Slip parameters for the Rann of Kachchh, India, 16 June 1819 earthquake, quantified from contemporary accounts

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Roger Bilham CIRES University of Colorado Boulder CO 80309-0216

Abstract
The 16 June 1819 Rann of Kachchh earthquake was felt throughout much of India. Significant vertical movements of the ground caused flooding of regions near sea level, damming of a distributary of the Indus river, widespread liquefaction, and a local tsunami, however, the geometry of the fault plane has hitherto remained obscure. Dislocation models based on deformation data gathered 7 and 25 years after the earthquake suggest that a near-surface reverse fault slipped locally more than 11 m. The absence of significant uplift on a ENE trending extension of surface trace of the fault in 1819, may signify that slip on the fault was directed to the north-east, consistent with focal mechanisms of recent earthquakes in the region. The inferred 50-70° N-dipping fault plane beneath the Allah Bund is unfavorably steep for reverse faulting, presumably requiring high fluid pressures in the nucleation zone. A geometric moment magnitude of M=7.7±.2 is obtained from the inferred slip parameters, consistent with a magnitude estimated empirically from the intensity distribution. While a recurrence of the Kachchh earthquake is unlikely soon because of low inferred contractional strain rates in the region, the Indus Delta and Kachchh rift zones could host several ruptures contiguous with the 1819 event, with important consequences for the city of Karachi.

Reference:

Bilham, R., Slip parameters for the Rann of Kachchh, India, 16 June 1819 earthquake quantified from contemporary accounts, in Stewart, I. S. & Vita-Finzi, C. (Eds) Coastal Tectonics. Geological Society London, 146, 295-318, 1999

Newspaper and verbatim accounts of the earthquake are found in an appendix to this article.

Introduction

The Rann of Kachchh (historically referred to as the Ran, Raun, or Runn of Cuch, Cutch, Kach or Kutch) is an arid region of western India devoid of vegetation that lies close to sea level. Rann derives from the Persian word Eriyan meaning "waste". In the dry season the lowest part of the Rann is covered with a hard crust of evaporites, but during a vigorous monsoon the region is flooded to shallow depth and impassable on foot. The low hills of Kachchh separate the Rann of Kachchh from the Gulf of Kachchh to the south, and because of the Rann's low elevation above sea level, in some maps Kachchh is depicted as an island. The Rann is underlain by rift-like features, which have been mapped offshore beneath the continental shelf with a general east-west trend (Biswas, 1989). The collision of India with Asia has initiated a compressional stress regime in a northwesterly direction, very different from that at the time of rifting, and the reactivation of these normal faults in a reverse sense is both anticipated (Khattri, 1992) and demonstrated (Chung; 1993; Chung and Gao, 1995).

Several authors speculate on substantial shifts in the coastline of NW India since the visit of Alexander the Great (c.f. Burnes, 1835; Haig, 1894). In Medieval times the Rann is believed to have been connected to the Arabian Sea to a sufficient depth to permit marine access by large boats. The stranded remains of these boats are reported to have been excavated from time to time and used as firewood by local villagers (Grindlay, 1808, cited by Burnes, 1839). On the basis of the burial rate of near-surface horizons the sedimentation rate for the past 9000 years is estimated as 2 mm/year by Gupta (1975).

Uplift in the 1819 event created an 80-km-long natural dam (the Allah Bund or Dam of God) across the Kori (Korree) branch of the Indus river (known as the Puran, Pharran, or Pooraun), which in 1826 was breached by a flood. The investigation of the 1826 flood resulted in surveys in 1827 and 1828 (Burnes, 1839) who estimated a 25 km width to the Allah Bund 7 years after the event. Lyell (1853) discusses the deformation in the earthquake including new materials elicited from Burnes and from the notebooks of early travelers. Suess (18??) and Wynne (1869) examine the evidence for uplift, but for want of unequivocal numerical data describing the deformation of 1819 conclude that it is unlikely to have occurred, a sentiment repeated as recently as 1976 (Glennie and Evans, 1976). Although Baker (1846) measured a profile of the uplifted Bund using survey instruments, his data were omitted from his 1846 publication and were not generally known until re-discovered by Oldham (1898). In 1926 Oldham collated and evaluated the available data, providing for the first time isoseismal maps and estimates of epicentral uplift and subsidence.

The deformation data are used in the following article to provide constraints on the mechanism, magnitude and location of the 1819 earthquake. The credibility of the interpretation depends largely on the accuracy of the data, and it has been found necessary to examine some of the original sources cited by Wynne (1883) and by Oldham (1926). The article first examines the characteristics of the Earth's surface near the epicentre and concludes that the surface was essentially featureless and that no former fault scarp was present. The reliability of the coseismic deformation data are next evaluated, and possible perturbation by post seismic effects and subsequent earthquakes in the period 1844-6. The numerical data are interpreted with the assumption that they were generated by a single event with northerly, or northwesterly, directed slip, with confidence intervals estimated from the original observations.

The surface of the Rann of Kachchh before the earthquake of 1819.
The Rann is absent from the New General Atlas published by Thomson (1817) despite two years of British rule. In 1808 Captain R. M. Grindlay traveled through the region and provided qualitative information concerning the pre-seismic topography of the northern Rann of Kachchh. His path took him through Kori Creek to join the Puran River, which he identified as the easternmost distributary of the Indus. In 1808 marine navigation in boats with moderate clearance was possible as far north as the Lallan Puttun dam, the first of several artificial dams encountered across the Puran river starting 24 km north of Sindri. A salt water anchorage existed south of this dam (bund), north of which fresh water was impounded for irrigation.

"We passed Sindri , and observed several inferior branches leading through the Rann, among which we saw a few straggling men and women. About 20 miles beyond Sindri we reached Aly Bunder at night and came to anchor close to the mound that contains the fresh water" (journal of R. M. Grindlay cited by Burnes, 1835).

No significant fault scarp or highland existed between Sindri and the next fort northward, prior to the earthquakes. Had there been, they would have been selected to site dwellings or defensive positions above the monsoon flood levels. In 1808 according to Grindlay (Burnes, 1833) the surface of the Rann consisted of shrubs and bushes near the edge of the Rann that extended as far north as Allybunder, 32 km north of the Allah Bund, and it was possible to navigate along the Puran to the foot of the Lallan Puttun dam in 1808. In a posthumous article MacMurdo (1839) states that "The Talpooras however erected two dams called the Morabund, which elevating the level draws the water into the Khattee and eastern districts, and another at Alibunder, with the same view. The waters do not know their way to the sea, which meeting no opposition is driven up to the dam of Alibunder. The mouths are gradually filling up with sand in the absence of the freshes that prevent its accumulation." (Fresh = flood)

16 June 1819 earthquake

At approximately 7 p.m., on 16 June 1819, Fort Sindri and masonry buildings in villages within a radius of 80 km were destroyed by a violent earthquake. A tsunami from the Arabian Sea surged across the Rann and sand vents in the region were active to a height of 2-3 m for three days, venting water and gas (Bombay Public Consultations, 1819; MacMurdo, 1835). Reliable eyewitness reports near the epicenter are available only from Bhooj and Anjar from where the British resident (Captain James MacMurdo) and an army officer (Lt. Colonel Colin Milnes) sent daily dispatches to the Government at Bombay. MacMurdo lists 1543 people killed in the event, mostly in Anjar and Bhooj where 1547 houses were completely destroyed and many more damaged. MacMurdo remarks that "had the accident occurred in the night time, perhaps one third if the population of the province would have been buried in the ruins of their dwelling-houses". He observes that damage to masonry structures was minor where these were constructed on rock, but catastrophic where constructed on soils. Macmurdo's meticulous records probably underestimate the total number of fatalities because they fail to record damage in the northern Rann of Kachchh and southern Scinde Province, which regions appear to have been close to the epicenter.

The fort at Anjar was destroyed, and a similar fate befell the fort at Sindri in the Rann of Kachchh. Sketches of Sindri fort before and after the earthquake collected by Lyell (1853) are reproduced in Johnson and Kanter (1992), and a view of the decaying ruins in 1869 is reproduced in Wynne (1872). According to testimony elicited by Burnes (1833, 1835) a tsunami flooded the Rann of Kachchh within minutes of the earthquake and survivors were forced to climb to the top of the ruin where they were rescued the following morning by boat. Ballantyne writing from Jooria on the northern shore of Kachchh on June 17 relates (MacMurdo, 1835) that "the whole town is a complete ruin" and on June 18th describes ground fissures symptomatic of catastrophic-lateral-spreading;

"on examining the different rents, we found them to be of various extent from an inch to a foot in breadth; the depth however, being considerable, being 10, 15 and 20 feet. In some places a gravely soil had been thrown out; in others a wet black earth."

Although the tsunami and subsequent sand venting caused transient flooding of the Rann, and numerous rivers were temporarily active in Kachchh, two permanent changes occurred in the Fort Sindri region: the foundations of the fort and the surrounding Rann for a radius of many km subsided by more than 1 m, and a region 7 km north of the fort, including the bed of the river Puran was elevated by 3-6 m, preventing navigation northward into Scinde province for several years. This natural dam became known as the Allah Bund (Dam of God). The details of the uplift and subsidence near Sindri are discussed in following sections.

Large public buildings were partly damaged 140 km to the east in Ahmedabad and Surat but damage to residential structures was insufficient to warrant claims for damage to the government (Bombay Public Consultations, 1819). At Ahmedabad a 15th century Mosque, famous for its shaking minarets (artificial simulation of resonance in one, caused sympathetic resonance of the other) was severely damaged, and its minarets destroyed. Arguing that they were merely ornamental, the government declined to rebuild the minarets. The earthquake was scarcely felt in Bombay, but reports were obtained of perceived motion at Kathmandu, Calcutta, the Baluchistan Hills and from Pondichery south of Madras (Oldham, 1926), a felt radius of 1600 km. Based on the felt area later compilations have assigned a magnitude of 8.3 to the event (c.f. Dunbar et al, 1997), however, many of the internsity reports are from secondary sources. Aftershocks occurred with decreasing frequency in the next several months. MacMurdo (1823) reports 2-3 events/day in June, one per day until August, one every three days in September, six in October and 3 in November.

Figure 1 Rann of Kachchh earthquake 1819. Dots indicate felt locations, crosses indicate minor damage, and stars indicate considerable damage to buildings (Oldham, 1926). Approximate isoseismals are indicated for the 1819 and 1897 earthquakes (Oldham 1999).

Earthquakes 1845-6

Damaging earthquakes in 1844, 1845 and 1846 are inferred from reports listed by Wynne (1872) but the information contained therein is sparse. Their closeness in time and the scant information available on damage led Oldham to suppose that the June 1845 event described in Nelson (1845) corresponds to the true date of the 1844 earthquake described by LeGrand Jacob (1860), who incorrectly ascribes Jest Sumvut 1901 to 1844. Hindu Jest Sumvut is June 1845, and in addition, a June 1844 event would have been reported by Baker (1846) who was in the region from May to October 1844. However, some aspects of Nelson's 1845 letter are enigmatic. The identity of the author and the date of the letter to Nelson (presumably R. J. Nelson) are neither recorded in the publication nor in the archives of the Geological Society of London for 15 Dec. 1845, when it was entered into the minutes.

"One of Capt. McMurdo's guides was travelling on foot to him from Bhooj. The day he reached Lackput there were shocks of an earthquake, which shook down part of the walls of the fort, and some lives were lost. At the same time as the shock the sea rolled up the Koree (the eastern) mouth of the Indus, overflowing the country as far westward as the Goongra river (a distance of 20 English miles), northward as far as a little north of Veyre(40 miles from the mouth of the Koree), and eastward to the Sindree lake. The guide was detained six days (from June 19th to 25th), during which time sixty-six shocks were counted. He then got across to Kotree, of which only a few small buildings on a bit of rising ground remain. Most of the habitants throughout the district must have been swept away, the best houses in Scinde being built of sun-dried bricks, and whole villages consisting only of huts made of a few crooked poles and reed huts. The guide traveled 20 miles through water on a camel, the water up to the beast's body. Of Lak nothing was above water but a Fakeer's pole (the flagstaff always erected by the tomb of some holy man); and of Veyre and other villages only the remains of a few houses were to be seen."
"There are said to be generally two earthquakes every year at Lackput. The Sindree Lake of late years became a salt marsh". (letter to Nelson, 1845)

Were it not for mention of Sindri Lake and the guide's route from Bhooj westward to Koti via Lackput, the letter could be describing to the 1819 event. Had this been written in 1819 the McMurdo referred to in the letter may would have been MacMurdo, the British Resident, who was visiting Anjar on the night of the earthquake, and whose name was spelled in both ways in contemporary accounts. LeGrand Jacob (1860) describes Lackput in Nov. 1851 as an abandoned city of 20 inhabitants (he saw 12 only), "the greater part of the houses deserted and many fallen down". However, despite vivid memories of the earthquake of 1819, 35 years prior to his visit, the inhabitants do not ascribe the ruins of Lakhput in 1951 to Nelson's alleged 1845 tsunami and earthquake, 6 years prior to his visit. Moreover, damage to the fort was not evident in 1851.

"The ramparts of the town completely encircling it, are lofty, nearly three miles round, with a parapet of about seven feet, banquette about six; numerous bastions, some boasting a cannon, all loop-holed for musketry and in good order". Although Koti in 1851 was a single "upper roomed cottage" 6 miles north of Lackput approached by a circuitous 15 mile passage by camel "owing to mud", consistent with the description of access to Koti Nelson's letter, this description also fits Lackput soon after the earthquake of 1819 (Burnes, 1833).

In contrast, Carless (1838) describes the Lackput garrison as a thriving community in 1837, suggesting that damage to the fort in the 1840's did indeed occur:

"the walls are defended by numerous bastions, with guns mounted on them of all sorts and sizes. Most of them are so old as to be entirely useless" "It is now garrisoned by 50 Arabs and 150 Native soldiers, and contains a population of about 5000 persons, composed principally of merchants and Hindus, who have fled the tyranny of the Amirs"

Of relevance to the current study is that LeGrand Jacob (1860) describes apparent uplift of the Allah Bund of 2-3 m in 1819 and widening of the Bund to 7.5 km in 1844, with 1 m of additional uplift at Sunda, 5 km south of Sindri:

"Spent all the afternoon with my tent filled by the best informed men in town and port, assembled for me by the karbharee before alluded to, as having been with Burnes in Sind etc, an intelligent man, himself giving information, and helping to get it from me from others. One of the Rao's garrison in Sindree at the time of its destruction in A.D. 1819 was also present. The following is an abstract of the notes made after much examination and cross examination.
"The earthquake of Sumvut 1875 (AD 1819) that submerged Sindree, elevated the bed of the river to the height of 2 or 3 yards for the distance of 2 to 3 kos (5-7.5 miles) commencing about 2 kos above Sindree: the spot is called Ullah Bund (God's embankment), but the monsoon has worn a water-way through it in an irregular narrow channel; the material being of clay, sand and gravel, this would soon be deepened and widened by any flow of water; the earth was also raised at a place called Sunda. The usual tide only reaches this Sunda, the spring tide now goes over it by a cubit, the earthquake of 1819 raised the ground as to leave the tide there waist high, but in Sumvut 1901 (AD 1844) a series of shocks occurred, that raised the earth still more, so as to leave a cubit (foot and a half) as the greatest depth of water ever found there: these shocks also extended the breadth of the Allah Bund to the extent of 3 kos: before they occurred the usual tide went over the Sunda by about half a foot, but now not at all. At spring tides, however, a boat drawing a cubit of water can with some labour be taken over the Sunda.

Pursuing the upward course of the river it is thus described:- After passing the Sunda, a pool (Chuch) is reached called Muthar, where the water is waist deep at all times; this is half a kos long; then comes the Ibraham Shah Peer flag-station, where there is nine feet or more, which continues past Sindri until the Ullah Bund is reached; through this Bund, as before explained, an irregular narrow channel continues the stream during the monsoon: at other seasons water terminates at the Ullah Bund so there is only the dry bed of the old river until we reach the "chuch" called the Bundrejo Duryao, some three kos higher up, where the water is waist high and salt; it lasts for 4 kos, and is terminated by the Suyundwalla Bund above described.

The earthquakes of 1844 here referred to I do not remember ever reading or hearing of, yet they are shown to have effected an important change in the earth's surface: the shocks are said to have lasted during a whole month (All Jeth Sumvut 1901), and were so threatening that whilst they lasted the inhabitants feared to sleep in their houses"

Oldham considers the changes in elevation described in LeGrand Jacob's account to be "very improbable" based on the observed elevation of the foundations at Sindri Fort in later years. Also, in view of its omission in Baker's account, it is fairly certain that no second event occurred that may have distorted the deformation field modeled below, so that these later, somewhat uncertain events, are ignored.

Other events in the region
The survival of the evidently precariously stable minarets at Ahmedabad for the 400 years preceding the 1819 event indicates that this was the largest earthquake to have occurred in the region in this time interval. Thus, an earthquake in May 1668 which caused 30,000 houses to sink into the ground in the Indus Delta, and another of unknown severity near Surat in 1684 (Oldham, 1883), were evidently too weak to cause the Ahmedabad minarets to collapse. Anjar, 60 km SE of the Allah, was close to the epicenter of a M=6.1 earthquake in 1956 in which 109 people were killed (Chung and Gao, 1995).

Fig. 2 Uplift during the 1819 Kachchh earthquake dammed the Kori River north of a zone of uplift termed the Allah Bund, and submerged the region to its south surrounding the fort at Sindri. On the basis of morphological changes recorded by Survey of India maps Oldham (1926) suggests that faulting may have extended a further 100 km to the east (dashed). Earthquakes epicenters 1941-96 3.5<M<5 from PDE

Deformation in the 1819 event

Although Burnes (1833) evidently did not travel as far as the first of the artificial dams north of the Allah Bund, and did not undertake any precise measurements of the profile of the Allah Bund, he offers two consecutive glimpses of the channel cut by the Puran after the flood of 1826. On his first visit (28 March 1827) he was unable to define a precise northern limit to the Bund

"for it extends very far inland, perhaps 16 miles and by gradually sloping to the north, unites with the land, which renders it impossible to define its breadth with correctness". In 1827; "the present channel through the Allah Bund, which is only one hundred and twenty feet wide, though from fifteen to eighteen feet deep", and when he revisits this on 9 August 1828; "The channel through the Allahbund I found to be wider, with more of the west side washed away, and changed from a sloping declevity, to a perpendicular bank like the eastern shore. I sailed two miles up the river or channel which the flood of 1826 cut through the Allah Bund, and found the water gradually to decrease from two and a half fathoms to as many feet, which I was informed was its depth as high up as Chatitar above the Allibund, and about 20 miles distant."
"The banks of the channel which it cut through are of clay, and as they are perpendicular, and the river comes directly from the north, without any windings, I can compare it to nothing so correctly as a canal, nor does its breadth, when a little way up, destroy the resemblance, being only sixty six feet. The natural bund, so called, is certainly the most singular effect of the earthquake of 1819. To the eye it does not appear more elevated in one place than another, and being covered with a saline soil, has the appearance of the Runn on all parts".

In 1844 a survey of Sinde irrigation by an engineer (Baker, 1846) yielded a 61-km-long profile along the bed and bank of the Puran and tributaries north of the Allah Bund. Baker describes the surface soil of the Allah Bund as "light and crumbling, and strongly impregnated with salt; at the depth of one and a quarter to two feet it has more consistency, and is mixed with shells such as are now found abundantly on the shores of the lake" Baker did not extend his measurements south to Sindri.

Baker's detailed leveling survey and map were accidentally omitted from his 1846 publication, and (despite an indication by editor to the contrary) from subsequent volumes of the Bombay Geographical Society, and it was not until 1889 before the map of Baker's survey was discovered and published (Oldham, 1889). Curiously, in his geological map of Kachchh, Wynne (1869) attributes features north of the Allah Bund to Baker's map which must have been available to him in some form, but his monograph was written apparently unaware of the leveling profile. The section through the Bund is reproduced in Figure 3 and a north-south profile from the Mora Bund to Lake Sindri is projected in this figure as a function of north-south distance. From his figure it is clear that the Lallan Puttun dam separated fresh water from sea water before the 1819 event.

Oldham (1926) summarizes Baker and Burnes' accounts as follows. The peak elevation of the Bund was 6.2 m with a 600 m wide scarp dipping at 0.65° to the south and 0.052° to the north. Estimates of the width of the northern scarp vary from 3-12 km (Baker) to 24 km (Burnes). Subsidence south of the scarp attained depths of 3.5 m (although where Baker measured this depth is unclear), and extended with diminishing amplitude to 24 km south of the scarp. Ft. Sindri is estimated to have subsided at least 1 m, probably 1.6m, and possibly >3.3 m.

Figure 3 Baker's 1844 profile of bank and bed levels projected on a north-south section, and close up view section through the Allah Bund. Artificial dams are shown as vertical lines. Sea level is inferred from Grindlay's 1808 observation, that the Lallan Puttun dam separated sea-level navigation from fresh-water portage. Sindri lake level approximates high tide level. The 1826 flood would have ponded only to the level indicated if the raised bed of the Puran continued 4 m below bank level through the Allah Bund.

One of the uncertainties in these estimates concerns the undeformed surface level of the Bund prior to the earthquake, because it is to this level that estimates of coseismic deformation must be referred. As discussed above, there is little doubt that the observed surface morphology was formed entirely by coseismic deformation associated with the 1819 sequence of earthquakes.

Oldham (1926. p.23) argues that if the observations are referred to a datum just north of the Allah Bund taken from Baker's map, absolute uplift may have been 1 m less, and absolute subsidence 1 m more, than maximum values estimated from local datums, e.g. the bed of the Puran or the level of Lake Sindri respectively. This however, does not take into account the pre-earthquake, seaward gradient of the land surface. The smooth surface of the bank of the Puran, mapped in Baker's profile, has utility in estimating the absolute amplitude of uplift beneath the Allah Bund. Baker's measurement datum was the level of water dammed behind the Mora Bund, but no precise estimate of sea level elevation is provided. The absolute level of Baker's datum above sea level can be estimated to approximately ±0.3 m because it was possible to navigate to the base of the Lallan Puttun Dam prior to the earthquake, and because the level of Lake Sindri was replenished by high tides after the earthquake. With this assumption, two approximations to the pre-seismic land surface beneath the Allah Bund are possible: in one, a smooth curve is fit to the bank of the Puran between 17 km and 50 km north of the Allah Bund and extrapolated beneath the Bund, and in the other the curve is, in addition, constrained to fit to lowest estimated sea level at a distance of 50 km south of the Bund (Figure 4). Using the first approximation the peak elevation approximately 1 km north of the Bund increases from 6.2 m to 6.6 m, and using the second it reduces to 6.1 m. The goodness of the fit to Baker's river bank data is superior (see residuals in Figure 4) if the sea level constraint is ignored, and because it is by no means certain that the bank surface should asymptotically approach sea-level, the higher estimate is thus considered more reliable. Data used in subsequent models are summarized in Table 1.

The recorded region of maximum subsidence occurs along the Puran river and the Sindri region along a well-traveled trade route. Numerical data for the Allah Bund is obtained only where navigation was impeded and where a clear uplift profile was visibly manifest after the 1826 flood. Few roads exist to the east and yet fewer roads to the west that might have been explored after the event, and our knowledge of deformation is biased by this historical circumstance. Neither Baker nor Burnes traveled the length of the Bund to establish its lateral extent. In 1827 Burnes estimates its width as ±16 miles (50 km), but in 1828 revises it on the basis of traveler's accounts of newly-necessary, circuitous routes around Lake Sindri, to 18 miles west to Ghari, and 24 miles east to Pacham Island ( 80 km). Baker indicates its length would be too difficult to survey because of the absence of water. The Survey of India maps later in the century were used by Oldham to confirm that the Bund was at least 80 km long, and that morphological features suggest faulting for more than 150 km.
__________________________________________________________________
Table 1 Deformation estimates for north-south section through the Allah Bund. Distances are measured relative to the inferred deformation-null separating uplift from subsidence. Uncertainties indicated as model input are used to estimate confidence levels of solutions.
__________________________________________________________________
parameter maximum minimum model input
northerly extent of uplift <0.1 m + 24km +6 km 6±1 km
maximum uplift +6.6 m +6.1 m 6.3±0.3 m
location of maximum uplift +1 km +0.6 km 1±0.2 km
antisymmetry null 0 0 -
location of maximum subsidence -1 km -200 m -
maximum subsidence -4.5 m -2.5 m -3.5±.3 m
subsidence at Sindri -3.5 m -1.5 m -1.5±.3 m
location of Sindri -6 km -5 km -6±1 km
southerly extent of subsidence >-0.1m -40 km -24 km -24±2 km

Fig. 4 Baker's 1844 profile, projected on a north-south line, with exponential approximations to the slope for the river bank (above), and residual elevations when these are subtracted from the observed data (below). A better fit to Baker's river-bank data is obtained if assumptions concerning morphologic relations to inferred sea level are ignored.

The southerly facing scarp width is likely to have been underestimated in 1826, since part of it was submerged, and in 1844, because it may then have been covered partly by sediments. Thus the south facing scarp could have been greater than the 600 m width estimated by Burnes, but because it determines only the closest approach of the subsurface fault to the surface, and has minor influence on deep slip parameters, its true width is of little consequence in the following analysis. The southern extent of subsidence is perhaps the most clearly defined because this formed a fresh water lake that eventually became saline and finally dried up. Unfortunately, because a deep channel existed through the lake, some of the depths in subsequent descriptions relate the channel depth and lake depth in ways that do not permit true bathymetry to be evaluated precisely. When Burnes visited this after the 1926 flood the main river channel was fresh, as was the surrounding water in Lake Sindri. In following years the Rann shallowed, and although much of this may have been due to sedimentation, it is possible that post-seismic deformation occurred (Oldham, 1926). In 1827 the width of the channel though the Bund was 40 m wide but by 1828 the flow had ceased and the waters of the Rann were saline. Deformation tapers to low values near the northern and southern limits of rupture, but no deformation is apparent >24 km from the Allah Bund (Table 1).

Figure 5. The ratio of maximum uplift to maximum subsidence determines the dip of the fault in an elastic half space. The 1.8 ratio of uplift to subsidence favors a dip close to 70° largely independent of down-dip parameters (top and bottom of down-dip width indicated for two diverse solutions ).

Slip on the fault is modeled as uniform slip in an elastic half-space using the formulation of Okada (1984). By assuming 2-D uniform slip, five unknowns remain to be determined - fault dip, slip, latitude, and the depth to the top and bottom of the rupture. In practice, the latitude and depth of the rupture are determined to first order by the width and location of the Allah Bund. That is, the approximate antisymmetry of the vertical deformation field requires an almost vertical fault whose surface extension must cut the Earth's surface at the southernmost expression of the Allah Bund. The half-width of the southward slope of the Allah Bund is approximately equal to the depth to the upper surface of the dislocation. In addition, simple numerical tests (Figure 5) show that a ratio of uplift to subsidence of 6: 3.3 requires the dip on the causal rupture to be to the north at 65°-70°, requiring reverse slip on the fault.
In principle, having assumed the location and depth of the dislocation by inspection, only three observations are required to constrain the dip, slip and down-dip-width of the Kachchh rupture. Five data are available in Table 1. However, the uncertainty associated with the absolute level of uplift and subsidence renders the solution ambiguous. Forward models were developed to estimate the sensitivity of the interpretation to each of the available data. The models emulate the subsidence at Sindri (±0.3 m), maximum uplift north of the rupture (±0.3 m), maximum subsidence south of the rupture (±0.3 m), and far-field constraints of uplift and subsidence less than 20±10 cm at distances ±24 km from the Bund. Least squares misfits between observations and model results for a range of possible slips and down-dip depths are estimated and contoured in terms of 1-3 sigma confidence intervals in Fig. 6.

Fig.6 Misfit contours for solutions for slip and down-dip-width for four alternative northerly dips to the inferred rupture zone using constraints listed in Table 1. A down-dip width of 10 km is favored by the data, with a dip of at least 60°N

Fig. 7 Contours showing the range of slip and dip solutions that fit the Kachchh data assuming 6 or 10 km deep dipping faults, or listric faults. The geometry and vertical surface deformation field for the best-fitting solution is shown left.

Figure 8 The profile of the Allah Bund, when used to constrain dislocation models independent of the Lake Sindri subsidence data, favors 12 m of slip, on a shorter, more gently inclined fault, than dislocation models adjusted to fit the entire data set. Note that a region of minor subsidence is predicted north of the Bund.

Assuming the values listed in Table 1, the model misfits in Figure 6 are consistently lower for down-dip widths of less than 10 km than for larger fault widths. Acceptable combinations of dip and coseismic slip for a down-dip width of 10 km are 11.5±1 m, and 68°±7° respectively (1 sigma, Figure 7).

The Allah Bund profile
In models illustrated in Figures 6 and 7 Baker's profile of the 6-km-wide Bund has not be used to constrain the 1819 rupture parameters. Although Baker's numerical data are presumably more precise than the estimates for subsidence and uplift listed in Table 1, the profile has some puzzling characteristics. The transition between the almost linear northern slope and the undeformed surface of the desert (6 km from the southern edge of the Allah Bund) is too abrupt to be caused by elastic deformation. If the shallowing of the bed of the Puran is used to estimate the northern limit of deformation, the width of the uplifted Allah Bund might be estimated to extend perhaps 4 km further north. Baker suggests that the channel may have filled by bank collapse at the mouth of the incised cut through the Bund but not to the north. A possible reason for the abrupt transition between the Bund, and the apparently undisturbed Rann north of the Bund, may be due to erosion of the bank caused by drainage of the impounded waters in 1926. A further problem with the data concerns the surprisingly linear northerly dip to the deformation field, again atypical of elastic deformation.

Notwithstanding these perceived problems with the data, slip parameters were estimated from Baker's sectional profile of the Allah Bund by comparing the slope at 0.5 km intervals, with the theoretical slope estimated from a dislocation model. An observational uncertainty of 0.2 m per 0.5 km was assigned to these slope data, limited mainly by digitizing errors from Oldham (1898). The favored models require a down-dip width of 5±1 km, dipping at 50±5° with 12±1 m of slip (Figure 6). The shallower dips for the Bund-profile result from the model's attempt to fit the steep northerly slope in addition to the subsidence evident between 6 and 8 km north of the southern edge of the Bund (Figure 4). A suite of models in which data were examined only from the southern 5.5 km of the Bund favored similar slip parameters. The models favored by the Bund data evidently prefer shallower down-dip widths than the maximum-minimum deformation field used in Figures 5 and 6, and are inconsistent with the reported subsidence in Lake Sindri. Subsidence at Ft. Sindri is required to be less than 1m, and maximum subsidence is preferred to be less than 2.2 m, values lower than those listed in Table 1.

Location and Magnitude of the 1819 Earthquake

No accurate estimates for the epicenter for the 1819 earthquake have hitherto been proposed although Chung and Gao (1995) attribute approximate locations south of the Allah Bund to Quittmeyer and Jacob, 1979 and Chandra, 1977. The above analytical procedures suggest that the 1819 rupture occurred 5-10 km north or northeast of the Allah Bund. The longitude is not determined by the surface deformation data.

The along-strike length of the Allah Bund is estimated by Oldham (1926) as 80-150 km, from which a geometric seismic moment can be estimated for the rupture. Using the relation Mo=µ*slip*L*W where Mw=2/3(logMo)+10.6 the range of parameters determined above correspond to a local magnitude of ML=7.7±0.2 using typical values for the rigidity modulus µ. Oldham speculates that the along-strike length of the earthquake could have attained 150 km which results in the high magnitude estimate of M=7.9. Increasing the down-dip width to 15 km would increase magnitude to M=8. The uplift data suggest very minor slip on the eastern extension of the fault, and a minimum magnitude of M=7.4 can be deduced from a mean slip of 10 m, confined to an along-strike length of 80 km. However, confining the slip to the western Allah Bund expression of the fault ignores important information concerning the strike of the fault. Had slip been directed in a north-easterly direction the easternward extension of the fault would be largely strike-slip, and uplift accompanying 10 m of left lateral slip would be relatively minor, consistent with that observed.

An alternative method to estimate the magnitude is to use the intensity data reported for the event. An empirical relation between intensity and area of shaking constrained by 6 Indian events including the Anjar (1956) event is discussed by Johnson (1994) who offers a magnitude of M=7.5-8 for the 1819 event (7.8 in Johnston and Kanter, 1990). A slightly lower intensity magnitude can be estimated from the data of Figure 1. Moment magnitude, Mo, of an earthquake in the F94 model is related to the area, S, enclosed within a specified isoseismal intensity contour, by an expression of the form
log Mo = a + blogS +cS (1)
where the constants a, b and c are determined empirically for each isoseismal area. Intensity magnitudes are shown in Table 2, although the intensity data from which they are derived are sparse and of uncertain quality. A mean magnitude estimated from the intensity data is M=7.5±0.2 in reasonable agreement with the deformation data. Combining the intensity and deformation data, a preferred magnitude of M=7.7±0.2 is assumed for the 1819 event.

_____________________________________________________________________
Table 2 Isoseismal Areas and estimated Moment Magnitudes for the 1819 earthquake.
Constants a, b, and c are preferred values from Johnson (1994).
_____________________________________________________________________
Intensity felt VIII
a 17.3 24.1
b 0.959 0.44
c 0.00126 0.00586
radius 1600 km 140 km
Mo F94C 27.23 27.66 log10(dyne cm).
M 7.4 7.7
_____________________________________________________________________

Discussion

Two forms of solution are preferred by the data. Maximum and minimum vertical deformation values estimated six years after the earthquake yield preferred solutions for a 67±5° dipping fault, with a down-dip width of 6-10 km, and the short profile across the Bund measured 25 years after the earthquake, favours a dislocation with 50±5° northerly dip, 12±1 m of slip and a down-dip width of 5-6 km. Is it possible to reconcile these two solutions?

In the above models slip is assumed to be directed north-south. As noted above, a more probable slip vector is to the north-east, consistent with both the Indo-Asian plate convergence vector (Paul et al., 1994) and the p-axes of regional earthquakes (Chung, 1993; Chung and Gao, 1995) This would require steeper dips, and shorter down-dip widths. Hence, the estimated dips are lower bounds, and a steep fault plane is a necessary, common feature of any interpretation of the data near the Allah Bund. At dips of 50°-59° "Byerlee" friction causes a fault to "lock" in response to horizontal compression, unless fluid overpressuring is available to reduce friction on the fault (Sibson and Xie, 1998). The geometry of the Kachchh rupture is thus severely misoriented for reverse slip, and may have required fluid overpressuring to promote rupture. Fluid overpressuring is believed to be widespread in the lower crust (Sibson, 1992. Reservoir-induced seismicity throughout India suggests that fluid pressures play an important role in triggering shallow seismicity, and it is possible that this may be a common slip mechanism for the Indian subcontinent. The thick sediments in the Indus fan and the Rann of Kachchh, moreover, have favorable conditions for overpressuring.

An important consequence of probable north-easterly directed slip in the earthquake is that the mapped fault east of the Allah Bund can absorb a large left-lateral strike-slip component with insignificant convergence, and thus minor vertical deformation (Figure 2). The proposed slip geometry shown in Figure 9 may also account for the apparently wide separation of significant aftershocks listed in Oldham (1926), some of these occurring near the eastern extremity of the inferred fault.

Figure 9 Simplified sketch of proposed NE-directed convergence during the 1819 earthquake. Steep reverse slip causes uplift NE the Allah Bund (barbs) with minor transpression along the inferred eastward extension of the rupture.

Oldham (1926) suggests that post-seismic surface changes occurred in the Sindri region that were not entirely the result of silting or precipitation of evaporites. The various sketches of Fort Sindri show it to have been initially surrounded by water close to the high-tide or monsoon-surge level, and a few decades later to have been surrounded by dry land. Oldham suggests that this change was caused by a relaxation of co-seismic subsidence. The wavelength of the vertical changes are considered too short to result from visco-elastic adjustment of the elastic crust. However, Brune (personal communication 1997) has demonstrated in computer simulations and foam rubber models, that dynamic effects associated with propagating wrinkles along the fault plane (Brune et al 1993; Mathews and BenZion, 1997), can cause overshoot or undershoot during rupture, that may differ substantially from the static-frictionless deformation of models examined in this article. Presumably aftershocks and afterslip would bring surface deformation closer to the static deformation field. However, if this were the case in the Sindri region, and initial subsidence at Fort Sindri were an artifact of dynamic rupture, we would expect that relaxation of the foot-wall would be evident also in relaxation of the hanging wall measured by Baker. Hence dynamic effects alone are insufficient to explain the observed discrepancy between the two solutions.

Both Baker's data and Burnes' data are obtained from isolated samples of a feature whose along-strike length and surface geometry renders approximate any simple elastic deformation model. It is possible that the inadequacy in sampling may be the principal cause for the apparent discrepancy between the two solutions, especially since each requires slip that is unexpectedly large for inferred fault widths of less than 10 km. The large amplitude of slip required in each solution requires along-strike dimensions greater than 80 km, hence Oldham's evidence for 150 km of along-strike slip is consistent with this aspect of the data. In contrast, a down-dip width of 5 km is unexpectedly small to permit >10 m of surface rupture. Had this occurred, mean dilatational extension along each side of the fault plane would have exceeded 1000 µstrain, with a correspondingly high stress drop.

The modeling presented here is insensitive to along-strike slip, and to variations of slip along strike. It is curious that the impressive dip-slip component resulted in no surface fault scarp since it appears to have reached at least to within a few hundred meters of the surface. Presumably, for this to occur, the surface alluvium would have to have been draped over the rupture in the near-surface. It is possible, also that a fault scarp, or several scarps and fissures did occur along parts of the Bund, the details of which were not related in second-hand accounts of the event.

Assuming that the down-dip width of the fault was 10 km requires 5 m of horizontal contraction across the fault for 11.5 m of slip, causing mean tensile volume dilatation exceeding 100 µstrain in the hanging wall and footwall flanking the fault (2.5 m in 24 km). Extensive strain has the co-seismic consequence of reducing pore pressures in the flanks of the fault, thereby inhibiting the ejection of water. The observed widespread ejection of water through mud volcanoes is thus apparently inconsistent with the inferred sense of motion on the fault. Although, liquefaction in sediments is observed after great Himalayan thrust earthquakes, presumably due to local sediment liquefaction processes, an alternative explanation for widespread fluid venting, consistent with fluid overpressuring at depth, is that the fault itself acted as a conduit for fluids as suggested by Sibson (1992) - so-called "fault-valve" behavior. The natural roughness of the fault plane that holds it locked in the interseismic period, is impermeable prior to rupture, but becomes very permeable during and following rupture, permitting the release to the surface of the high fluid pressures that initiated rupture at depth.

A curious feature of the region is the absence of a pronounced physiographic feature along the Bund (the Bund is a mound, not a mountain). This suggests that recurrence intervals are low, or that reverse slip is a relatively recent process for the Kachchh fault, which like nearby faults associated with the Kachchh rift system are currently being reactivated in a reverse sense. The recurrence of earthquakes in the Kachchh region would appear to be accessible to paleoseismic techniques and several issues associated with the 1819 event are worthy of field investigation. For example, the 1826 flood will have deposited fresh-water sediments above the salt deposits on the floor of Lake Sindri, providing a measure of the current form of the subsidence basin. Investigations of ponding south of the Bund, along the Rann to the west and far east of the mapped expression of the 1819 Bund, would clarify the along-strike length of faulting, and its potential sinestral component. Investigations of ponding north of the Bund might also reveal the transient strand line of the 1826 flood. Surface studies of the eastern expression of the fault might reveal evidence for left lateral slip, although many of the drainages across the scarp would have been initiated only after the earthquake.

The rate of secular strain contraction of India is not known in the Kachchh region but is immeasurably small (<0.1 µstrain per century) on the Indian Peninsula (Paul et al, 1992). If similar rates prevail in the Kachchh region, the strain contraction released by the Kachchh event would require 100 kyears for its renewal, an interval long compared to the time needed to erode the 1819 scarp, a problem common to Peninsular India earthquakes (Rajendran et al. 1996). It is therefore unlikely that future large events will recur soon near the epicenter of the 1819 Kachchh event. However, it is possible that the 1819 event may have broken a section of a larger fault system. The epicenters of large historical earthquakes are not well known. Oldham (1883) describes a severe earthquake that destroyed "Daibul or Dabil" in 803 or 894 AD but locates towns of this name far to the west, following Arabic sources. Hobson Jobson (Yule and Burnell, 1903), however, locates Dabul (Dabhul or Dabyl) between Goa and Bombay at 17°34'N, a location shown on early European maps of navigation around the Indian coast. If this were the near the epicenter, the event would be too far south to have been an Indus Delta event. However, in 1534 a tsunami in the Gulf of Cambay (Logan, 1887 p. 322) was reported by the crew of Vasco da Gama's fleet when it was anchored offshore at Dabul. A tsunami from the north Arabian coast could conceivably have caused this observation. A severe earthquake in the Indus Delta, to the east of Kachchh, occurred in 1668 in which 15,000 houses reportedly sunk into the ground (Oldham 1883).

Cities along the northern Arabian Sea are much larger now than when historical earthquakes visited nearby geographic regions. In particular, Karachi, less than 200 km from Kachchh, now hosts a population of more than 12 million people. An M>7 earthquake within 50 km of Karachi cannot be excluded

Conclusions

The mechanism and magnitude of the Rann of Kachchh 1819 earthquake is constrained using quantitative deformation data collated and evaluated from contemporary sources by Oldham (1926). Two solutions derived from subsets of data obtained 6 years, and 25 years after the earthquake share in common, coseismic reverse slip exceeding 11 m on a northerly, or north-easterly, dipping fault, terminating in the shallow subsurface. The amount of slip is large for inferred down-dip widths of 5-10 km, although it is consistent with an along-strike length of 150 km. The absence of significant vertical deformation along the ENE striking extension of the fault suggests that slip was oriented NE, approximately parallel to the Indo-Asian convergence direction, and to the p-axes of recent earthquakes in the region. Hence, although no contemporary observations confirm its existence, left-lateral slip on the eastern extension of the fault may have exceeded 10 m. The details of the deformation field across the uplifted Bund are inconsistent with simple elastic deformation, and it is considered possible that the deformation near Sindri was amplified by dynamic processes during rupture. The geometric moment magnitude of the event is estimated as M=7.7±0.2, similar to a magnitude of M=7.5±0.4 obtained from the intensity distribution.

Reverse slip on a fault dipping greater than 50° requires fluid overpressuring of the rupture plane for slip to occur. Although this is not common in the near-surface, it may be ubiquitous at mid-crustal depths in India where artificial reservoirs frequently induce local earthquakes. Moreover, the Rann of Kachchh and Indus Delta are clearly locations of sediment compaction where fluid overpressuring would not be unexpected. Because earthquake recurrence intervals may exceed many thousands of years it is likely that future large earthquakes near the Arabian coastline of India will occur in intervening regions, and not near the epicentral regions of recent moderate events. This has important consequences for seismic hazards near Karachi.

Acknowledgments
I am indebted to N. Ambraseys, P. Bodin, An Yin and librarians at the India Office, Royal Geographic Society and Geological Society of London, who assisted in the location of the references cited. The research was funded by the National Science Foundation.

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