidence limits. We also invert breakouts in the offshore Santa Maria Basin, California. These data show a “thrust faulting” stress state with the maximum principal stress, S1, at N148.5°E plunging 31.5°. The 95% confidence range for the azimuth of S1 ranges from N143.0°E to N198.1°E. The stress ratio ϕ was found to be 0.8210.5841.

Nd-Sr isotopic and trace element study of rocks and fluids from the continental deep drilling Project (KTB), Germany

Geochemical analyses were interpreted on the dominant lithological units and on a deep crustal fluid from the Continental Deep Drilling Project (KTB) Pilot Hole, situated at the western margin of the Variscan Bohemian Massif. The biotite gneiss (from 384 m depth) shows a rare earth element pattern very similar to the European shale composite with Nd model ages of 940 Ma (CHUR) and 1.4 Ga (DM). The lamprophyre dike in the upper profile (1549 m), a nepheline and olivine normative basalt, is geochemically and isotopically similar to rocks from the Tertiary Central European Volcanic Province. The lower metabasite sequence (3575–4000 m), with an intrusion age of approximately 500 Ma, is made up primarily of highly metamorphosed subalkalic olivine basalts. The geochemical characteristics of the metabasites are a (La/Yb)N of 5–10, an La concentration of 20–50 times chondrite as well as (87Sr/86Sr)i of 0.7035–0.7038 and ɛeNd(T) of 4–6. These values suggest a depleted mantle source for the igneous precursors, evolving by assimilation-fractional crystallization processes with up to 25% of upper crust into the ultramafic, basaltic, and intermediate rock types of the metabasite sequence. The strong geochemical and chronological similarities between the KTB metabasites and rocks from the Munchberg Massif suggest that these units belong to the same lithological complex. The high salinity as well as the radiogenic 87Sr/86Sr ratio of 0.709413 in the KTB fluid from 4000 m depth might be the result of migrating fluids reacting with the regional Permo-Mesozoic evaporite deposits, followed by extensive Sr isotopic exchange with the upper crust.

Scaling behaviour of vertical magnetic susceptibility and its fractal characterization: an example from the German continental deep drilling project (KTB)

The variations of rock magnetism reflect the geological inhomogeneities of the earth's crust, i.e. its petrological-mineralogical and structural organization. The present state of the crust bears meaningful information of its past dynamic processes and evolution. We analysed magnetic susceptibility data series from the boreholes of the German Continental Deep Drilling Project (KTB). By means of spectral and rescaled-range (R/S) analyses we could detect a scaling behaviour of magnetic data series and quantify it in fractal terms. In particular, the R/S method yields more precise results than the Fourier analysis and leads to Hurst coefficients H > 0.5, which means that the magnetic variations exhibit some persistence with depth. Because of the relation between rock magnetism and crustal features, we suggest that the magnetic vertical inhomogeneities in the KTB area can be described by a self-affine model with H ≌ 0.8, corresponding to a fractal dimension D ≌ 1.2.

Nd–Sr isotopic and trace element study of rocks and fluids from the continental deep drilling Project (KTB), Germany

Nd–Sr isotopic and trace element study of rocks and fluids from the continental deep drilling Project (KTB), Germany

Scaling behaviour of vertical magnetic susceptibility and its fractal characterization: an example from the German Continental Deep Drilling Project (KTB)

Scaling behaviour of vertical magnetic susceptibility and its fractal characterization: an example from the German Continental Deep Drilling Project (KTB)

Application of continuum analysis to borehole gamma-ray spectra obtained from the German continental deep drilling project : A. N. Thakur, J. R. Arnold & J. S. Schweitzer, Nuclear Geophysics, 9(1), 1995, pp 19–33

Application of continuum analysis to borehole gamma-ray spectra obtained from the German continental deep drilling project : A. N. Thakur, J. R. Arnold & J. S. Schweitzer, Nuclear Geophysics, 9(1), 1995, pp 19–33

The statistical nature of the upper continental crystalline crust derived from in situ seismic measurements

SUMMARY In situ measurements in the main borehole of the German continental deep drilling project (KTB) point to the statistical nature of the continental crystalline crust between 286 and 6000 m depth. P-wave, S-wave and density logs display deviations from Gaussian distribution functions that may be partly due to the approximately bimodal nature of the lithology, because the crust consists mainly of metabasites and paragneisses. The autocovariance functions and power spectra of the logs indicate that the velocity and density perturbations have a complex statistical nature, but the autocovariance functions can be approximated by a superposition of two exponential functions with correlation lengths of 1 m and 20 m. The associated relative standard deviations for each exponential function are about 3 per cent of the mean for the sonic logs, and nearly 6 per cent of the mean for the density. A vertical seismic profile measured between 3000 and 6000 m depth shows small traveltime fluctuations, which can be explained by a generalization of a recently published scattering theory for transverse wavefield fluctuations to include the case of longitudinal fluctuations. The theory is valid for harmonic scalar plane-wave propagation in random media with isotropic statistics, and scattering mainly in the forward direction. One important theoretical result is that, although longitudinal and transverse autocovariance functions of amplitudes and phases differ, the expectations of their respective autovariances are the same. The observed traveltime fluctuations agree with theoretical predictions based on normally distributed velocity perturbations that are described by the average of the autocovariance functions of the two P-wave logs measured from 286 to 3000 m and between 3000 and 6000 m depth. Owing to the lack of traveltime information that can be averaged, and because the traveltime fluctuations predicted by the theory do not differ sufficiently for 2-D and 3-D random perturbations, no statement can be made on how anisotropic the observed random velocity perturbations are. The observed heterogeneities are, however, consistent with the fact that reflection seismic profiles reveal a nearly transparent upper crystalline crust.

Potential field power spectrum inversion for scaling geology

We propose a method for inverting the power spectrum of gravity and magnetic data. The method is demonstrated on aeromagnetic and borewell data from the German Continental Deep Drilling Project (KTB). Density and susceptibility distributions in the Earth's crust exhibit scaling behavior with power spectra proportional to ƒ−β, where f is the wavenumber and β is the scaling exponent of the source distribution. We model the sources of the potential field by a random function with scaling properties, defined on a half‐space with its top at a specified depth beneath the observation plane. Comparing the theoretical power spectrum for this model with the power spectrum of the measured data, we obtain the best values for the depth to source and the scaling exponent as a global minimum of the misfit function. Despite the simplicity of the model, it offers a new understanding of the factors influencing the shape of the potential field power spectrum. In particular, the low wavenumber part of the power spectrum can be dominated by the scaling properties of the source distribution and not by the depth to some kind of basement. The scaling exponent of the field varies with the type of surface geology. The question of whether the scaling exponent can actually be used to identify different types of geology gives an interesting new aspect to power spectrum inversion.