Pitfalls in Nonlinear Inversion

— We discuss and illustrate graphically with simple 2-D problems, four common pitfalls in geophysical nonlinear inversion. The first one establishes that the Lagrange multiplier, used to incorporate a priori information in the geophysical inverse problem, should be the largest value still compatible with a reasonable data fitting. This procedure should be used only when the interpreter is sure about the importance of the a priori information used to stabilize the inverse problem relative to the geophysical observations. Because this is rarely the case, the user should use the smallest Lagrange multiplier still producing stable solutions. The second pitfall is an attempt to automatically estimate the Lagrange multiplier by decreasing it along the iterative process used to solve the nonlinear optimization problem. Consequently, at the last iteration, the Lagrange multiplier may be so small that the problem may become ill-posed and any computed solution in this case is meaningless. The third pitfall is related to the incorporation of a priori information by a technique known as “Jumping.” This formulation, from the viewpoint of the class of Acceptable Gradient Methods, is incomplete and may lead to a premature halt in the iteration, and, consequently, to solutions far from the true one. Finally, the fourth pitfall is an inadequate convergence criterion which stops the iteration when the data misfit drops just below the noise level, irrespective of the fact that the functional to be minimized may not have attained its minimum. This means that the a priori information has not been completely incorporated, so that this stopping criterion partially neutralizes the effect of the stabilizing functional, and opens the possibility of obtaining unstable, meaningless estimates.     

The physical volcanology of the 1600 eruption of Huaynaputina, southern Peru

Volcán Huaynaputina is a group of four vents located at 16°36'S, 70°51'W in southern Peru that produced one of the largest eruptions of historical times when ~11 km³ of magma was erupted during the period 19 February to 6 March 1600. The main eruptive vents are located at 4200 m within an erosion-modified amphitheater of a significantly older stratovolcano. The eruption proceeded in three stages. Stage I was an ~20-h sustained plinian eruption on 19-20 February that produced an extensive dacite pumice fall deposit (magma volume ~2.6 km³). Throughout medial-distal and distal parts of the dispersal area, a fine-grained plinian ashfall unit overlies the pumice fall deposit. This very widespread ash (magma volume ~6.2 km³) has been recognized in Antarctic ice cores. A short period of quiescence allowed local erosion of the uppermost stage-I deposits and was followed by renewed but intermittent explosive activity between 22 and 26 February (stage II). This activity resulted in intercalated pyroclastic flow and pumice fall deposits (~1 km³). The flow deposits are valley confined, whereas associated co-ignimbrite ash fall is found overlying the plinian ash deposit. Following another period of quiescence, vulcanian-type explosions of stage III commenced on 28 February and produced crudely bedded ash, lapilli, and bombs of dense dacite (~1 km³). Activity ceased on 6 March. Compositions erupted are predominantly high-K dacites with a phenocryst assemblage of plagioclase>hornblende>biotite>Fe-Ti oxides-apatite. Major elements are broadly similar in all three stages, but there are a few important differences. Stage-I pumice has less evolved glass compositions (~73% SiO₂), lower crystal contents (17-20%), lower density (1.0-1.3 g/cm³), and phase equilibria suggest higher temperature and volatile contents. Stage-II and stage-III juvenile clasts have more evolved glass (~76% SiO₂) compositions, higher crystal contents (25-35%), higher densities (up to 2.2 g/cm³), and lower temperature and volatile contents. All juvenile clasts show mineralogical evidence for thermal disequilibrium. Inflections on a plot of log thickness vs area^1/2 for the fall deposits suggest that the pumice fall and the plinian ash fall were dispersed under different conditions and may have been derived from different parts of the eruption column system. The ash appears to have been dispersed mainly from the uppermost parts of the umbrella cloud by upper-level winds, whereas the pumice fall may have been derived from the lower parts of the umbrella cloud and vertical part of the eruption column and transported by a lower-altitude wind field. Thickness half distances and clast half distances for the pumice fall deposit suggests a column neutral buoyancy height of 24-32 km and a total column height of 34-46 km. The estimated mass discharge rate for the ~20-h-long stage-I eruption is 2.4᎒⁸ kg/s and the volumetric discharge rate is ~3.6᎒⁵ m³/s. The pumice fall deposit has a dispersal index (Hildreth and Drake 1992) of 4.4, and its index of fragmentation is at least 89%, reflecting the dominant volume of fines produced. Of the 11 km³ total volume of dacite magma erupted in 1600, approximately 85% was evacuated during stage 1. The three main vents range in size from ~70 to ~400 m. Alignment of these vents and a late-stage dyke parallel to the NNW-SSE trend defined by older volcanics suggest that the eruption initiated along a fissure that developed along pre-existing weaknesses. During stage I this fissure evolved into a large flared vent, vent 2, with a diameter of approximately 400 m. This vent was active throughout stage II, at the end of which a dome was emplaced within it. During stage III this dome was eviscerated forming the youngest vent in the group, vent 3. A minor extra-amphitheater vent was produced during the final event of the eruptive sequence. Recharge may have induced magma to rise away from a deep zone of magma generation and storage. Subsequently, vesiculation in the rising magma batch, possibly enhanced by interaction with an ancient hydrothermal system, triggered and fueled the sustained Plinian eruption of stage I. A lower volatile content in the stage-II and stage-III magma led to transitional column behavior and pyroclastic flow generation in stage II. Continued magma uprise led to emplacement of a dome which was subsequently destroyed during stage III. No caldera collapse occurred because no shallow magma chamber developed beneath this volcano.     

Two Brazilian archaeological sites investigated by GPR: Serrano and Morro Grande

The application of the ground penetrating radar (GPR) at two archaeological sites, Serrano and Morro Grande, situated in Araruama County, Rio de Janeiro, Brazil, aids the study of a prehistoric indigenous culture, associated with the “Tupinambá” that inhabited the region during prehistoric times.The archaeological remains of the study area are mainly characterized by pottery artifacts for several uses, including funerary urns, which were buried within layers of sand and clay. Several profiles were acquired using a RAMAC system, with a 200 and 400 MHz frequency antennae. At the Serrano site, the profiles were acquired around some partially exposed pottery shards, due to sand exploitation. The resultant profiles provided a response model to guide the interpretation of new profiles acquired at other sites in the area, which present similar characteristics.The results showed the great importance of the dielectric permittivity contrast which exists between the targets and the host media, in order for possibly significant features to be identified in radar data.     

Pegmatite Emplacement in the Seridó Belt, Northeastern Brazil: Late Stage Kinematics of the Brasiliano Orogen

Geometric and kinematic analysis was performed in an area located in the central part of the Seridó Belt (NE Brazil), where supracrustal rocks affected by polyphase deformation are well exposed. The first event recognized in this area (and regionally known as the D₂ deformation) is characterized by top to the south thrust tectonics while a second one (D₃ deformation) is marked by upright folds, strike-slip or transpressive shear zones and the development of flower structures. Major pegmatite swarms were emplaced during and late as regards the second event (dated ca. 580 Ma), being part of the Brasiliano orogeny; similar dyke swarms are known from the Nigerian Shield. These pegmatite swarms provide reliable kinematic markers of the late evolutionary stage of the Neoproterozoic Trans-Sahara-Borborema collisional belt. Mineralogical, geometric and kinematic features support two stages of pegmatite emplacement during the strike-slip event: (i) older, syn-D₃ homogeneous pegmatites intruded mostly along lithological and structural discontinuities, such as foliation surfaces; (ii) late, D₃ heterogeneous pegmatites were emplaced along tension gashes and other dilation structures. The heterogeneous pegmatites are economically more important, being exploited for precious metals and stones, as well as industrial minerals.     

Fine sediment transport and accumulations at the mouth of the Seine estuary (France)

A comprehensive study of fine sediment transport in the macrotidal Seine estuary has been conducted, including observations of suspended particulate matter (SPM), surficial sediment, and bathymetric data, as well as use of a three dimensional mathematical model. Tide, river regime, wind, and wave forcings are accounted. The simulated turbidity maximum (TM) is described in terms of concentration and location according to tidal amplitude and the discharge of the Seine River. The TM is mainly generated by tidal pumping, but can be concentrated or stretched by the salinity front. The computed deposition patterns depend on the TM location and are seasonally dependent. The agreement with observations is reasonable, although resuspension by waves may be overestimated. Although wave resuspension is likely to increase the TM mass, it generally occurs simultaneously with westerly winds that induce a transverse circulation at the mouth of the estuary and then disperse the suspended material. The resulting effect is an output of material related to wind and wave events, more than to high river discharge. The mass of the computed TM remains stable over 6 months and independent of the river regime, depending mainly on the spring tide amplitude. Computed fluxes at different cross-sections of the lower estuary show the shift to the TM according to the river flow and point out the rapidity of the TM adjustment to any change of river discharge. The time for renewing the TM by riverine particles has been estimated to be one year.     

Late- to post-orogenic basins of the Pan-African – Brasiliano collision orogen in southern Africa and southern Brazil

Late- to post-orogenic basins formed on both sides of the Pan-African – Brasiliano orogen when the Congo and Kalahari Cratons collided with the Rio de la Plata Craton during the formation of western Gondwana. Trace fossil evidence and radiometric age dating indicate that deposits on both sides are coeval and span the Cambrian–Precambrian boundary. A peripheral foreland basin, the Nama Basin, developed on the subducting southern African plate. Lower, craton-derived fluviomarine clastics are overlain by marine platform carbonates and deltaic flysch derived in part from the rising subduction complex along the northern (Damara Belt) and western (Gariep Belt) orogenic margins. Rare, thin volcanic ash layers (tuffs and cherts) are present. Upper sediments consist of unconformable red molasse related to collisional orogenesis. Orogenic loading from the north and west led to crustal flexure and the formation of a remnant ocean that drained to the south and closed progressively from north to south. During final collision SE-, E- and NE-verging nappes overrode the active basin margins. Although younger than most of the post-orogenic magmatism, its setting on the cratonic edge of the subducting plate precluded marked volcanism or granitic intrusion, the only exception being the youngest intrusions of the Kuboos-Bremen Suite dated at 521±6 Ma to 491±8 Ma. Two foreland-type basins, perhaps faulted remnants of a much larger NE–SW elongated retroarc foreland basin, are found west of the Dom Feliciano Belt on the edge of the Rio de la Plata Craton in southern Brazil. In the southern Camaqua Basin, basal fluvial deposits are followed by cyclical marine and coarsening-up deltaic deposits with a notable volcanic and volcaniclastic component. This lower deformed succession, comprising mainly red beds, contain stratabound Cu and Pb–Zn deposits and is overlain unconformably by a fluviodeltaic to aeolian succession of sandstones and conglomerates (with minor andesitic volcanics), derived primarily from an eastern orogenic source and showing southerly longitudinal transport. In the northern Itajaí Basin, sediments range from basal fluvial and platform sediments to fining-up submarine fan and turbidite deposits with intercalated acid tuffs. The Brazilian basins had faulted margins off which alluvial fans were shed. They also overlie parts of the Ribeira Belt. Thrust deformation along the orogenic margin bordering the Dom Feliciano Belt was directed westward in the Camaqua and Itajaí basins, but reactivated strike-slip and normal faults are also present. Late- to post-orogenic granitoids and volcanics of the Dom Feliciano Belt, ranging in age from 568±6 Ma to 529±4 Ma, occur in the foreland basins and are geochemically related to some of the synsedimentary volcanics.     

Controls on Quaternary coastal evolution of the east-northeastern coast of Brazil: roles of sea-level history, trade winds and climate

East-northeastern Brazil has a wave-dominated, micro- to meso-tidal coast, lying entirely within the southern Atlantic trade wind belt. Integration of geologic mapping, radiocarbon dating and vibracoring data shows that the Quaternary coastal evolution of this area was controlled by three major factors: (1) sea-level history; (2) trade winds; and (3) climate change.

Sea-level history. Along the east-northeastern coast of Brazil, relative sea level has fallen approximately 5 m during the last 5000 y. Correlation of this sea-level history with the evolution of beach-ridge, lagoonal and coastal plain deposits shows that: (1) sea-level rise favours the formation of barrier island—lagoonal systems and the construction of intralagoonal deltas; (2) sea-level lowering is not conductive to barrier island formation. Rather, lagoons and bays become emergent and beach-ridge plains rapidly prograde.

Trade winds. Sediment dispersal systems along the coastal zone of east-northeastern Brazil have been highly persistent since Pleistocene time, as deduced from beach-ridge orientation. This persistence results from the fact that sediment dispersal in wave-dominated settings is ultimately controlled by atmospheric circulation which, for the east-northeastern coast of Brazil is associated with the South Atlantic high-pressure cell. The remarkable stability of this cell through time, has allowed the accumulation of extensive beach-ridge plains at the longshore drift sinks located along the coast.

Climate change. Effects of Quaternary climate changes on coastal sedimentation are twofold. Climate changes may affect rainfall patterns, thus exerting an important control on coastal dune development. Along the coast of northeastern Brazil, active coastal dunes are only present in those areas in which at least four consecutive dry months occur during the year. Mapping of these areas has shown that dune development during the Holocene has been episodic, these episodes being probably controlled by variations in rainfall patterns associated with climate changes. Secondly, despite its overall stability, the position of the high-pressure cell has experienced small shifts in position during the Holocene in response to climate changes. Changes in wind direction associated with these shifts have induced modifications in the coastal dispersion system, which are recorded in the strandplains as small truncations in the beach-ridge alignments.

These results have important implications in understanding accumulation of ancient sandstone shoreline sequences.     

Observational study of the seasonality of the submonthly and intraseasonal signal over the tropics

Summary Atmospheric variability in outgoing long-wave radiation (OLR) and tropospheric relative vorticity (VOR) over the South American region was studied from 1979 to 1996 using the complex Morlet wavelet function. The analyses focus on spatial variation in intraseasonal and submonthly scales. Scalograms were used to measure submonthly intraseasonal oscillations in convection, which were found to be predominant in the tropical regions. However, 7-day and 15-day oscillations were observed at tropical and extratropical latitudes in spring and winter, indicating that transient disturbances play a more prominent role. Regarding VOR, tropical energy intensities were highest in the spring and summer, whereas subtropical and extratropical energy intensities were highest in the autumn and winter. The dynamics of the 25-day and 45-day VOR oscillations indicates a possible correlation with Rossby waves over the eastern tropical Pacific Ocean, mainly during the summer. During winter, the 7-day and 15-day VOR oscillations are more frequent at higher latitudes and are enhanced along storm tracks. It was also observed that convection amplitudes in the regions of maximum intensity change appreciably from year to year and from season to season, showing that the behavior of the submonthly and intraseasonal oscillations is nonperiodic and correlates strongly with El Ni?o/Southern Oscillation years. These results confirm the efficiency of wavelet analysis for time-scale studies of atmospheric variability.     

Images of Gradual Millimeter Emission and Multi-Wavelength Observations of the 17 august 1994 Solar Flare

We present a comprehensive analysis of the 17 August 1994 flare, the first flare imaged at millimeter (86 GHz) wavelengths. The temporal evolution of this flare displays a prominent impulsive peak shortly after 01:02 UT, observed in hard X-rays and at microwave frequencies, followed by a gradual decay phase. The gradual phase was also detected at 86 GHz. Soft X-ray images show a compact emitting region (20), which is resolved into two sources: a footpoint and a loop top source. Nonthermal emissions at microwave and hard X-ray wavelengths are analyzed and the accelerated electron spectrum is calculated. This energy spectrum derived from the microwave and hard X-ray observations suggests that these emissions were created by the same electron population. The millimeter emission during the gradual phase is thermal bremsstrahlung originating mostly from the top of the flaring loop. The soft X-rays and the millimeter flux density from the footpoint source are only consistent with the presence of a multi-temperature plasma at the footpoint.     

A current ribbon model for energy storage and release with application to the flare of 7 January 1992

Observations of the flare on 7 January 1992 are interpreted using a topological model of the magnetic field. The model, developed here, applies a theory of three-dimensional reconnection to the inferred magnetic field configuration for 7 January. In the model field a new bipole ( 10²¹ Mx) emerges amidst pre-existing active region flux. This emergence gives rise to two current ribbons along the boundaries (separators) separating the distinct, new and old, flux systems. Sudden reconnection across these boundary curves transfers 3 ×10²⁰ Mx of flux from the bipole into the surrounding flux. The model also predicts the simultaneous (sympathetic) flaring of the two current ribbons. This explains the complex two-loop structure noted in previous observations of this flare. We subject the model predictions to comparisons with observations of the flare. The locations of current ribbons in the model correspond closely with those of observed soft X-ray loops. In addition the footpoints and apexes of the ribbons correspond with observed sources of microwave and hard X-ray emission. The magnitude of energy stored by the current ribbons compares favorably to the inferred energy content of accelerated electrons in the flare.