Search

Reciprocal acoustic transmissions are analyzed to determine the general circulation of the region between Bermuda and Puerto Rico. Six tomographic transceivers were moored from March 1991 to March 1992 in the region centered at 25°N, 66°W during the Acoustic Mid‐Ocean Dynamics Experiment (AMODE). Large‐scale range averages (over 300 to 700 km sections) of temperature and velocity and large‐scale areal averages of relative vorticity have been estimated through inversion of tomographic travel time data. The barotropic and first baroclinic mode are well resolved by the acoustic sampling, with poorer resolution of the second baroclinic mode. The 300‐day mean circulation of the region indicates a band of westward flow of a few cm/s in the surface and thermocline waters. An active and resolvable mesoscale eddy field is present, with variability typically dominated by motions with spatial scales of 100–200 km, and with a general westward drift of mesoscale eddy features. The tomographic observations have been co...

A low‐frequency acoustic source suspended from R/P FLIP approximately 340 nautical miles WSW of San Diego transmitted to receivers 90 to 10 000 km distant during the Acoustic Engineering Test of the Acoustic Thermometry of Ocean Climate (ATOC) Program. The source was sus‐pended for 7 days during November 1994 near the depth of the sound channel axis (about 650 m) in water over 4000 m deep, in order to avoid near‐source bottom interactions. The source transmitted a phase‐coded m‐sequence with a center frequency of 75 Hz and a digit length of 27 ms [Metzger et al., this meeting]. Measured receptions on five bottom‐mounted SOSUS receivers at ranges from 300–4000 km, on two vertical line array receivers at ranges of 90 and 3300 km, and on a sonobuoy modified to have the hydrophone on the sound channel axis at about 10 000‐km range, are compared with ray theoretic, adiabatic normal mode, and broadband parabolic equation predictions. [Work supported by the Strategic Environmental Research and Development Program through ARPA.]

Time series of ray travel times were obtained at 350‐, 410‐, and 670‐km ranges in the western North Atlantic during the 1991–2 Acoustic Mid‐Ocean Dynamics Experiment (AMODE). Transmissions were recorded for approximately 300 days between six transceivers in a pentagonal array. Sound‐speed variability is separated from current variability by calculating the sum of reciprocal travel times. Both phase‐locked and narrow‐band internal‐tide sound‐speed variability, caused by the internal‐tide isotach displacement, are observed by the sum travel times. The description of the acoustic array as a high‐directivity antenna for the incident internal tide will be given. Beamforming the internal tide M2 and K1 harmonic constants determined on each of the 15 acoustic paths suggests two origins of significant internal tide generation are the Blake Escarpment and the continental shelf north of Puerto Rico. The nontidal, high‐frequency variability (≳1 cpd) is due to internal‐wave sound‐speed and current variability.

Time series of ray travel times were obtained at 350‐, 410‐, and 670‐km ranges in the western North Atlantic during the 1991–2 Acoustic Mid‐Ocean Dynamics Experiment (AMODE). Transmissions were recorded for approximately 300 days between six transceivers in a pentagonal array. Sound‐speed (current) variability is observed by calculating the sum (difference) of reciprocal travel times. The sum and difference of reciprocal travel times are high‐pass filtered by removing a daily average. The barotropic‐tide current is measured by the differential travel times. Both phase‐locked and narrow‐band internal‐tide sound‐speed variability, caused by the internal‐tide isotach displacement, are observed by the sum travel times. The acoustic array acts as a high‐directivity antenna for the incident internal tide. The observed internal tide is likely generated at the continental shelf surrounding the North American Basin, or perhaps the Mid‐Atlantic Ridge. The nontidal, high‐frequency variability (≳1 cpd) is due to internal‐wave sound‐speed and current variability.

Large-scale depth-integrated currents and relative vorticity were measured in the central North Pacific Ocean during summer 1987 using long-range reciprocal acoustic transmissions between transceivers in a triangle approximately 1000 km on a side. Inverse techniques were used to estimate the depth-averaged (barotropic) current bihourly at 4-day intervals from differential travel times. Tidal constituent amplitudes and phases found from the acoustically determined currents agree with those found from current meters and with the tidal models of Schwiderski (1980) and Cartwright et al. (1992), providing confirmation that the tomographically derived barotropic currents are correct within the expected uncertainties. The estimated low-frequency, large-scale currents are compared with depth-averaged currents determined by point measurements using current meters and bottom-mounted electrometers. Meridional and zonal currents are calculated using the topographic Sverdrup balance with the Fleet Numerical Oceanography Center wind field. The measured time derivative of the areally averaged relative vorticity is shown to be insignificant to the Sverdrup balance. Currents and vorticity calculated using the Sverdrup balance are an order of magnitude smaller than the observations. The magnitude and variability of the large-scale currents and vorticity determined from the Semtner and Chervin (1988) eddy-resolving model of ocean circulation are similar to the direct measurements.

The velocity structure of Jasper Seamount was modeled using one- and three-dimensional inversions of P wave travel times. The results represent the first detailed seismic images of a submerged, intraplate volcano. Two seismic refraction experiments were completed on Jasper Seamount, incorporating ocean bottom seismometers and navigated seafloor shots. The P wave travel times were first used to compute a one-dimensional velocity profile which served as a starting model for a three-dimensional tomographic inversion. The seamount P velocities are significantly slower than those observed in typical oceanic crust at equivalent subbasement depths. This suggests that Jasper Seamount is constructed predominantly of extrusive lavas with high average porosity. The velocity models confirm morphological predictions: Jasper Seamount is a shield volcano with rift zone development. High seismic velocities were detected beneath the large radial ridges while low velocities characterize the shallow summit and flanks. Comparisons between P velocity models of Jasper Seamount and the island of Hawaii reveal that these two shield volcanoes are not structurally proportional. Jasper Seamount is far smaller than Hawaii, yet both volcanoes exhibit an outer extrusive layer of similar thickness. This suggests that seamount size influences the intrusive/extrusive proportions; density equilibrium between melt and country rock may explain this behavior.

Broadband acoustic signals transmitted from a moored 250-Hz source to a 3-km-long vertical line array of hydrophones 1000 km distant in the north central Pacific Ocean were used to determine the amount of information available from tomographic techniques used in the vertical plane connecting a source-receiver pair. A range-independent, pure acoustic inverse to obtain the sound speed field using travel time data from the array is shown to be possible by iterating from climatological data without using any information from concurrent environmental measurements. Range-dependent inversions indicate resolution of components of oceanic variability with horizontal wavelengths shorter than 50 km, although the limited spatial resolution of concurrent direct measurements does not provide a strong cross-validation, since the typical cast spacing of 20–25 km gives a Nyquist wavelength of 40–50 km. The small travel time signals associated with high-wavenumber ocean variability place stringent but achievable requirements on travel time measurement precision. The forward problem for the high-wavenumber components of the model is found to be subject to relatively large linearization errors, however, unless the sound speed field at wavelengths greater than about 50 km is known from other measurements or from a two-dimensional tomographic array. The high-ocean-wavenumber resolution that is in principle available from tomographic measurements is therefore achievable only under restricted conditions.

Objective mapping can remove the equatorial singularity from the problem of estimating geostrophic shear from noisy density measurements. The method uses the complete thermal wind relation, so it is valid uniformly on and off the equator. Errors in the thermal wind balance are due to neglected terms in the momentum balance, which are treated as noise in the inverse problem. The question of whether the geostrophic balance holds near the equator is restated as a need to estimate the size of the ageostrophic noise in the thermal wind equation. Objective mapping formalizes the assumptions about the magnitudes and scales of the geostrophic currents and about the magnitudes and scales of the ageostrophic terms and measurement errors. The uncertainty of the velocity estimates is calculated as part of the mapping and depends on the signal to noise ratio (geostrophic density signal to ageostrophic “noise”) in the data, as well as the station spacing and the scales assumed for the geostrophic velocities. The method is used to map zonal velocity from a mean Hawaii-Tahiti Shuttle density section. These are compared with previous velocity estimates for the same dataset calculated using other techniques. By choosing appropriate scales, the objective map can duplicate previous results. New temperature data are presented from a repeating, high-resolution expendable bathythermograph section crossing the equator at about 170° W with four cruises a year between 1987–1991. There appear to be significant differences between this mean temperature and the shuttle mean temperature. Temperature is converted to density with the aid of a mean T-S relation and geostrophic velocity maps are calculated for the 4-year mean. The mean geostrophic undercurrent obtained from our sections is weaker than in the shuttle estimate and is centered slightly north of the equator. Enforcing symmetry about the equator removes the offset of the current, giving a stronger, but narrow undercurrent. The density field apparently includes significant (O (0.5 kg m−3)) large-scale ageostrophic variability which makes velocity estimates from single cruises poorly determined near the equator.

Geometric rays were traced for a variety of source–receiver configurations in the test ocean sound‐speed field constructed for the 124th Meeting of the Acoustical Society of America. A stochastic inverse incorporating the statistical information distributed with the test ocean was performed using only one‐way travel times as data. Realistic errors in travel times and source–receiver positions were allowed for. The travel times were assumed to be contaminated with internal‐wave‐induced travel time fluctuations. The fluctuation variance increased linearly with range, with a magnitude of 10 ms rms at 1000 km. This internal wave noise can be reduced by a factor of N−1/2 by assuming that the mesoscale sound‐speed structure remains static over N internal‐wave‐induced decorrelation times. Decorrelation times shorter than 10 min have been observed in the North Pacific at 1000‐km range, so a daily average can yield a net contamination below 1 ms, neglecting the effects of longer period fluctuations like internal t...

The evolution of the depth integrated heat content in the Northeast Pacific during summer 1987 has been measured using long‐range acoustic transmissions between transceivers deployed in a triangle approximately 1000 km on a side. Transmissions at 4‐day intervals gave travel times that were inverted to obtain estimates of the range‐average sound‐speed fields along the sides of the triangle. The estimated sound‐speed fields are converted to temperature fields and integrated to obtain depth and range averaged heat content. The acoustically determined sound‐speed and temperature fields agree with conventional CTD and XBT data. The accuracy of acoustical measurements of heat content are comparable to estimates from CTD and XBT data and can be made much more frequently. The acoustically measured variability of heat content at short‐time time scales limits the accuracy of studies using infrequent XBT sections. Ocean/atmosphere heat exchange from bulk formulas cannot fully explain the observed heat content change; the excess heat change is calculated to be of order 50–150 W m−2. [Work supported by NSF and ONR.]

Long‐range acoustic transmissions made in conjunction with extensive environmental measurements and accurate mooring position determinations have been used to test the accuracy of equations used to calculate sound speed from pressure, temperature, and salinity. The sound‐speed field computed using the Del Grosso equation [V. A. Del Grosso, J. Acoust. Soc. Am. 56, 1084–1091 (1974)] give predictions of acoustic arrival patterns which agree significantly better with the long‐range measurements than those computed using the Chen and Millero equation [C. Chen and F. J. Millero, J. Acoust. Soc. Am. 62, 1129–1135 (1977)]. The predicted ray travel times and travel time error have been calculated using objectively mapped sound‐speed fields computed from CTD and XBT data. Using the measured and predicted ray travel times, a negligible correction to Del Grosso’s equation of 0.05±0.05 m/s at 4000‐m depth is calculated. Small errors of about 50 m in the GPS determination of mooring positions lends a depth‐independent error of 0.1 m/s to the sound‐speed equation correction. [Work supported by NSF and ONR.]

A 1000‐km acoustical transmission experiment has been carried out in the North Pacific in order to quantify long‐range acoustic fluctuations at periods of hours to days, and to measure mesoscale and internal‐wave sound‐speed structure within the source‐to‐receiver vertical slice. Pseudo‐random‐sequence pulses were transmitted by a moored broadband sound source (centered at 250 Hz) to a moored 3‐km vertical array of 50 receivers. Data are available in the form of approximately 1000 transmisions at 1/h (spanning nine days), with an embedded sequence of another 1000 transmissions at 6/h (spanning 21 h). The multipath arrivals form a clear expected pattern of a single, folded wave front in the earlier part of the received pulses. Each point on the folded wave front represents a specific ray trajectory through the ocean. Several hundred points are available on each of the pulses. Removal of barotropic tides and equipment‐motional fluctuations was carried out by averaging techniques, yielding residuals that are...

In ocean acoustic tomography, the travel time along a ray path is a weighted average of the propagation speed along the path. Because oceanographers generally have intuition about point measurements or simple averages, it has been necessary to transform travel time data into point values (maps) before communicating the results. The transformation can be done with a variety of methods, ranging from exhaustive Monte Carlo searches to Backus‐Gilbert constrained estimation. The transformation converts travel time data with more or less independent errors to point value estimates with correlated errors that may have complicated, nonlocal structure. Since the error bars usually presented with an ocean map do not include the correlations, they do not accurately reflect the information content of a tomographic dataset. In addition, it is no longer possible to distinguish between the data errors and sampling blind spots by examining the error bars (or even the error covariances). Communicating tomographic results ...

Broadband signals were transmitted from a near‐axial source to a long vertical receiving array 1000 km distant in the North Pacific for 9 days in July 1989. The signals were received at 50 hydrophones spaced 60 m apart in the vertical, starting near the surface. Pulses were recorded at 10‐min intervals for two periods, totaling 24 h, while hourly pulses were recorded for the duration, giving a total of about 320 pulses. Individual ray arrivals were resolved and their arrival times measured with a precision of a few milliseconds using phase‐coded transmissions centered at 250 Hz with a bandwidth of 83 Hz (12‐ms resolution). The pulse arrivals as a function of time and depth correspond well with predictions based on geometric (ray) and physical (WKBJ) optics. In each transmission, 600 to 900 ray arrivals can be identified with rays from numerical analysis, distributed along up to 24 distinct wave fronts. The ray arrivals evolve at the time scales of ocean processes. The longest period travel time changes can be inverted to infer changes in the mean sound‐speed field between the source and receiver and in high‐wave‐number ocean features with wavelengths correspondng to ray loop lengths and their harmonics (70 km and shorter wavelengths). Simultaneous CTD and XBT surveys are available for comparison. Temporal and vertically lagged fluctuation statistics of the individual arrivals quantify internal wave and fine‐structure effects. [Work supported by ONT.]

The results of the experiment conducted in the northwest Atlantic in 1981 have demonstrated the possibilities of acoustic tomography. The first maps, based only on purely refracted rays, showed the evolution of a cold eddy, confirmed by direct measurement of temperature and salinity. A more complete use of the 1981 dataset, with incorporation of surface-reflected rays, is proposed here. The addition of new data reduces the statistical error on the estimation of the sound speed field. Resolution at levels already well estimated in the earlier computations is improved, and individual maps exhibit a better continuity. Information is now available about the average properties of the upper layers of the ocean, which could not be monitored with purely refracted rays.

A field test of ocean acoustic tomography was conducted in 1981 for a two month period in a 300 km square at 26°N, 70°W in the North Atlantic (just south of the MODE region). Nine acoustic deep-sea moorings with sea floor transponders for automated position keeping and with provisions for precise time keeping were set and recovered. From the measured travel times between moorings, various displays of the three-dimensional field of sound speed (closely related to temperature) have been obtained by inversion procedures. These procedures use historical ocean data as a reference, but all information from the in situ surveys has been withheld; the “pure” tomographic results were then compared to direct in situ observations. The tomographically derived spatial mean profile compares favorably to an equivalent profile from the in situ observations; both differ significantly from the historical average. Maps constructed at three day intervals for a two month period show a pattern of eddy structure in agre...

A study was undertaken of signal digitization and temperature calibration in expendable bathythermographs (XBT's) to learn how to minimize temperature errors in that system. An XBT digitizer was built into a PC-type microcomputer and used to calibrate 24 XBT probes at 5 temperature points, and later, to calibrate 72 probes at a single temperature. Twenty of the first set of probes were fastened rigidly in pairs and dropped in the ocean as a field test of the calibrations. Calibration of individual probes reduced the standard deviation of temperature calibration errors from around 0.05°C to

Over the past decade oceanographers have become increasingly aware of an intense and compact ocean ‘mesoscale’ eddy structure (the ocean weather) that is superimposed on a generally sluggish large-scale circulation (the ocean climate). Traditional ship-based observing systems are not adequate for monitoring the ocean at mesoscale resolution. A 1981 experiment mapped the waters within a 300 × 300 km square south-west of Bermuda, using a peripheral array of moored midwater acoustic sources and receivers. The variable acoustic travel times between all source–receiver pairs were used to construct the three-dimensional (time-variable) eddy fields, using inverse theory. Preliminary results from inversions are consistent with the shipborne and airborne surveys.

A vertical section of the interior structure of Jasper Seamount was modeled using a spectral tomographic inversion of P wave travel times. An array of ocean bottom seismographs (OBSs) deployed over the seamount detected the arrivals from a series of ocean bottom shots. A reference velocity model reveals that average compressional velocities within the seamount are similar to those found within Kilauea and are consistently slower than velocities at equivalent depths in typical oceanic crust. This suggests Jasper Seamount has a high average porosity. Perturbations from the reference model were imaged by tomographic inversion. A high velocity zone within the northwest flank of the seamount may result from dikes associated with a radial rift or from a shallow solidified magma reservoir. A low velocity summit may result from shallow, explosive eruptions. The tomographic model is consistent with the results of gravity, magnetic and dredging analyses.

In this paper, data from a Gulf Stream tomographic experiment carried out in October 1984 are analyzed. The experiment used acoustic sources and receivers bottom mounted beneath the stream to measure Gulf Stream dynamics. However, due to an unfortunate electronic malfunction of the source, only 2 days of acoustically measured travel time data are available. Nevertheless, some new and positive results are obtained. Bottom reflected acoustic rays having up to two bottom bounces are unambiguously identified by solving the direct problem of tracing rays both in a reference climatological profile and in actual range‐dependent sound‐speed sections from a hydrographic survey carried out during the experiment. It is also shown that these rays do not appear to be affected by important nonlinearities so that they can be used to provide consistent results in inverse solutions.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Sciences, 1983.

Acoustic normal mode group velocity data are extracted from tomographic receptions in the Greenland Sea using a combination of spatial filtering with data from a six-element hydrophone array and variable time windowing. The mode group velocity data, together with ray travel time data, are used in inversions to obtain the range average sound speed profile. The modal data significantly improve near-surface resolution, which is where the largest oceanographic signals occur. Inverse results using only acoustic data are consistent with point measurements, a Seasoar section, and sparse conductivity-temperature-depth data.

Variability of the subtropical gyre in the South Pacific Ocean was investigated using high-resolution expendable bathythermograph sections along a repeated track between New Zealand and Hawaii. The southern part of the section sampled most of the zonal flow in the subtropical gyre with the eastward flowing branch between New Zealand and Fiji and the westward branch extending north of Fiji to approximately 10°S. The time series began in September 1987 and extended through 1994, averaging four cruises every year. The geostrophic shear field was calculated, relative to 800 m, with the aid of a mean T − S relationship. Variability was present at a broad range of spatial and temporal scales but annual fluctuations were particularly prominent. The authors conclude that 30 snapshots of temperature, measured over a period of seven years, are sufficient to resolve the annual cycle of the gyre-scale circulation along the transect. The shape and intensity of the gyre varied seasonally throughout the water c...

For 300‐km ranges the expected size of the rms travel time variations due to eddies in the MODE region is 40 ms. Low‐power oscillators can drift 40 ms per month, mooring anchor position uncertainty is ±2 km, and instruments move hundreds of meters as moorings lean in currents. Without sophisticated mooring tracking and clock corrections, the oceanic signal is swamped by this mooring “noise.” The preliminary inversions presented by the Ocean Tomography Group [Nature 299, 121–125 (1982)] were limited to a few days when all corrective systems were operating and required an initializing CTD survey because of the unknown anchor positions. After identifying the structure of mooring and clock offsets, they may be included in the inverse to produce estimates of clock offset and mooring position along the sound‐speed maps. This yields useful inversions without mooring tracking or CTD data, so future tomography experiments can be designed with more flexibility, and ship‐based tomography is possible even without 1‐m...

Ocean tomography as originally proposed required all sources and recievers to be tautly moored and acoustically tracked to separate travel time perturbations due to mooring motion from those due to ocean features. It is possible to process the tomographic travel times to estimate both ocean sound speed perturbations and mooring offsets, effecting a separation without external tracking. A side effect of this processing is a check on the ray identification, since the varying instrument positions can be used as a synthetic array for estimating ray angle. Simulations and examples with actual data were used to contrast mapping performance with and without mooring tracking for a variety of ray data sets. In general, the ocean maps degrade when the tracking data are withheld. However, when many high-precision ray travel time measurements are available, the degradation is small; in these cases it would be possible to deploy free-drifting instruments as part of a monitoring experiment.

Mesoscale mapping of the ocean sound speed field in a 1000×1000 km area by means of ocean acoustic tomography is greatly enhanced by augmenting a few acoustic moorings with a movable ship-based receiver. Computer simulations based on realistic noise levels in the measured acoustic travel times give 5% (1%) residual variance in ΔC(x;y,z) for four (six) acoustic source moorings in an ocean perturbed in the gravest baroclinic mode. For comparison, objective mapping based on traditional vertical profiles requires 3 times the steaming distance to yield equivalent residual error. Detailed results depend on many parameters: the assumed mesoscale spectrum and vertical mode structure, the number of observed multipaths, the mooring configuration, the number of ship stations and the travel time signal level (due to mesoscale eddies) and noise level (due to internal waves and position-keeping errors). These parameters have critical values, below which there is distinct deterioration and beyond which there is little gain. We believe that the critical values can be attained in practice so the ultimate limit on mesoscale mapping is imposed by the internal wave-induced travel time error. This assumes that position keeping of the submerged acoustic sources and receiver by a combination of satellite navigation and high-frequency acoustics can be achieved with ±10-m accuracy. The present study assumes a stationary ocean; a second paper will deal with reciprocal transmissions yielding currents and hence the barotropic mode. This is required in a dynamic ocean model for estimating ΔC(x,y,z;t). All this is preparatory to a tomography experiment in the Greenland Sea in 1988–1989.

The ocean acoustic tomography experiments conducted to date can be divided into mapping experiments, in which many sources and/or receivers are used to generate sufficient crossing ray paths to resolve the mesoscale ocean structure, and overaging experiments, in which data are obtained in a vertical slice between a single pair of sources and/or receivers in order to construct horizontally averaged vertical profiles. While it is economically feasible to deploy enough instruments to construct an array capable of mapping an area a few hundred kilometers on a side, it becomes prohibitive for areas one megameter and larger in scale, even though many fewer tomography instruments are required than conventional point measurements. One possible approach to make high‐resolution, three‐dimensional maps of large areas of the ocean is to develop a hybrid system, in which a combination of moored instruments and precisely positioned sources and/or receivers suspended from ships are used to generate a dense set of crossi...

In the spring of 1981, an acoustic tomography experiment consisting of 4 moorings with low‐frequency (224 Hz) sources and 5 moorings carrying receivers was deployed as an array about 300 km on a side centered at approximately 26 N, 70 W. Subsurface moorings were used in order to minimize motion, so that the acoustic instruments were placed at about 2100‐m depth, well below the sound channel. The array was sited in a region of moderate mesoscale activity, overlapping the MODE region somewhat, and CTD surveys during the experiment showed a cold eddy in the experimental area, with 2‐ to 3‐degree amplitude at 500‐decibars depth. Rays traveling from a source to a receiver within a volume of ocean sample the velocity and sound speed of the water along their propagation paths. The fields of dynamic significance are coupled to the acoustic fluctuations primarily through sound speed changes, so that the ability of a tomographic array to directly measure a given feature is partly limited by the degree to which the ...

Acoustic tomography uses integrating measurements which require inverse methods to resolve the averages into estimates of spatial structure. Statistical inverse methods have been extensively used to solve the reconstruction problem over different tomographic ranges and configurations. These inverses become very difficult to apply in frontal regions like the Gulf Stream (GS) system, where the statistics are acutely inhomogeneous and anisotropic and the mean is not a likely representation of the GS front at any time. In this paper we propose an alternative inverse which asks for the solution which gives a front instead of asking for the smoothest solution. The inverse solution minimizes the errors in the fit to the data while simultaneously maximizing the sum of the squares of the gradients observed in the reconstructed section and minimizing the absolute value norm for stability. The inverse is aimed at detecting changes in the GS front, thus the data are used to estimate the perturbations to a previous estimate of the frontal structure, instead of reconstructing the entire front as a perturbation from some average state. This approach is intended to merge well with eventual dynamic updating schemes and can be used with various types of data, given a proper model. Several examples have been run intercomparing the traditional linear least squares (LLSI) with the maximum gradient inverse (MGI), from very idealized cases to a real Gulf Stream section reconstructed from hydrographic data. Different transceiver configurations were also compared and mid-depth instruments were found to be superior to bottom mounted instruments. The simplest cases show a significant improvement in the estimate of the Gulf Stream front by the MGI compared to the weighted least squares inverse (LLSI). As the cases became more complicated (and more realistic), the differences between inverse methods become less pronounced, although the strength and location of the perturbation maxima were always determined more accurately by the MGI. The decline is at least partially due to the numerical algorithm which lumps data misfits and external constraints (the maximum gradient) into a single penalty criterion which is minimized. The most immediate way to overcome this limitation is to break up the problem into a two-step procedure, first a least squares inverse to fit the data and second an iterative, nonlinear optimization maximizing the gradient and minimizing the absolute value norm.